def noise4d(self, x, y, z, w):
        """
        Generate 4D OpenSimplex noise from X,Y,Z,W coordinates.
        """
        # Place input coordinates on simplectic honeycomb.
        stretch_offset = (x + y + z + w) * STRETCH_CONSTANT_4D
        xs = x + stretch_offset
        ys = y + stretch_offset
        zs = z + stretch_offset
        ws = w + stretch_offset

        # Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin.
        xsb = floor(xs)
        ysb = floor(ys)
        zsb = floor(zs)
        wsb = floor(ws)

        # Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later.
        squish_offset = (xsb + ysb + zsb + wsb) * SQUISH_CONSTANT_4D
        xb = xsb + squish_offset
        yb = ysb + squish_offset
        zb = zsb + squish_offset
        wb = wsb + squish_offset

        # Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin.
        xins = xs - xsb
        yins = ys - ysb
        zins = zs - zsb
        wins = ws - wsb

        # Sum those together to get a value that determines which region we're in.
        in_sum = xins + yins + zins + wins

        # Positions relative to origin po.
        dx0 = x - xb
        dy0 = y - yb
        dz0 = z - zb
        dw0 = w - wb

        value = 0
        extrapolate = self._extrapolate4d
        if in_sum <= 1: # We're inside the pentachoron (4-Simplex) at (0,0,0,0)

            # Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest.
            a_po = 0x01
            a_score = xins
            b_po = 0x02
            b_score = yins
            if a_score >= b_score and zins > b_score:
                b_score = zins
                b_po = 0x04
            elif a_score < b_score and zins > a_score:
                a_score = zins
                a_po = 0x04

            if a_score >= b_score and wins > b_score:
                b_score = wins
                b_po = 0x08
            elif a_score < b_score and wins > a_score:
                a_score = wins
                a_po = 0x08

            # Now we determine the three lattice pos not part of the pentachoron that may contribute.
            # This depends on the closest two pentachoron vertices, including (0,0,0,0)
            uins = 1 - in_sum
            if uins > a_score or uins > b_score: # (0,0,0,0) is one of the closest two pentachoron vertices.
                c = b_po if (b_score > a_score) else a_po # Our other closest vertex is the closest out of a and b.
                if (c & 0x01) == 0:
                    xsv_ext0 = xsb - 1
                    xsv_ext1 = xsv_ext2 = xsb
                    dx_ext0 = dx0 + 1
                    dx_ext1 = dx_ext2 = dx0
                else:
                    xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1
                    dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1

                if (c & 0x02) == 0:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb
                    dy_ext0 = dy_ext1 = dy_ext2 = dy0
                    if (c & 0x01) == 0x01:
                        ysv_ext0 -= 1
                        dy_ext0 += 1
                    else:
                        ysv_ext1 -= 1
                        dy_ext1 += 1

                else:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1
                    dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1

                if (c & 0x04) == 0:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb
                    dz_ext0 = dz_ext1 = dz_ext2 = dz0
                    if (c & 0x03) != 0:
                        if (c & 0x03) == 0x03:
                            zsv_ext0 -= 1
                            dz_ext0 += 1
                        else:
                            zsv_ext1 -= 1
                            dz_ext1 += 1

                    else:
                        zsv_ext2 -= 1
                        dz_ext2 += 1

                else:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1
                    dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1


                if (c & 0x08) == 0:
                    wsv_ext0 = wsv_ext1 = wsb
                    wsv_ext2 = wsb - 1
                    dw_ext0 = dw_ext1 = dw0
                    dw_ext2 = dw0 + 1
                else:
                    wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1
                    dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1

            else: # (0,0,0,0) is not one of the closest two pentachoron vertices.
                c = (a_po | b_po) # Our three extra vertices are determined by the closest two.

                if (c & 0x01) == 0:
                    xsv_ext0 = xsv_ext2 = xsb
                    xsv_ext1 = xsb - 1
                    dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D
                    dx_ext2 = dx0 - SQUISH_CONSTANT_4D
                else:
                    xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1
                    dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx_ext2 = dx0 - 1 - SQUISH_CONSTANT_4D

                if (c & 0x02) == 0:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb
                    dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D
                    dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT_4D
                    if (c & 0x01) == 0x01:
                        ysv_ext1 -= 1
                        dy_ext1 += 1
                    else:
                        ysv_ext2 -= 1
                        dy_ext2 += 1

                else:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1
                    dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dy_ext1 = dy_ext2 = dy0 - 1 - SQUISH_CONSTANT_4D

                if (c & 0x04) == 0:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb
                    dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D
                    dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT_4D
                    if (c & 0x03) == 0x03:
                        zsv_ext1 -= 1
                        dz_ext1 += 1
                    else:
                        zsv_ext2 -= 1
                        dz_ext2 += 1

                else:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1
                    dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dz_ext1 = dz_ext2 = dz0 - 1 - SQUISH_CONSTANT_4D


                if (c & 0x08) == 0:
                    wsv_ext0 = wsv_ext1 = wsb
                    wsv_ext2 = wsb - 1
                    dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw0 - SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 + 1 - SQUISH_CONSTANT_4D
                else:
                    wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1
                    dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw_ext2 = dw0 - 1 - SQUISH_CONSTANT_4D

            # Contribution (0,0,0,0)
            attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0
            if attn0 > 0:
                attn0 *= attn0
                value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0)

            # Contribution (1,0,0,0)
            dx1 = dx0 - 1 - SQUISH_CONSTANT_4D
            dy1 = dy0 - 0 - SQUISH_CONSTANT_4D
            dz1 = dz0 - 0 - SQUISH_CONSTANT_4D
            dw1 = dw0 - 0 - SQUISH_CONSTANT_4D
            attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1
            if attn1 > 0:
                attn1 *= attn1
                value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1)

            # Contribution (0,1,0,0)
            dx2 = dx0 - 0 - SQUISH_CONSTANT_4D
            dy2 = dy0 - 1 - SQUISH_CONSTANT_4D
            dz2 = dz1
            dw2 = dw1
            attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2
            if attn2 > 0:
                attn2 *= attn2
                value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2)

            # Contribution (0,0,1,0)
            dx3 = dx2
            dy3 = dy1
            dz3 = dz0 - 1 - SQUISH_CONSTANT_4D
            dw3 = dw1
            attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3
            if attn3 > 0:
                attn3 *= attn3
                value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3)

            # Contribution (0,0,0,1)
            dx4 = dx2
            dy4 = dy1
            dz4 = dz1
            dw4 = dw0 - 1 - SQUISH_CONSTANT_4D
            attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4
            if attn4 > 0:
                attn4 *= attn4
                value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4)

        elif in_sum >= 3: # We're inside the pentachoron (4-Simplex) at (1,1,1,1)
            # Determine which two of (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) are closest.
            a_po = 0x0E
            a_score = xins
            b_po = 0x0D
            b_score = yins
            if a_score <= b_score and zins < b_score:
                b_score = zins
                b_po = 0x0B
            elif a_score > b_score and zins < a_score:
                a_score = zins
                a_po = 0x0B

            if a_score <= b_score and wins < b_score:
                b_score = wins
                b_po = 0x07
            elif a_score > b_score and wins < a_score:
                a_score = wins
                a_po = 0x07

            # Now we determine the three lattice pos not part of the pentachoron that may contribute.
            # This depends on the closest two pentachoron vertices, including (0,0,0,0)
            uins = 4 - in_sum
            if uins < a_score or uins < b_score: # (1,1,1,1) is one of the closest two pentachoron vertices.
                c = b_po if (b_score < a_score) else a_po # Our other closest vertex is the closest out of a and b.

                if (c & 0x01) != 0:
                    xsv_ext0 = xsb + 2
                    xsv_ext1 = xsv_ext2 = xsb + 1
                    dx_ext0 = dx0 - 2 - 4 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D
                else:
                    xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb
                    dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * SQUISH_CONSTANT_4D

                if (c & 0x02) != 0:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1
                    dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D
                    if (c & 0x01) != 0:
                        ysv_ext1 += 1
                        dy_ext1 -= 1
                    else:
                        ysv_ext0 += 1
                        dy_ext0 -= 1

                else:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb
                    dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 4 * SQUISH_CONSTANT_4D

                if (c & 0x04) != 0:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1
                    dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D
                    if (c & 0x03) != 0x03:
                        if (c & 0x03) == 0:
                            zsv_ext0 += 1
                            dz_ext0 -= 1
                        else:
                            zsv_ext1 += 1
                            dz_ext1 -= 1

                    else:
                        zsv_ext2 += 1
                        dz_ext2 -= 1

                else:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb
                    dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 4 * SQUISH_CONSTANT_4D

                if (c & 0x08) != 0:
                    wsv_ext0 = wsv_ext1 = wsb + 1
                    wsv_ext2 = wsb + 2
                    dw_ext0 = dw_ext1 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 - 2 - 4 * SQUISH_CONSTANT_4D
                else:
                    wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb
                    dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * SQUISH_CONSTANT_4D

            else: # (1,1,1,1) is not one of the closest two pentachoron vertices.
                c = (a_po & b_po) # Our three extra vertices are determined by the closest two.

                if (c & 0x01) != 0:
                    xsv_ext0 = xsv_ext2 = xsb + 1
                    xsv_ext1 = xsb + 2
                    dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D
                    dx_ext2 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
                else:
                    xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb
                    dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx_ext2 = dx0 - 3 * SQUISH_CONSTANT_4D

                if (c & 0x02) != 0:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1
                    dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dy_ext1 = dy_ext2 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
                    if (c & 0x01) != 0:
                        ysv_ext2 += 1
                        dy_ext2 -= 1
                    else:
                        ysv_ext1 += 1
                        dy_ext1 -= 1

                else:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb
                    dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D
                    dy_ext1 = dy_ext2 = dy0 - 3 * SQUISH_CONSTANT_4D

                if (c & 0x04) != 0:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1
                    dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dz_ext1 = dz_ext2 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
                    if (c & 0x03) != 0:
                        zsv_ext2 += 1
                        dz_ext2 -= 1
                    else:
                        zsv_ext1 += 1
                        dz_ext1 -= 1

                else:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb
                    dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D
                    dz_ext1 = dz_ext2 = dz0 - 3 * SQUISH_CONSTANT_4D

                if (c & 0x08) != 0:
                    wsv_ext0 = wsv_ext1 = wsb + 1
                    wsv_ext2 = wsb + 2
                    dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D
                else:
                    wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb
                    dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw_ext2 = dw0 - 3 * SQUISH_CONSTANT_4D

            # Contribution (1,1,1,0)
            dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
            dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
            dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
            dw4 = dw0 - 3 * SQUISH_CONSTANT_4D
            attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4
            if attn4 > 0:
                attn4 *= attn4
                value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4)

            # Contribution (1,1,0,1)
            dx3 = dx4
            dy3 = dy4
            dz3 = dz0 - 3 * SQUISH_CONSTANT_4D
            dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
            attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3
            if attn3 > 0:
                attn3 *= attn3
                value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3)

            # Contribution (1,0,1,1)
            dx2 = dx4
            dy2 = dy0 - 3 * SQUISH_CONSTANT_4D
            dz2 = dz4
            dw2 = dw3
            attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2
            if attn2 > 0:
                attn2 *= attn2
                value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2)

            # Contribution (0,1,1,1)
            dx1 = dx0 - 3 * SQUISH_CONSTANT_4D
            dz1 = dz4
            dy1 = dy4
            dw1 = dw3
            attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1
            if attn1 > 0:
                attn1 *= attn1
                value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1)

            # Contribution (1,1,1,1)
            dx0 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D
            dy0 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D
            dz0 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D
            dw0 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D
            attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0
            if attn0 > 0:
                attn0 *= attn0
                value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 1, dx0, dy0, dz0, dw0)

        elif in_sum <= 2: # We're inside the first dispentachoron (Rectified 4-Simplex)
            a_is_bigger_side = True
            b_is_bigger_side = True

            # Decide between (1,1,0,0) and (0,0,1,1)
            if xins + yins > zins + wins:
                a_score = xins + yins
                a_po = 0x03
            else:
                a_score = zins + wins
                a_po = 0x0C

            # Decide between (1,0,1,0) and (0,1,0,1)
            if xins + zins > yins + wins:
                b_score = xins + zins
                b_po = 0x05
            else:
                b_score = yins + wins
                b_po = 0x0A

            # Closer between (1,0,0,1) and (0,1,1,0) will replace the further of a and b, if closer.
            if xins + wins > yins + zins:
                score = xins + wins
                if a_score >= b_score and score > b_score:
                    b_score = score
                    b_po = 0x09
                elif a_score < b_score and score > a_score:
                    a_score = score
                    a_po = 0x09

            else:
                score = yins + zins
                if a_score >= b_score and score > b_score:
                    b_score = score
                    b_po = 0x06
                elif a_score < b_score and score > a_score:
                    a_score = score
                    a_po = 0x06

            # Decide if (1,0,0,0) is closer.
            p1 = 2 - in_sum + xins
            if a_score >= b_score and p1 > b_score:
                b_score = p1
                b_po = 0x01
                b_is_bigger_side = False
            elif a_score < b_score and p1 > a_score:
                a_score = p1
                a_po = 0x01
                a_is_bigger_side = False

            # Decide if (0,1,0,0) is closer.
            p2 = 2 - in_sum + yins
            if a_score >= b_score and p2 > b_score:
                b_score = p2
                b_po = 0x02
                b_is_bigger_side = False
            elif a_score < b_score and p2 > a_score:
                a_score = p2
                a_po = 0x02
                a_is_bigger_side = False

            # Decide if (0,0,1,0) is closer.
            p3 = 2 - in_sum + zins
            if a_score >= b_score and p3 > b_score:
                b_score = p3
                b_po = 0x04
                b_is_bigger_side = False
            elif a_score < b_score and p3 > a_score:
                a_score = p3
                a_po = 0x04
                a_is_bigger_side = False

            # Decide if (0,0,0,1) is closer.
            p4 = 2 - in_sum + wins
            if a_score >= b_score and p4 > b_score:
                b_po = 0x08
                b_is_bigger_side = False
            elif a_score < b_score and p4 > a_score:
                a_po = 0x08
                a_is_bigger_side = False

            # Where each of the two closest pos are determines how the extra three vertices are calculated.
            if a_is_bigger_side == b_is_bigger_side:
                if a_is_bigger_side: # Both closest pos on the bigger side
                    c1 = (a_po | b_po)
                    c2 = (a_po & b_po)
                    if (c1 & 0x01) == 0:
                        xsv_ext0 = xsb
                        xsv_ext1 = xsb - 1
                        dx_ext0 = dx0 - 3 * SQUISH_CONSTANT_4D
                        dx_ext1 = dx0 + 1 - 2 * SQUISH_CONSTANT_4D
                    else:
                        xsv_ext0 = xsv_ext1 = xsb + 1
                        dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
                        dx_ext1 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D

                    if (c1 & 0x02) == 0:
                        ysv_ext0 = ysb
                        ysv_ext1 = ysb - 1
                        dy_ext0 = dy0 - 3 * SQUISH_CONSTANT_4D
                        dy_ext1 = dy0 + 1 - 2 * SQUISH_CONSTANT_4D
                    else:
                        ysv_ext0 = ysv_ext1 = ysb + 1
                        dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
                        dy_ext1 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D

                    if (c1 & 0x04) == 0:
                        zsv_ext0 = zsb
                        zsv_ext1 = zsb - 1
                        dz_ext0 = dz0 - 3 * SQUISH_CONSTANT_4D
                        dz_ext1 = dz0 + 1 - 2 * SQUISH_CONSTANT_4D
                    else:
                        zsv_ext0 = zsv_ext1 = zsb + 1
                        dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
                        dz_ext1 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D

                    if (c1 & 0x08) == 0:
                        wsv_ext0 = wsb
                        wsv_ext1 = wsb - 1
                        dw_ext0 = dw0 - 3 * SQUISH_CONSTANT_4D
                        dw_ext1 = dw0 + 1 - 2 * SQUISH_CONSTANT_4D
                    else:
                        wsv_ext0 = wsv_ext1 = wsb + 1
                        dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
                        dw_ext1 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D

                    # One combination is a _permutation of (0,0,0,2) based on c2
                    xsv_ext2 = xsb
                    ysv_ext2 = ysb
                    zsv_ext2 = zsb
                    wsv_ext2 = wsb
                    dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D
                    dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D
                    dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D
                    if (c2 & 0x01) != 0:
                        xsv_ext2 += 2
                        dx_ext2 -= 2
                    elif (c2 & 0x02) != 0:
                        ysv_ext2 += 2
                        dy_ext2 -= 2
                    elif (c2 & 0x04) != 0:
                        zsv_ext2 += 2
                        dz_ext2 -= 2
                    else:
                        wsv_ext2 += 2
                        dw_ext2 -= 2

                else: # Both closest pos on the smaller side
                    # One of the two extra pos is (0,0,0,0)
                    xsv_ext2 = xsb
                    ysv_ext2 = ysb
                    zsv_ext2 = zsb
                    wsv_ext2 = wsb
                    dx_ext2 = dx0
                    dy_ext2 = dy0
                    dz_ext2 = dz0
                    dw_ext2 = dw0

                    # Other two pos are based on the omitted axes.
                    c = (a_po | b_po)

                    if (c & 0x01) == 0:
                        xsv_ext0 = xsb - 1
                        xsv_ext1 = xsb
                        dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D
                        dx_ext1 = dx0 - SQUISH_CONSTANT_4D
                    else:
                        xsv_ext0 = xsv_ext1 = xsb + 1
                        dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D

                    if (c & 0x02) == 0:
                        ysv_ext0 = ysv_ext1 = ysb
                        dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D
                        if (c & 0x01) == 0x01:
                            ysv_ext0 -= 1
                            dy_ext0 += 1
                        else:
                            ysv_ext1 -= 1
                            dy_ext1 += 1

                    else:
                        ysv_ext0 = ysv_ext1 = ysb + 1
                        dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D

                    if (c & 0x04) == 0:
                        zsv_ext0 = zsv_ext1 = zsb
                        dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D
                        if (c & 0x03) == 0x03:
                            zsv_ext0 -= 1
                            dz_ext0 += 1
                        else:
                            zsv_ext1 -= 1
                            dz_ext1 += 1

                    else:
                        zsv_ext0 = zsv_ext1 = zsb + 1
                        dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D


                    if (c & 0x08) == 0:
                        wsv_ext0 = wsb
                        wsv_ext1 = wsb - 1
                        dw_ext0 = dw0 - SQUISH_CONSTANT_4D
                        dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D
                    else:
                        wsv_ext0 = wsv_ext1 = wsb + 1
                        dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D

            else: # One po on each "side"
                if a_is_bigger_side:
                    c1 = a_po
                    c2 = b_po
                else:
                    c1 = b_po
                    c2 = a_po

                # Two contributions are the bigger-sided po with each 0 replaced with -1.
                if (c1 & 0x01) == 0:
                    xsv_ext0 = xsb - 1
                    xsv_ext1 = xsb
                    dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D
                    dx_ext1 = dx0 - SQUISH_CONSTANT_4D
                else:
                    xsv_ext0 = xsv_ext1 = xsb + 1
                    dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D

                if (c1 & 0x02) == 0:
                    ysv_ext0 = ysv_ext1 = ysb
                    dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D
                    if (c1 & 0x01) == 0x01:
                        ysv_ext0 -= 1
                        dy_ext0 += 1
                    else:
                        ysv_ext1 -= 1
                        dy_ext1 += 1

                else:
                    ysv_ext0 = ysv_ext1 = ysb + 1
                    dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D

                if (c1 & 0x04) == 0:
                    zsv_ext0 = zsv_ext1 = zsb
                    dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D
                    if (c1 & 0x03) == 0x03:
                        zsv_ext0 -= 1
                        dz_ext0 += 1
                    else:
                        zsv_ext1 -= 1
                        dz_ext1 += 1

                else:
                    zsv_ext0 = zsv_ext1 = zsb + 1
                    dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D

                if (c1 & 0x08) == 0:
                    wsv_ext0 = wsb
                    wsv_ext1 = wsb - 1
                    dw_ext0 = dw0 - SQUISH_CONSTANT_4D
                    dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D
                else:
                    wsv_ext0 = wsv_ext1 = wsb + 1
                    dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D

                # One contribution is a _permutation of (0,0,0,2) based on the smaller-sided po
                xsv_ext2 = xsb
                ysv_ext2 = ysb
                zsv_ext2 = zsb
                wsv_ext2 = wsb
                dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D
                dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D
                dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D
                dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D
                if (c2 & 0x01) != 0:
                    xsv_ext2 += 2
                    dx_ext2 -= 2
                elif (c2 & 0x02) != 0:
                    ysv_ext2 += 2
                    dy_ext2 -= 2
                elif (c2 & 0x04) != 0:
                    zsv_ext2 += 2
                    dz_ext2 -= 2
                else:
                    wsv_ext2 += 2
                    dw_ext2 -= 2

            # Contribution (1,0,0,0)
            dx1 = dx0 - 1 - SQUISH_CONSTANT_4D
            dy1 = dy0 - 0 - SQUISH_CONSTANT_4D
            dz1 = dz0 - 0 - SQUISH_CONSTANT_4D
            dw1 = dw0 - 0 - SQUISH_CONSTANT_4D
            attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1
            if attn1 > 0:
                attn1 *= attn1
                value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1)

            # Contribution (0,1,0,0)
            dx2 = dx0 - 0 - SQUISH_CONSTANT_4D
            dy2 = dy0 - 1 - SQUISH_CONSTANT_4D
            dz2 = dz1
            dw2 = dw1
            attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2
            if attn2 > 0:
                attn2 *= attn2
                value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2)

            # Contribution (0,0,1,0)
            dx3 = dx2
            dy3 = dy1
            dz3 = dz0 - 1 - SQUISH_CONSTANT_4D
            dw3 = dw1
            attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3
            if attn3 > 0:
                attn3 *= attn3
                value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3)

            # Contribution (0,0,0,1)
            dx4 = dx2
            dy4 = dy1
            dz4 = dz1
            dw4 = dw0 - 1 - SQUISH_CONSTANT_4D
            attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4
            if attn4 > 0:
                attn4 *= attn4
                value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4)

            # Contribution (1,1,0,0)
            dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5
            if attn5 > 0:
                attn5 *= attn5
                value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5)

            # Contribution (1,0,1,0)
            dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6
            if attn6 > 0:
                attn6 *= attn6
                value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6)

            # Contribution (1,0,0,1)
            dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7
            if attn7 > 0:
                attn7 *= attn7
                value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7)

            # Contribution (0,1,1,0)
            dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8
            if attn8 > 0:
                attn8 *= attn8
                value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8)

            # Contribution (0,1,0,1)
            dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9
            if attn9 > 0:
                attn9 *= attn9
                value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9)

            # Contribution (0,0,1,1)
            dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10
            if attn10 > 0:
                attn10 *= attn10
                value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10)

        else: # We're inside the second dispentachoron (Rectified 4-Simplex)
            a_is_bigger_side = True
            b_is_bigger_side = True

            # Decide between (0,0,1,1) and (1,1,0,0)
            if xins + yins < zins + wins:
                a_score = xins + yins
                a_po = 0x0C
            else:
                a_score = zins + wins
                a_po = 0x03

            # Decide between (0,1,0,1) and (1,0,1,0)
            if xins + zins < yins + wins:
                b_score = xins + zins
                b_po = 0x0A
            else:
                b_score = yins + wins
                b_po = 0x05

            # Closer between (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer.
            if xins + wins < yins + zins:
                score = xins + wins
                if a_score <= b_score and score < b_score:
                    b_score = score
                    b_po = 0x06
                elif a_score > b_score and score < a_score:
                    a_score = score
                    a_po = 0x06

            else:
                score = yins + zins
                if a_score <= b_score and score < b_score:
                    b_score = score
                    b_po = 0x09
                elif a_score > b_score and score < a_score:
                    a_score = score
                    a_po = 0x09

            # Decide if (0,1,1,1) is closer.
            p1 = 3 - in_sum + xins
            if a_score <= b_score and p1 < b_score:
                b_score = p1
                b_po = 0x0E
                b_is_bigger_side = False
            elif a_score > b_score and p1 < a_score:
                a_score = p1
                a_po = 0x0E
                a_is_bigger_side = False

            # Decide if (1,0,1,1) is closer.
            p2 = 3 - in_sum + yins
            if a_score <= b_score and p2 < b_score:
                b_score = p2
                b_po = 0x0D
                b_is_bigger_side = False
            elif a_score > b_score and p2 < a_score:
                a_score = p2
                a_po = 0x0D
                a_is_bigger_side = False

            # Decide if (1,1,0,1) is closer.
            p3 = 3 - in_sum + zins
            if a_score <= b_score and p3 < b_score:
                b_score = p3
                b_po = 0x0B
                b_is_bigger_side = False
            elif a_score > b_score and p3 < a_score:
                a_score = p3
                a_po = 0x0B
                a_is_bigger_side = False

            # Decide if (1,1,1,0) is closer.
            p4 = 3 - in_sum + wins
            if a_score <= b_score and p4 < b_score:
                b_po = 0x07
                b_is_bigger_side = False
            elif a_score > b_score and p4 < a_score:
                a_po = 0x07
                a_is_bigger_side = False

            # Where each of the two closest pos are determines how the extra three vertices are calculated.
            if a_is_bigger_side == b_is_bigger_side:
                if a_is_bigger_side: # Both closest pos on the bigger side
                    c1 = (a_po & b_po)
                    c2 = (a_po | b_po)

                    # Two contributions are _permutations of (0,0,0,1) and (0,0,0,2) based on c1
                    xsv_ext0 = xsv_ext1 = xsb
                    ysv_ext0 = ysv_ext1 = ysb
                    zsv_ext0 = zsv_ext1 = zsb
                    wsv_ext0 = wsv_ext1 = wsb
                    dx_ext0 = dx0 - SQUISH_CONSTANT_4D
                    dy_ext0 = dy0 - SQUISH_CONSTANT_4D
                    dz_ext0 = dz0 - SQUISH_CONSTANT_4D
                    dw_ext0 = dw0 - SQUISH_CONSTANT_4D
                    dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_4D
                    dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_4D
                    dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw0 - 2 * SQUISH_CONSTANT_4D
                    if (c1 & 0x01) != 0:
                        xsv_ext0 += 1
                        dx_ext0 -= 1
                        xsv_ext1 += 2
                        dx_ext1 -= 2
                    elif (c1 & 0x02) != 0:
                        ysv_ext0 += 1
                        dy_ext0 -= 1
                        ysv_ext1 += 2
                        dy_ext1 -= 2
                    elif (c1 & 0x04) != 0:
                        zsv_ext0 += 1
                        dz_ext0 -= 1
                        zsv_ext1 += 2
                        dz_ext1 -= 2
                    else:
                        wsv_ext0 += 1
                        dw_ext0 -= 1
                        wsv_ext1 += 2
                        dw_ext1 -= 2

                    # One contribution is a _permutation of (1,1,1,-1) based on c2
                    xsv_ext2 = xsb + 1
                    ysv_ext2 = ysb + 1
                    zsv_ext2 = zsb + 1
                    wsv_ext2 = wsb + 1
                    dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
                    if (c2 & 0x01) == 0:
                        xsv_ext2 -= 2
                        dx_ext2 += 2
                    elif (c2 & 0x02) == 0:
                        ysv_ext2 -= 2
                        dy_ext2 += 2
                    elif (c2 & 0x04) == 0:
                        zsv_ext2 -= 2
                        dz_ext2 += 2
                    else:
                        wsv_ext2 -= 2
                        dw_ext2 += 2

                else: # Both closest pos on the smaller side
                    # One of the two extra pos is (1,1,1,1)
                    xsv_ext2 = xsb + 1
                    ysv_ext2 = ysb + 1
                    zsv_ext2 = zsb + 1
                    wsv_ext2 = wsb + 1
                    dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D
                    dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D
                    dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D

                    # Other two pos are based on the shared axes.
                    c = (a_po & b_po)
                    if (c & 0x01) != 0:
                        xsv_ext0 = xsb + 2
                        xsv_ext1 = xsb + 1
                        dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D
                        dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
                    else:
                        xsv_ext0 = xsv_ext1 = xsb
                        dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D

                    if (c & 0x02) != 0:
                        ysv_ext0 = ysv_ext1 = ysb + 1
                        dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
                        if (c & 0x01) == 0:
                            ysv_ext0 += 1
                            dy_ext0 -= 1
                        else:
                            ysv_ext1 += 1
                            dy_ext1 -= 1

                    else:
                        ysv_ext0 = ysv_ext1 = ysb
                        dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D

                    if (c & 0x04) != 0:
                        zsv_ext0 = zsv_ext1 = zsb + 1
                        dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
                        if (c & 0x03) == 0:
                            zsv_ext0 += 1
                            dz_ext0 -= 1
                        else:
                            zsv_ext1 += 1
                            dz_ext1 -= 1

                    else:
                        zsv_ext0 = zsv_ext1 = zsb
                        dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D


                    if (c & 0x08) != 0:
                        wsv_ext0 = wsb + 1
                        wsv_ext1 = wsb + 2
                        dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
                        dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D
                    else:
                        wsv_ext0 = wsv_ext1 = wsb
                        dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D

            else: # One po on each "side"
                if a_is_bigger_side:
                    c1 = a_po
                    c2 = b_po
                else:
                    c1 = b_po
                    c2 = a_po

                # Two contributions are the bigger-sided po with each 1 replaced with 2.
                if (c1 & 0x01) != 0:
                    xsv_ext0 = xsb + 2
                    xsv_ext1 = xsb + 1
                    dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
                else:
                    xsv_ext0 = xsv_ext1 = xsb
                    dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D

                if (c1 & 0x02) != 0:
                    ysv_ext0 = ysv_ext1 = ysb + 1
                    dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
                    if (c1 & 0x01) == 0:
                        ysv_ext0 += 1
                        dy_ext0 -= 1
                    else:
                        ysv_ext1 += 1
                        dy_ext1 -= 1

                else:
                    ysv_ext0 = ysv_ext1 = ysb
                    dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D

                if (c1 & 0x04) != 0:
                    zsv_ext0 = zsv_ext1 = zsb + 1
                    dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
                    if (c1 & 0x03) == 0:
                        zsv_ext0 += 1
                        dz_ext0 -= 1
                    else:
                        zsv_ext1 += 1
                        dz_ext1 -= 1

                else:
                    zsv_ext0 = zsv_ext1 = zsb
                    dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D

                if (c1 & 0x08) != 0:
                    wsv_ext0 = wsb + 1
                    wsv_ext1 = wsb + 2
                    dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D
                else:
                    wsv_ext0 = wsv_ext1 = wsb
                    dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D

                # One contribution is a _permutation of (1,1,1,-1) based on the smaller-sided po
                xsv_ext2 = xsb + 1
                ysv_ext2 = ysb + 1
                zsv_ext2 = zsb + 1
                wsv_ext2 = wsb + 1
                dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
                dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
                dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
                dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
                if (c2 & 0x01) == 0:
                    xsv_ext2 -= 2
                    dx_ext2 += 2
                elif (c2 & 0x02) == 0:
                    ysv_ext2 -= 2
                    dy_ext2 += 2
                elif (c2 & 0x04) == 0:
                    zsv_ext2 -= 2
                    dz_ext2 += 2
                else:
                    wsv_ext2 -= 2
                    dw_ext2 += 2

            # Contribution (1,1,1,0)
            dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
            dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
            dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
            dw4 = dw0 - 3 * SQUISH_CONSTANT_4D
            attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4
            if attn4 > 0:
                attn4 *= attn4
                value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4)

            # Contribution (1,1,0,1)
            dx3 = dx4
            dy3 = dy4
            dz3 = dz0 - 3 * SQUISH_CONSTANT_4D
            dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
            attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3
            if attn3 > 0:
                attn3 *= attn3
                value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3)

            # Contribution (1,0,1,1)
            dx2 = dx4
            dy2 = dy0 - 3 * SQUISH_CONSTANT_4D
            dz2 = dz4
            dw2 = dw3
            attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2
            if attn2 > 0:
                attn2 *= attn2
                value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2)

            # Contribution (0,1,1,1)
            dx1 = dx0 - 3 * SQUISH_CONSTANT_4D
            dz1 = dz4
            dy1 = dy4
            dw1 = dw3
            attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1
            if attn1 > 0:
                attn1 *= attn1
                value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1)

            # Contribution (1,1,0,0)
            dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5
            if attn5 > 0:
                attn5 *= attn5
                value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5)

            # Contribution (1,0,1,0)
            dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6
            if attn6 > 0:
                attn6 *= attn6
                value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6)

            # Contribution (1,0,0,1)
            dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7
            if attn7 > 0:
                attn7 *= attn7
                value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7)

            # Contribution (0,1,1,0)
            dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8
            if attn8 > 0:
                attn8 *= attn8
                value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8)

            # Contribution (0,1,0,1)
            dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9
            if attn9 > 0:
                attn9 *= attn9
                value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9)

            # Contribution (0,0,1,1)
            dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10
            if attn10 > 0:
                attn10 *= attn10
                value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10)

        # First extra vertex
        attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 - dw_ext0 * dw_ext0
        if attn_ext0 > 0:
            attn_ext0 *= attn_ext0
            value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0)

        # Second extra vertex
        attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 - dw_ext1 * dw_ext1
        if attn_ext1 > 0:
            attn_ext1 *= attn_ext1
            value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1)

        # Third extra vertex
        attn_ext2 = 2 - dx_ext2 * dx_ext2 - dy_ext2 * dy_ext2 - dz_ext2 * dz_ext2 - dw_ext2 * dw_ext2
        if attn_ext2 > 0:
            attn_ext2 *= attn_ext2
            value += attn_ext2 * attn_ext2 * extrapolate(xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2)

        return value / NORM_CONSTANT_4D
def noise4d(self, x, y, z, w):
        """
        Generate 4D OpenSimplex noise from X,Y,Z,W coordinates.
        """
        # Place input coordinates on simplectic honeycomb.
        stretch_offset = (x + y + z + w) * STRETCH_CONSTANT_4D
        xs = x + stretch_offset
        ys = y + stretch_offset
        zs = z + stretch_offset
        ws = w + stretch_offset

        # Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin.
        xsb = floor(xs)
        ysb = floor(ys)
        zsb = floor(zs)
        wsb = floor(ws)

        # Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later.
        squish_offset = (xsb + ysb + zsb + wsb) * SQUISH_CONSTANT_4D
        xb = xsb + squish_offset
        yb = ysb + squish_offset
        zb = zsb + squish_offset
        wb = wsb + squish_offset

        # Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin.
        xins = xs - xsb
        yins = ys - ysb
        zins = zs - zsb
        wins = ws - wsb

        # Sum those together to get a value that determines which region we're in.
        in_sum = xins + yins + zins + wins

        # Positions relative to origin po.
        dx0 = x - xb
        dy0 = y - yb
        dz0 = z - zb
        dw0 = w - wb

        value = 0
        extrapolate = self._extrapolate4d
        if in_sum <= 1: # We're inside the pentachoron (4-Simplex) at (0,0,0,0)

            # Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest.
            a_po = 0x01
            a_score = xins
            b_po = 0x02
            b_score = yins
            if a_score >= b_score and zins > b_score:
                b_score = zins
                b_po = 0x04
            elif a_score < b_score and zins > a_score:
                a_score = zins
                a_po = 0x04

            if a_score >= b_score and wins > b_score:
                b_score = wins
                b_po = 0x08
            elif a_score < b_score and wins > a_score:
                a_score = wins
                a_po = 0x08

            # Now we determine the three lattice pos not part of the pentachoron that may contribute.
            # This depends on the closest two pentachoron vertices, including (0,0,0,0)
            uins = 1 - in_sum
            if uins > a_score or uins > b_score: # (0,0,0,0) is one of the closest two pentachoron vertices.
                c = b_po if (b_score > a_score) else a_po # Our other closest vertex is the closest out of a and b.
                if (c & 0x01) == 0:
                    xsv_ext0 = xsb - 1
                    xsv_ext1 = xsv_ext2 = xsb
                    dx_ext0 = dx0 + 1
                    dx_ext1 = dx_ext2 = dx0
                else:
                    xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1
                    dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1

                if (c & 0x02) == 0:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb
                    dy_ext0 = dy_ext1 = dy_ext2 = dy0
                    if (c & 0x01) == 0x01:
                        ysv_ext0 -= 1
                        dy_ext0 += 1
                    else:
                        ysv_ext1 -= 1
                        dy_ext1 += 1

                else:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1
                    dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1

                if (c & 0x04) == 0:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb
                    dz_ext0 = dz_ext1 = dz_ext2 = dz0
                    if (c & 0x03) != 0:
                        if (c & 0x03) == 0x03:
                            zsv_ext0 -= 1
                            dz_ext0 += 1
                        else:
                            zsv_ext1 -= 1
                            dz_ext1 += 1

                    else:
                        zsv_ext2 -= 1
                        dz_ext2 += 1

                else:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1
                    dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1


                if (c & 0x08) == 0:
                    wsv_ext0 = wsv_ext1 = wsb
                    wsv_ext2 = wsb - 1
                    dw_ext0 = dw_ext1 = dw0
                    dw_ext2 = dw0 + 1
                else:
                    wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1
                    dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1

            else: # (0,0,0,0) is not one of the closest two pentachoron vertices.
                c = (a_po | b_po) # Our three extra vertices are determined by the closest two.

                if (c & 0x01) == 0:
                    xsv_ext0 = xsv_ext2 = xsb
                    xsv_ext1 = xsb - 1
                    dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D
                    dx_ext2 = dx0 - SQUISH_CONSTANT_4D
                else:
                    xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1
                    dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx_ext2 = dx0 - 1 - SQUISH_CONSTANT_4D

                if (c & 0x02) == 0:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb
                    dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D
                    dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT_4D
                    if (c & 0x01) == 0x01:
                        ysv_ext1 -= 1
                        dy_ext1 += 1
                    else:
                        ysv_ext2 -= 1
                        dy_ext2 += 1

                else:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1
                    dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dy_ext1 = dy_ext2 = dy0 - 1 - SQUISH_CONSTANT_4D

                if (c & 0x04) == 0:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb
                    dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D
                    dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT_4D
                    if (c & 0x03) == 0x03:
                        zsv_ext1 -= 1
                        dz_ext1 += 1
                    else:
                        zsv_ext2 -= 1
                        dz_ext2 += 1

                else:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1
                    dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dz_ext1 = dz_ext2 = dz0 - 1 - SQUISH_CONSTANT_4D


                if (c & 0x08) == 0:
                    wsv_ext0 = wsv_ext1 = wsb
                    wsv_ext2 = wsb - 1
                    dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw0 - SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 + 1 - SQUISH_CONSTANT_4D
                else:
                    wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1
                    dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw_ext2 = dw0 - 1 - SQUISH_CONSTANT_4D

            # Contribution (0,0,0,0)
            attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0
            if attn0 > 0:
                attn0 *= attn0
                value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0)

            # Contribution (1,0,0,0)
            dx1 = dx0 - 1 - SQUISH_CONSTANT_4D
            dy1 = dy0 - 0 - SQUISH_CONSTANT_4D
            dz1 = dz0 - 0 - SQUISH_CONSTANT_4D
            dw1 = dw0 - 0 - SQUISH_CONSTANT_4D
            attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1
            if attn1 > 0:
                attn1 *= attn1
                value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1)

            # Contribution (0,1,0,0)
            dx2 = dx0 - 0 - SQUISH_CONSTANT_4D
            dy2 = dy0 - 1 - SQUISH_CONSTANT_4D
            dz2 = dz1
            dw2 = dw1
            attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2
            if attn2 > 0:
                attn2 *= attn2
                value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2)

            # Contribution (0,0,1,0)
            dx3 = dx2
            dy3 = dy1
            dz3 = dz0 - 1 - SQUISH_CONSTANT_4D
            dw3 = dw1
            attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3
            if attn3 > 0:
                attn3 *= attn3
                value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3)

            # Contribution (0,0,0,1)
            dx4 = dx2
            dy4 = dy1
            dz4 = dz1
            dw4 = dw0 - 1 - SQUISH_CONSTANT_4D
            attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4
            if attn4 > 0:
                attn4 *= attn4
                value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4)

        elif in_sum >= 3: # We're inside the pentachoron (4-Simplex) at (1,1,1,1)
            # Determine which two of (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) are closest.
            a_po = 0x0E
            a_score = xins
            b_po = 0x0D
            b_score = yins
            if a_score <= b_score and zins < b_score:
                b_score = zins
                b_po = 0x0B
            elif a_score > b_score and zins < a_score:
                a_score = zins
                a_po = 0x0B

            if a_score <= b_score and wins < b_score:
                b_score = wins
                b_po = 0x07
            elif a_score > b_score and wins < a_score:
                a_score = wins
                a_po = 0x07

            # Now we determine the three lattice pos not part of the pentachoron that may contribute.
            # This depends on the closest two pentachoron vertices, including (0,0,0,0)
            uins = 4 - in_sum
            if uins < a_score or uins < b_score: # (1,1,1,1) is one of the closest two pentachoron vertices.
                c = b_po if (b_score < a_score) else a_po # Our other closest vertex is the closest out of a and b.

                if (c & 0x01) != 0:
                    xsv_ext0 = xsb + 2
                    xsv_ext1 = xsv_ext2 = xsb + 1
                    dx_ext0 = dx0 - 2 - 4 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D
                else:
                    xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb
                    dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * SQUISH_CONSTANT_4D

                if (c & 0x02) != 0:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1
                    dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D
                    if (c & 0x01) != 0:
                        ysv_ext1 += 1
                        dy_ext1 -= 1
                    else:
                        ysv_ext0 += 1
                        dy_ext0 -= 1

                else:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb
                    dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 4 * SQUISH_CONSTANT_4D

                if (c & 0x04) != 0:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1
                    dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D
                    if (c & 0x03) != 0x03:
                        if (c & 0x03) == 0:
                            zsv_ext0 += 1
                            dz_ext0 -= 1
                        else:
                            zsv_ext1 += 1
                            dz_ext1 -= 1

                    else:
                        zsv_ext2 += 1
                        dz_ext2 -= 1

                else:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb
                    dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 4 * SQUISH_CONSTANT_4D

                if (c & 0x08) != 0:
                    wsv_ext0 = wsv_ext1 = wsb + 1
                    wsv_ext2 = wsb + 2
                    dw_ext0 = dw_ext1 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 - 2 - 4 * SQUISH_CONSTANT_4D
                else:
                    wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb
                    dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * SQUISH_CONSTANT_4D

            else: # (1,1,1,1) is not one of the closest two pentachoron vertices.
                c = (a_po & b_po) # Our three extra vertices are determined by the closest two.

                if (c & 0x01) != 0:
                    xsv_ext0 = xsv_ext2 = xsb + 1
                    xsv_ext1 = xsb + 2
                    dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D
                    dx_ext2 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
                else:
                    xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb
                    dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx_ext2 = dx0 - 3 * SQUISH_CONSTANT_4D

                if (c & 0x02) != 0:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1
                    dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dy_ext1 = dy_ext2 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
                    if (c & 0x01) != 0:
                        ysv_ext2 += 1
                        dy_ext2 -= 1
                    else:
                        ysv_ext1 += 1
                        dy_ext1 -= 1

                else:
                    ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb
                    dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D
                    dy_ext1 = dy_ext2 = dy0 - 3 * SQUISH_CONSTANT_4D

                if (c & 0x04) != 0:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1
                    dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dz_ext1 = dz_ext2 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
                    if (c & 0x03) != 0:
                        zsv_ext2 += 1
                        dz_ext2 -= 1
                    else:
                        zsv_ext1 += 1
                        dz_ext1 -= 1

                else:
                    zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb
                    dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D
                    dz_ext1 = dz_ext2 = dz0 - 3 * SQUISH_CONSTANT_4D

                if (c & 0x08) != 0:
                    wsv_ext0 = wsv_ext1 = wsb + 1
                    wsv_ext2 = wsb + 2
                    dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D
                else:
                    wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb
                    dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw_ext2 = dw0 - 3 * SQUISH_CONSTANT_4D

            # Contribution (1,1,1,0)
            dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
            dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
            dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
            dw4 = dw0 - 3 * SQUISH_CONSTANT_4D
            attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4
            if attn4 > 0:
                attn4 *= attn4
                value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4)

            # Contribution (1,1,0,1)
            dx3 = dx4
            dy3 = dy4
            dz3 = dz0 - 3 * SQUISH_CONSTANT_4D
            dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
            attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3
            if attn3 > 0:
                attn3 *= attn3
                value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3)

            # Contribution (1,0,1,1)
            dx2 = dx4
            dy2 = dy0 - 3 * SQUISH_CONSTANT_4D
            dz2 = dz4
            dw2 = dw3
            attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2
            if attn2 > 0:
                attn2 *= attn2
                value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2)

            # Contribution (0,1,1,1)
            dx1 = dx0 - 3 * SQUISH_CONSTANT_4D
            dz1 = dz4
            dy1 = dy4
            dw1 = dw3
            attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1
            if attn1 > 0:
                attn1 *= attn1
                value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1)

            # Contribution (1,1,1,1)
            dx0 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D
            dy0 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D
            dz0 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D
            dw0 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D
            attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0
            if attn0 > 0:
                attn0 *= attn0
                value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 1, dx0, dy0, dz0, dw0)

        elif in_sum <= 2: # We're inside the first dispentachoron (Rectified 4-Simplex)
            a_is_bigger_side = True
            b_is_bigger_side = True

            # Decide between (1,1,0,0) and (0,0,1,1)
            if xins + yins > zins + wins:
                a_score = xins + yins
                a_po = 0x03
            else:
                a_score = zins + wins
                a_po = 0x0C

            # Decide between (1,0,1,0) and (0,1,0,1)
            if xins + zins > yins + wins:
                b_score = xins + zins
                b_po = 0x05
            else:
                b_score = yins + wins
                b_po = 0x0A

            # Closer between (1,0,0,1) and (0,1,1,0) will replace the further of a and b, if closer.
            if xins + wins > yins + zins:
                score = xins + wins
                if a_score >= b_score and score > b_score:
                    b_score = score
                    b_po = 0x09
                elif a_score < b_score and score > a_score:
                    a_score = score
                    a_po = 0x09

            else:
                score = yins + zins
                if a_score >= b_score and score > b_score:
                    b_score = score
                    b_po = 0x06
                elif a_score < b_score and score > a_score:
                    a_score = score
                    a_po = 0x06

            # Decide if (1,0,0,0) is closer.
            p1 = 2 - in_sum + xins
            if a_score >= b_score and p1 > b_score:
                b_score = p1
                b_po = 0x01
                b_is_bigger_side = False
            elif a_score < b_score and p1 > a_score:
                a_score = p1
                a_po = 0x01
                a_is_bigger_side = False

            # Decide if (0,1,0,0) is closer.
            p2 = 2 - in_sum + yins
            if a_score >= b_score and p2 > b_score:
                b_score = p2
                b_po = 0x02
                b_is_bigger_side = False
            elif a_score < b_score and p2 > a_score:
                a_score = p2
                a_po = 0x02
                a_is_bigger_side = False

            # Decide if (0,0,1,0) is closer.
            p3 = 2 - in_sum + zins
            if a_score >= b_score and p3 > b_score:
                b_score = p3
                b_po = 0x04
                b_is_bigger_side = False
            elif a_score < b_score and p3 > a_score:
                a_score = p3
                a_po = 0x04
                a_is_bigger_side = False

            # Decide if (0,0,0,1) is closer.
            p4 = 2 - in_sum + wins
            if a_score >= b_score and p4 > b_score:
                b_po = 0x08
                b_is_bigger_side = False
            elif a_score < b_score and p4 > a_score:
                a_po = 0x08
                a_is_bigger_side = False

            # Where each of the two closest pos are determines how the extra three vertices are calculated.
            if a_is_bigger_side == b_is_bigger_side:
                if a_is_bigger_side: # Both closest pos on the bigger side
                    c1 = (a_po | b_po)
                    c2 = (a_po & b_po)
                    if (c1 & 0x01) == 0:
                        xsv_ext0 = xsb
                        xsv_ext1 = xsb - 1
                        dx_ext0 = dx0 - 3 * SQUISH_CONSTANT_4D
                        dx_ext1 = dx0 + 1 - 2 * SQUISH_CONSTANT_4D
                    else:
                        xsv_ext0 = xsv_ext1 = xsb + 1
                        dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
                        dx_ext1 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D

                    if (c1 & 0x02) == 0:
                        ysv_ext0 = ysb
                        ysv_ext1 = ysb - 1
                        dy_ext0 = dy0 - 3 * SQUISH_CONSTANT_4D
                        dy_ext1 = dy0 + 1 - 2 * SQUISH_CONSTANT_4D
                    else:
                        ysv_ext0 = ysv_ext1 = ysb + 1
                        dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
                        dy_ext1 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D

                    if (c1 & 0x04) == 0:
                        zsv_ext0 = zsb
                        zsv_ext1 = zsb - 1
                        dz_ext0 = dz0 - 3 * SQUISH_CONSTANT_4D
                        dz_ext1 = dz0 + 1 - 2 * SQUISH_CONSTANT_4D
                    else:
                        zsv_ext0 = zsv_ext1 = zsb + 1
                        dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
                        dz_ext1 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D

                    if (c1 & 0x08) == 0:
                        wsv_ext0 = wsb
                        wsv_ext1 = wsb - 1
                        dw_ext0 = dw0 - 3 * SQUISH_CONSTANT_4D
                        dw_ext1 = dw0 + 1 - 2 * SQUISH_CONSTANT_4D
                    else:
                        wsv_ext0 = wsv_ext1 = wsb + 1
                        dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
                        dw_ext1 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D

                    # One combination is a _permutation of (0,0,0,2) based on c2
                    xsv_ext2 = xsb
                    ysv_ext2 = ysb
                    zsv_ext2 = zsb
                    wsv_ext2 = wsb
                    dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D
                    dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D
                    dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D
                    if (c2 & 0x01) != 0:
                        xsv_ext2 += 2
                        dx_ext2 -= 2
                    elif (c2 & 0x02) != 0:
                        ysv_ext2 += 2
                        dy_ext2 -= 2
                    elif (c2 & 0x04) != 0:
                        zsv_ext2 += 2
                        dz_ext2 -= 2
                    else:
                        wsv_ext2 += 2
                        dw_ext2 -= 2

                else: # Both closest pos on the smaller side
                    # One of the two extra pos is (0,0,0,0)
                    xsv_ext2 = xsb
                    ysv_ext2 = ysb
                    zsv_ext2 = zsb
                    wsv_ext2 = wsb
                    dx_ext2 = dx0
                    dy_ext2 = dy0
                    dz_ext2 = dz0
                    dw_ext2 = dw0

                    # Other two pos are based on the omitted axes.
                    c = (a_po | b_po)

                    if (c & 0x01) == 0:
                        xsv_ext0 = xsb - 1
                        xsv_ext1 = xsb
                        dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D
                        dx_ext1 = dx0 - SQUISH_CONSTANT_4D
                    else:
                        xsv_ext0 = xsv_ext1 = xsb + 1
                        dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D

                    if (c & 0x02) == 0:
                        ysv_ext0 = ysv_ext1 = ysb
                        dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D
                        if (c & 0x01) == 0x01:
                            ysv_ext0 -= 1
                            dy_ext0 += 1
                        else:
                            ysv_ext1 -= 1
                            dy_ext1 += 1

                    else:
                        ysv_ext0 = ysv_ext1 = ysb + 1
                        dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D

                    if (c & 0x04) == 0:
                        zsv_ext0 = zsv_ext1 = zsb
                        dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D
                        if (c & 0x03) == 0x03:
                            zsv_ext0 -= 1
                            dz_ext0 += 1
                        else:
                            zsv_ext1 -= 1
                            dz_ext1 += 1

                    else:
                        zsv_ext0 = zsv_ext1 = zsb + 1
                        dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D


                    if (c & 0x08) == 0:
                        wsv_ext0 = wsb
                        wsv_ext1 = wsb - 1
                        dw_ext0 = dw0 - SQUISH_CONSTANT_4D
                        dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D
                    else:
                        wsv_ext0 = wsv_ext1 = wsb + 1
                        dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D

            else: # One po on each "side"
                if a_is_bigger_side:
                    c1 = a_po
                    c2 = b_po
                else:
                    c1 = b_po
                    c2 = a_po

                # Two contributions are the bigger-sided po with each 0 replaced with -1.
                if (c1 & 0x01) == 0:
                    xsv_ext0 = xsb - 1
                    xsv_ext1 = xsb
                    dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D
                    dx_ext1 = dx0 - SQUISH_CONSTANT_4D
                else:
                    xsv_ext0 = xsv_ext1 = xsb + 1
                    dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D

                if (c1 & 0x02) == 0:
                    ysv_ext0 = ysv_ext1 = ysb
                    dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D
                    if (c1 & 0x01) == 0x01:
                        ysv_ext0 -= 1
                        dy_ext0 += 1
                    else:
                        ysv_ext1 -= 1
                        dy_ext1 += 1

                else:
                    ysv_ext0 = ysv_ext1 = ysb + 1
                    dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D

                if (c1 & 0x04) == 0:
                    zsv_ext0 = zsv_ext1 = zsb
                    dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D
                    if (c1 & 0x03) == 0x03:
                        zsv_ext0 -= 1
                        dz_ext0 += 1
                    else:
                        zsv_ext1 -= 1
                        dz_ext1 += 1

                else:
                    zsv_ext0 = zsv_ext1 = zsb + 1
                    dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D

                if (c1 & 0x08) == 0:
                    wsv_ext0 = wsb
                    wsv_ext1 = wsb - 1
                    dw_ext0 = dw0 - SQUISH_CONSTANT_4D
                    dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D
                else:
                    wsv_ext0 = wsv_ext1 = wsb + 1
                    dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D

                # One contribution is a _permutation of (0,0,0,2) based on the smaller-sided po
                xsv_ext2 = xsb
                ysv_ext2 = ysb
                zsv_ext2 = zsb
                wsv_ext2 = wsb
                dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D
                dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D
                dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D
                dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D
                if (c2 & 0x01) != 0:
                    xsv_ext2 += 2
                    dx_ext2 -= 2
                elif (c2 & 0x02) != 0:
                    ysv_ext2 += 2
                    dy_ext2 -= 2
                elif (c2 & 0x04) != 0:
                    zsv_ext2 += 2
                    dz_ext2 -= 2
                else:
                    wsv_ext2 += 2
                    dw_ext2 -= 2

            # Contribution (1,0,0,0)
            dx1 = dx0 - 1 - SQUISH_CONSTANT_4D
            dy1 = dy0 - 0 - SQUISH_CONSTANT_4D
            dz1 = dz0 - 0 - SQUISH_CONSTANT_4D
            dw1 = dw0 - 0 - SQUISH_CONSTANT_4D
            attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1
            if attn1 > 0:
                attn1 *= attn1
                value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1)

            # Contribution (0,1,0,0)
            dx2 = dx0 - 0 - SQUISH_CONSTANT_4D
            dy2 = dy0 - 1 - SQUISH_CONSTANT_4D
            dz2 = dz1
            dw2 = dw1
            attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2
            if attn2 > 0:
                attn2 *= attn2
                value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2)

            # Contribution (0,0,1,0)
            dx3 = dx2
            dy3 = dy1
            dz3 = dz0 - 1 - SQUISH_CONSTANT_4D
            dw3 = dw1
            attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3
            if attn3 > 0:
                attn3 *= attn3
                value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3)

            # Contribution (0,0,0,1)
            dx4 = dx2
            dy4 = dy1
            dz4 = dz1
            dw4 = dw0 - 1 - SQUISH_CONSTANT_4D
            attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4
            if attn4 > 0:
                attn4 *= attn4
                value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4)

            # Contribution (1,1,0,0)
            dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5
            if attn5 > 0:
                attn5 *= attn5
                value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5)

            # Contribution (1,0,1,0)
            dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6
            if attn6 > 0:
                attn6 *= attn6
                value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6)

            # Contribution (1,0,0,1)
            dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7
            if attn7 > 0:
                attn7 *= attn7
                value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7)

            # Contribution (0,1,1,0)
            dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8
            if attn8 > 0:
                attn8 *= attn8
                value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8)

            # Contribution (0,1,0,1)
            dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9
            if attn9 > 0:
                attn9 *= attn9
                value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9)

            # Contribution (0,0,1,1)
            dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10
            if attn10 > 0:
                attn10 *= attn10
                value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10)

        else: # We're inside the second dispentachoron (Rectified 4-Simplex)
            a_is_bigger_side = True
            b_is_bigger_side = True

            # Decide between (0,0,1,1) and (1,1,0,0)
            if xins + yins < zins + wins:
                a_score = xins + yins
                a_po = 0x0C
            else:
                a_score = zins + wins
                a_po = 0x03

            # Decide between (0,1,0,1) and (1,0,1,0)
            if xins + zins < yins + wins:
                b_score = xins + zins
                b_po = 0x0A
            else:
                b_score = yins + wins
                b_po = 0x05

            # Closer between (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer.
            if xins + wins < yins + zins:
                score = xins + wins
                if a_score <= b_score and score < b_score:
                    b_score = score
                    b_po = 0x06
                elif a_score > b_score and score < a_score:
                    a_score = score
                    a_po = 0x06

            else:
                score = yins + zins
                if a_score <= b_score and score < b_score:
                    b_score = score
                    b_po = 0x09
                elif a_score > b_score and score < a_score:
                    a_score = score
                    a_po = 0x09

            # Decide if (0,1,1,1) is closer.
            p1 = 3 - in_sum + xins
            if a_score <= b_score and p1 < b_score:
                b_score = p1
                b_po = 0x0E
                b_is_bigger_side = False
            elif a_score > b_score and p1 < a_score:
                a_score = p1
                a_po = 0x0E
                a_is_bigger_side = False

            # Decide if (1,0,1,1) is closer.
            p2 = 3 - in_sum + yins
            if a_score <= b_score and p2 < b_score:
                b_score = p2
                b_po = 0x0D
                b_is_bigger_side = False
            elif a_score > b_score and p2 < a_score:
                a_score = p2
                a_po = 0x0D
                a_is_bigger_side = False

            # Decide if (1,1,0,1) is closer.
            p3 = 3 - in_sum + zins
            if a_score <= b_score and p3 < b_score:
                b_score = p3
                b_po = 0x0B
                b_is_bigger_side = False
            elif a_score > b_score and p3 < a_score:
                a_score = p3
                a_po = 0x0B
                a_is_bigger_side = False

            # Decide if (1,1,1,0) is closer.
            p4 = 3 - in_sum + wins
            if a_score <= b_score and p4 < b_score:
                b_po = 0x07
                b_is_bigger_side = False
            elif a_score > b_score and p4 < a_score:
                a_po = 0x07
                a_is_bigger_side = False

            # Where each of the two closest pos are determines how the extra three vertices are calculated.
            if a_is_bigger_side == b_is_bigger_side:
                if a_is_bigger_side: # Both closest pos on the bigger side
                    c1 = (a_po & b_po)
                    c2 = (a_po | b_po)

                    # Two contributions are _permutations of (0,0,0,1) and (0,0,0,2) based on c1
                    xsv_ext0 = xsv_ext1 = xsb
                    ysv_ext0 = ysv_ext1 = ysb
                    zsv_ext0 = zsv_ext1 = zsb
                    wsv_ext0 = wsv_ext1 = wsb
                    dx_ext0 = dx0 - SQUISH_CONSTANT_4D
                    dy_ext0 = dy0 - SQUISH_CONSTANT_4D
                    dz_ext0 = dz0 - SQUISH_CONSTANT_4D
                    dw_ext0 = dw0 - SQUISH_CONSTANT_4D
                    dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_4D
                    dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_4D
                    dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw0 - 2 * SQUISH_CONSTANT_4D
                    if (c1 & 0x01) != 0:
                        xsv_ext0 += 1
                        dx_ext0 -= 1
                        xsv_ext1 += 2
                        dx_ext1 -= 2
                    elif (c1 & 0x02) != 0:
                        ysv_ext0 += 1
                        dy_ext0 -= 1
                        ysv_ext1 += 2
                        dy_ext1 -= 2
                    elif (c1 & 0x04) != 0:
                        zsv_ext0 += 1
                        dz_ext0 -= 1
                        zsv_ext1 += 2
                        dz_ext1 -= 2
                    else:
                        wsv_ext0 += 1
                        dw_ext0 -= 1
                        wsv_ext1 += 2
                        dw_ext1 -= 2

                    # One contribution is a _permutation of (1,1,1,-1) based on c2
                    xsv_ext2 = xsb + 1
                    ysv_ext2 = ysb + 1
                    zsv_ext2 = zsb + 1
                    wsv_ext2 = wsb + 1
                    dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
                    if (c2 & 0x01) == 0:
                        xsv_ext2 -= 2
                        dx_ext2 += 2
                    elif (c2 & 0x02) == 0:
                        ysv_ext2 -= 2
                        dy_ext2 += 2
                    elif (c2 & 0x04) == 0:
                        zsv_ext2 -= 2
                        dz_ext2 += 2
                    else:
                        wsv_ext2 -= 2
                        dw_ext2 += 2

                else: # Both closest pos on the smaller side
                    # One of the two extra pos is (1,1,1,1)
                    xsv_ext2 = xsb + 1
                    ysv_ext2 = ysb + 1
                    zsv_ext2 = zsb + 1
                    wsv_ext2 = wsb + 1
                    dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D
                    dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D
                    dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D
                    dw_ext2 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D

                    # Other two pos are based on the shared axes.
                    c = (a_po & b_po)
                    if (c & 0x01) != 0:
                        xsv_ext0 = xsb + 2
                        xsv_ext1 = xsb + 1
                        dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D
                        dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
                    else:
                        xsv_ext0 = xsv_ext1 = xsb
                        dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D

                    if (c & 0x02) != 0:
                        ysv_ext0 = ysv_ext1 = ysb + 1
                        dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
                        if (c & 0x01) == 0:
                            ysv_ext0 += 1
                            dy_ext0 -= 1
                        else:
                            ysv_ext1 += 1
                            dy_ext1 -= 1

                    else:
                        ysv_ext0 = ysv_ext1 = ysb
                        dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D

                    if (c & 0x04) != 0:
                        zsv_ext0 = zsv_ext1 = zsb + 1
                        dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
                        if (c & 0x03) == 0:
                            zsv_ext0 += 1
                            dz_ext0 -= 1
                        else:
                            zsv_ext1 += 1
                            dz_ext1 -= 1

                    else:
                        zsv_ext0 = zsv_ext1 = zsb
                        dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D


                    if (c & 0x08) != 0:
                        wsv_ext0 = wsb + 1
                        wsv_ext1 = wsb + 2
                        dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
                        dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D
                    else:
                        wsv_ext0 = wsv_ext1 = wsb
                        dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D

            else: # One po on each "side"
                if a_is_bigger_side:
                    c1 = a_po
                    c2 = b_po
                else:
                    c1 = b_po
                    c2 = a_po

                # Two contributions are the bigger-sided po with each 1 replaced with 2.
                if (c1 & 0x01) != 0:
                    xsv_ext0 = xsb + 2
                    xsv_ext1 = xsb + 1
                    dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D
                    dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
                else:
                    xsv_ext0 = xsv_ext1 = xsb
                    dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D

                if (c1 & 0x02) != 0:
                    ysv_ext0 = ysv_ext1 = ysb + 1
                    dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
                    if (c1 & 0x01) == 0:
                        ysv_ext0 += 1
                        dy_ext0 -= 1
                    else:
                        ysv_ext1 += 1
                        dy_ext1 -= 1

                else:
                    ysv_ext0 = ysv_ext1 = ysb
                    dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D

                if (c1 & 0x04) != 0:
                    zsv_ext0 = zsv_ext1 = zsb + 1
                    dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
                    if (c1 & 0x03) == 0:
                        zsv_ext0 += 1
                        dz_ext0 -= 1
                    else:
                        zsv_ext1 += 1
                        dz_ext1 -= 1

                else:
                    zsv_ext0 = zsv_ext1 = zsb
                    dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D

                if (c1 & 0x08) != 0:
                    wsv_ext0 = wsb + 1
                    wsv_ext1 = wsb + 2
                    dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
                    dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D
                else:
                    wsv_ext0 = wsv_ext1 = wsb
                    dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D

                # One contribution is a _permutation of (1,1,1,-1) based on the smaller-sided po
                xsv_ext2 = xsb + 1
                ysv_ext2 = ysb + 1
                zsv_ext2 = zsb + 1
                wsv_ext2 = wsb + 1
                dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
                dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
                dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
                dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
                if (c2 & 0x01) == 0:
                    xsv_ext2 -= 2
                    dx_ext2 += 2
                elif (c2 & 0x02) == 0:
                    ysv_ext2 -= 2
                    dy_ext2 += 2
                elif (c2 & 0x04) == 0:
                    zsv_ext2 -= 2
                    dz_ext2 += 2
                else:
                    wsv_ext2 -= 2
                    dw_ext2 += 2

            # Contribution (1,1,1,0)
            dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D
            dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D
            dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D
            dw4 = dw0 - 3 * SQUISH_CONSTANT_4D
            attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4
            if attn4 > 0:
                attn4 *= attn4
                value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4)

            # Contribution (1,1,0,1)
            dx3 = dx4
            dy3 = dy4
            dz3 = dz0 - 3 * SQUISH_CONSTANT_4D
            dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D
            attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3
            if attn3 > 0:
                attn3 *= attn3
                value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3)

            # Contribution (1,0,1,1)
            dx2 = dx4
            dy2 = dy0 - 3 * SQUISH_CONSTANT_4D
            dz2 = dz4
            dw2 = dw3
            attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2
            if attn2 > 0:
                attn2 *= attn2
                value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2)

            # Contribution (0,1,1,1)
            dx1 = dx0 - 3 * SQUISH_CONSTANT_4D
            dz1 = dz4
            dy1 = dy4
            dw1 = dw3
            attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1
            if attn1 > 0:
                attn1 *= attn1
                value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1)

            # Contribution (1,1,0,0)
            dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5
            if attn5 > 0:
                attn5 *= attn5
                value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5)

            # Contribution (1,0,1,0)
            dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6
            if attn6 > 0:
                attn6 *= attn6
                value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6)

            # Contribution (1,0,0,1)
            dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D
            dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7
            if attn7 > 0:
                attn7 *= attn7
                value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7)

            # Contribution (0,1,1,0)
            dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D
            attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8
            if attn8 > 0:
                attn8 *= attn8
                value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8)

            # Contribution (0,1,0,1)
            dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D
            dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D
            dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9
            if attn9 > 0:
                attn9 *= attn9
                value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9)

            # Contribution (0,0,1,1)
            dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D
            dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D
            dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D
            dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D
            attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10
            if attn10 > 0:
                attn10 *= attn10
                value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10)

        # First extra vertex
        attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 - dw_ext0 * dw_ext0
        if attn_ext0 > 0:
            attn_ext0 *= attn_ext0
            value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0)

        # Second extra vertex
        attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 - dw_ext1 * dw_ext1
        if attn_ext1 > 0:
            attn_ext1 *= attn_ext1
            value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1)

        # Third extra vertex
        attn_ext2 = 2 - dx_ext2 * dx_ext2 - dy_ext2 * dy_ext2 - dz_ext2 * dz_ext2 - dw_ext2 * dw_ext2
        if attn_ext2 > 0:
            attn_ext2 *= attn_ext2
            value += attn_ext2 * attn_ext2 * extrapolate(xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2)

        return value / NORM_CONSTANT_4D
def noise4d ( self , x , y , z , w ) : # Place input coordinates on simplectic honeycomb. stretch_offset = ( x + y + z + w ) * STRETCH_CONSTANT_4D xs = x + stretch_offset ys = y + stretch_offset zs = z + stretch_offset ws = w + stretch_offset # Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin. xsb = floor ( xs ) ysb = floor ( ys ) zsb = floor ( zs ) wsb = floor ( ws ) # Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later. squish_offset = ( xsb + ysb + zsb + wsb ) * SQUISH_CONSTANT_4D xb = xsb + squish_offset yb = ysb + squish_offset zb = zsb + squish_offset wb = wsb + squish_offset # Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin. xins = xs - xsb yins = ys - ysb zins = zs - zsb wins = ws - wsb # Sum those together to get a value that determines which region we're in. in_sum = xins + yins + zins + wins # Positions relative to origin po. dx0 = x - xb dy0 = y - yb dz0 = z - zb dw0 = w - wb value = 0 extrapolate = self . _extrapolate4d if in_sum <= 1 : # We're inside the pentachoron (4-Simplex) at (0,0,0,0) # Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest. a_po = 0x01 a_score = xins b_po = 0x02 b_score = yins if a_score >= b_score and zins > b_score : b_score = zins b_po = 0x04 elif a_score < b_score and zins > a_score : a_score = zins a_po = 0x04 if a_score >= b_score and wins > b_score : b_score = wins b_po = 0x08 elif a_score < b_score and wins > a_score : a_score = wins a_po = 0x08 # Now we determine the three lattice pos not part of the pentachoron that may contribute. # This depends on the closest two pentachoron vertices, including (0,0,0,0) uins = 1 - in_sum if uins > a_score or uins > b_score : # (0,0,0,0) is one of the closest two pentachoron vertices. c = b_po if ( b_score > a_score ) else a_po # Our other closest vertex is the closest out of a and b. if ( c & 0x01 ) == 0 : xsv_ext0 = xsb - 1 xsv_ext1 = xsv_ext2 = xsb dx_ext0 = dx0 + 1 dx_ext1 = dx_ext2 = dx0 else : xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1 dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1 if ( c & 0x02 ) == 0 : ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb dy_ext0 = dy_ext1 = dy_ext2 = dy0 if ( c & 0x01 ) == 0x01 : ysv_ext0 -= 1 dy_ext0 += 1 else : ysv_ext1 -= 1 dy_ext1 += 1 else : ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1 dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 if ( c & 0x04 ) == 0 : zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb dz_ext0 = dz_ext1 = dz_ext2 = dz0 if ( c & 0x03 ) != 0 : if ( c & 0x03 ) == 0x03 : zsv_ext0 -= 1 dz_ext0 += 1 else : zsv_ext1 -= 1 dz_ext1 += 1 else : zsv_ext2 -= 1 dz_ext2 += 1 else : zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1 dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 if ( c & 0x08 ) == 0 : wsv_ext0 = wsv_ext1 = wsb wsv_ext2 = wsb - 1 dw_ext0 = dw_ext1 = dw0 dw_ext2 = dw0 + 1 else : wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1 dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1 else : # (0,0,0,0) is not one of the closest two pentachoron vertices. c = ( a_po | b_po ) # Our three extra vertices are determined by the closest two. if ( c & 0x01 ) == 0 : xsv_ext0 = xsv_ext2 = xsb xsv_ext1 = xsb - 1 dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D dx_ext2 = dx0 - SQUISH_CONSTANT_4D else : xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1 dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dx_ext1 = dx_ext2 = dx0 - 1 - SQUISH_CONSTANT_4D if ( c & 0x02 ) == 0 : ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT_4D if ( c & 0x01 ) == 0x01 : ysv_ext1 -= 1 dy_ext1 += 1 else : ysv_ext2 -= 1 dy_ext2 += 1 else : ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1 dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dy_ext1 = dy_ext2 = dy0 - 1 - SQUISH_CONSTANT_4D if ( c & 0x04 ) == 0 : zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT_4D if ( c & 0x03 ) == 0x03 : zsv_ext1 -= 1 dz_ext1 += 1 else : zsv_ext2 -= 1 dz_ext2 += 1 else : zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1 dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dz_ext1 = dz_ext2 = dz0 - 1 - SQUISH_CONSTANT_4D if ( c & 0x08 ) == 0 : wsv_ext0 = wsv_ext1 = wsb wsv_ext2 = wsb - 1 dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - SQUISH_CONSTANT_4D dw_ext2 = dw0 + 1 - SQUISH_CONSTANT_4D else : wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1 dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D dw_ext1 = dw_ext2 = dw0 - 1 - SQUISH_CONSTANT_4D # Contribution (0,0,0,0) attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0 if attn0 > 0 : attn0 *= attn0 value += attn0 * attn0 * extrapolate ( xsb + 0 , ysb + 0 , zsb + 0 , wsb + 0 , dx0 , dy0 , dz0 , dw0 ) # Contribution (1,0,0,0) dx1 = dx0 - 1 - SQUISH_CONSTANT_4D dy1 = dy0 - 0 - SQUISH_CONSTANT_4D dz1 = dz0 - 0 - SQUISH_CONSTANT_4D dw1 = dw0 - 0 - SQUISH_CONSTANT_4D attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1 if attn1 > 0 : attn1 *= attn1 value += attn1 * attn1 * extrapolate ( xsb + 1 , ysb + 0 , zsb + 0 , wsb + 0 , dx1 , dy1 , dz1 , dw1 ) # Contribution (0,1,0,0) dx2 = dx0 - 0 - SQUISH_CONSTANT_4D dy2 = dy0 - 1 - SQUISH_CONSTANT_4D dz2 = dz1 dw2 = dw1 attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2 if attn2 > 0 : attn2 *= attn2 value += attn2 * attn2 * extrapolate ( xsb + 0 , ysb + 1 , zsb + 0 , wsb + 0 , dx2 , dy2 , dz2 , dw2 ) # Contribution (0,0,1,0) dx3 = dx2 dy3 = dy1 dz3 = dz0 - 1 - SQUISH_CONSTANT_4D dw3 = dw1 attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3 if attn3 > 0 : attn3 *= attn3 value += attn3 * attn3 * extrapolate ( xsb + 0 , ysb + 0 , zsb + 1 , wsb + 0 , dx3 , dy3 , dz3 , dw3 ) # Contribution (0,0,0,1) dx4 = dx2 dy4 = dy1 dz4 = dz1 dw4 = dw0 - 1 - SQUISH_CONSTANT_4D attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4 if attn4 > 0 : attn4 *= attn4 value += attn4 * attn4 * extrapolate ( xsb + 0 , ysb + 0 , zsb + 0 , wsb + 1 , dx4 , dy4 , dz4 , dw4 ) elif in_sum >= 3 : # We're inside the pentachoron (4-Simplex) at (1,1,1,1) # Determine which two of (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) are closest. a_po = 0x0E a_score = xins b_po = 0x0D b_score = yins if a_score <= b_score and zins < b_score : b_score = zins b_po = 0x0B elif a_score > b_score and zins < a_score : a_score = zins a_po = 0x0B if a_score <= b_score and wins < b_score : b_score = wins b_po = 0x07 elif a_score > b_score and wins < a_score : a_score = wins a_po = 0x07 # Now we determine the three lattice pos not part of the pentachoron that may contribute. # This depends on the closest two pentachoron vertices, including (0,0,0,0) uins = 4 - in_sum if uins < a_score or uins < b_score : # (1,1,1,1) is one of the closest two pentachoron vertices. c = b_po if ( b_score < a_score ) else a_po # Our other closest vertex is the closest out of a and b. if ( c & 0x01 ) != 0 : xsv_ext0 = xsb + 2 xsv_ext1 = xsv_ext2 = xsb + 1 dx_ext0 = dx0 - 2 - 4 * SQUISH_CONSTANT_4D dx_ext1 = dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D else : xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * SQUISH_CONSTANT_4D if ( c & 0x02 ) != 0 : ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1 dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D if ( c & 0x01 ) != 0 : ysv_ext1 += 1 dy_ext1 -= 1 else : ysv_ext0 += 1 dy_ext0 -= 1 else : ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 4 * SQUISH_CONSTANT_4D if ( c & 0x04 ) != 0 : zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1 dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D if ( c & 0x03 ) != 0x03 : if ( c & 0x03 ) == 0 : zsv_ext0 += 1 dz_ext0 -= 1 else : zsv_ext1 += 1 dz_ext1 -= 1 else : zsv_ext2 += 1 dz_ext2 -= 1 else : zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 4 * SQUISH_CONSTANT_4D if ( c & 0x08 ) != 0 : wsv_ext0 = wsv_ext1 = wsb + 1 wsv_ext2 = wsb + 2 dw_ext0 = dw_ext1 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 2 - 4 * SQUISH_CONSTANT_4D else : wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * SQUISH_CONSTANT_4D else : # (1,1,1,1) is not one of the closest two pentachoron vertices. c = ( a_po & b_po ) # Our three extra vertices are determined by the closest two. if ( c & 0x01 ) != 0 : xsv_ext0 = xsv_ext2 = xsb + 1 xsv_ext1 = xsb + 2 dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dx_ext1 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D dx_ext2 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D else : xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D dx_ext1 = dx_ext2 = dx0 - 3 * SQUISH_CONSTANT_4D if ( c & 0x02 ) != 0 : ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1 dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dy_ext1 = dy_ext2 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D if ( c & 0x01 ) != 0 : ysv_ext2 += 1 dy_ext2 -= 1 else : ysv_ext1 += 1 dy_ext1 -= 1 else : ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D dy_ext1 = dy_ext2 = dy0 - 3 * SQUISH_CONSTANT_4D if ( c & 0x04 ) != 0 : zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1 dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dz_ext1 = dz_ext2 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D if ( c & 0x03 ) != 0 : zsv_ext2 += 1 dz_ext2 -= 1 else : zsv_ext1 += 1 dz_ext1 -= 1 else : zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D dz_ext1 = dz_ext2 = dz0 - 3 * SQUISH_CONSTANT_4D if ( c & 0x08 ) != 0 : wsv_ext0 = wsv_ext1 = wsb + 1 wsv_ext2 = wsb + 2 dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D else : wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D dw_ext1 = dw_ext2 = dw0 - 3 * SQUISH_CONSTANT_4D # Contribution (1,1,1,0) dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D dw4 = dw0 - 3 * SQUISH_CONSTANT_4D attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4 if attn4 > 0 : attn4 *= attn4 value += attn4 * attn4 * extrapolate ( xsb + 1 , ysb + 1 , zsb + 1 , wsb + 0 , dx4 , dy4 , dz4 , dw4 ) # Contribution (1,1,0,1) dx3 = dx4 dy3 = dy4 dz3 = dz0 - 3 * SQUISH_CONSTANT_4D dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3 if attn3 > 0 : attn3 *= attn3 value += attn3 * attn3 * extrapolate ( xsb + 1 , ysb + 1 , zsb + 0 , wsb + 1 , dx3 , dy3 , dz3 , dw3 ) # Contribution (1,0,1,1) dx2 = dx4 dy2 = dy0 - 3 * SQUISH_CONSTANT_4D dz2 = dz4 dw2 = dw3 attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2 if attn2 > 0 : attn2 *= attn2 value += attn2 * attn2 * extrapolate ( xsb + 1 , ysb + 0 , zsb + 1 , wsb + 1 , dx2 , dy2 , dz2 , dw2 ) # Contribution (0,1,1,1) dx1 = dx0 - 3 * SQUISH_CONSTANT_4D dz1 = dz4 dy1 = dy4 dw1 = dw3 attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1 if attn1 > 0 : attn1 *= attn1 value += attn1 * attn1 * extrapolate ( xsb + 0 , ysb + 1 , zsb + 1 , wsb + 1 , dx1 , dy1 , dz1 , dw1 ) # Contribution (1,1,1,1) dx0 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D dy0 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D dz0 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D dw0 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0 if attn0 > 0 : attn0 *= attn0 value += attn0 * attn0 * extrapolate ( xsb + 1 , ysb + 1 , zsb + 1 , wsb + 1 , dx0 , dy0 , dz0 , dw0 ) elif in_sum <= 2 : # We're inside the first dispentachoron (Rectified 4-Simplex) a_is_bigger_side = True b_is_bigger_side = True # Decide between (1,1,0,0) and (0,0,1,1) if xins + yins > zins + wins : a_score = xins + yins a_po = 0x03 else : a_score = zins + wins a_po = 0x0C # Decide between (1,0,1,0) and (0,1,0,1) if xins + zins > yins + wins : b_score = xins + zins b_po = 0x05 else : b_score = yins + wins b_po = 0x0A # Closer between (1,0,0,1) and (0,1,1,0) will replace the further of a and b, if closer. if xins + wins > yins + zins : score = xins + wins if a_score >= b_score and score > b_score : b_score = score b_po = 0x09 elif a_score < b_score and score > a_score : a_score = score a_po = 0x09 else : score = yins + zins if a_score >= b_score and score > b_score : b_score = score b_po = 0x06 elif a_score < b_score and score > a_score : a_score = score a_po = 0x06 # Decide if (1,0,0,0) is closer. p1 = 2 - in_sum + xins if a_score >= b_score and p1 > b_score : b_score = p1 b_po = 0x01 b_is_bigger_side = False elif a_score < b_score and p1 > a_score : a_score = p1 a_po = 0x01 a_is_bigger_side = False # Decide if (0,1,0,0) is closer. p2 = 2 - in_sum + yins if a_score >= b_score and p2 > b_score : b_score = p2 b_po = 0x02 b_is_bigger_side = False elif a_score < b_score and p2 > a_score : a_score = p2 a_po = 0x02 a_is_bigger_side = False # Decide if (0,0,1,0) is closer. p3 = 2 - in_sum + zins if a_score >= b_score and p3 > b_score : b_score = p3 b_po = 0x04 b_is_bigger_side = False elif a_score < b_score and p3 > a_score : a_score = p3 a_po = 0x04 a_is_bigger_side = False # Decide if (0,0,0,1) is closer. p4 = 2 - in_sum + wins if a_score >= b_score and p4 > b_score : b_po = 0x08 b_is_bigger_side = False elif a_score < b_score and p4 > a_score : a_po = 0x08 a_is_bigger_side = False # Where each of the two closest pos are determines how the extra three vertices are calculated. if a_is_bigger_side == b_is_bigger_side : if a_is_bigger_side : # Both closest pos on the bigger side c1 = ( a_po | b_po ) c2 = ( a_po & b_po ) if ( c1 & 0x01 ) == 0 : xsv_ext0 = xsb xsv_ext1 = xsb - 1 dx_ext0 = dx0 - 3 * SQUISH_CONSTANT_4D dx_ext1 = dx0 + 1 - 2 * SQUISH_CONSTANT_4D else : xsv_ext0 = xsv_ext1 = xsb + 1 dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D dx_ext1 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D if ( c1 & 0x02 ) == 0 : ysv_ext0 = ysb ysv_ext1 = ysb - 1 dy_ext0 = dy0 - 3 * SQUISH_CONSTANT_4D dy_ext1 = dy0 + 1 - 2 * SQUISH_CONSTANT_4D else : ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D dy_ext1 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D if ( c1 & 0x04 ) == 0 : zsv_ext0 = zsb zsv_ext1 = zsb - 1 dz_ext0 = dz0 - 3 * SQUISH_CONSTANT_4D dz_ext1 = dz0 + 1 - 2 * SQUISH_CONSTANT_4D else : zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D dz_ext1 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D if ( c1 & 0x08 ) == 0 : wsv_ext0 = wsb wsv_ext1 = wsb - 1 dw_ext0 = dw0 - 3 * SQUISH_CONSTANT_4D dw_ext1 = dw0 + 1 - 2 * SQUISH_CONSTANT_4D else : wsv_ext0 = wsv_ext1 = wsb + 1 dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D # One combination is a _permutation of (0,0,0,2) based on c2 xsv_ext2 = xsb ysv_ext2 = ysb zsv_ext2 = zsb wsv_ext2 = wsb dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D if ( c2 & 0x01 ) != 0 : xsv_ext2 += 2 dx_ext2 -= 2 elif ( c2 & 0x02 ) != 0 : ysv_ext2 += 2 dy_ext2 -= 2 elif ( c2 & 0x04 ) != 0 : zsv_ext2 += 2 dz_ext2 -= 2 else : wsv_ext2 += 2 dw_ext2 -= 2 else : # Both closest pos on the smaller side # One of the two extra pos is (0,0,0,0) xsv_ext2 = xsb ysv_ext2 = ysb zsv_ext2 = zsb wsv_ext2 = wsb dx_ext2 = dx0 dy_ext2 = dy0 dz_ext2 = dz0 dw_ext2 = dw0 # Other two pos are based on the omitted axes. c = ( a_po | b_po ) if ( c & 0x01 ) == 0 : xsv_ext0 = xsb - 1 xsv_ext1 = xsb dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D dx_ext1 = dx0 - SQUISH_CONSTANT_4D else : xsv_ext0 = xsv_ext1 = xsb + 1 dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D if ( c & 0x02 ) == 0 : ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D if ( c & 0x01 ) == 0x01 : ysv_ext0 -= 1 dy_ext0 += 1 else : ysv_ext1 -= 1 dy_ext1 += 1 else : ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D if ( c & 0x04 ) == 0 : zsv_ext0 = zsv_ext1 = zsb dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D if ( c & 0x03 ) == 0x03 : zsv_ext0 -= 1 dz_ext0 += 1 else : zsv_ext1 -= 1 dz_ext1 += 1 else : zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D if ( c & 0x08 ) == 0 : wsv_ext0 = wsb wsv_ext1 = wsb - 1 dw_ext0 = dw0 - SQUISH_CONSTANT_4D dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D else : wsv_ext0 = wsv_ext1 = wsb + 1 dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D else : # One po on each "side" if a_is_bigger_side : c1 = a_po c2 = b_po else : c1 = b_po c2 = a_po # Two contributions are the bigger-sided po with each 0 replaced with -1. if ( c1 & 0x01 ) == 0 : xsv_ext0 = xsb - 1 xsv_ext1 = xsb dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D dx_ext1 = dx0 - SQUISH_CONSTANT_4D else : xsv_ext0 = xsv_ext1 = xsb + 1 dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D if ( c1 & 0x02 ) == 0 : ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D if ( c1 & 0x01 ) == 0x01 : ysv_ext0 -= 1 dy_ext0 += 1 else : ysv_ext1 -= 1 dy_ext1 += 1 else : ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D if ( c1 & 0x04 ) == 0 : zsv_ext0 = zsv_ext1 = zsb dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D if ( c1 & 0x03 ) == 0x03 : zsv_ext0 -= 1 dz_ext0 += 1 else : zsv_ext1 -= 1 dz_ext1 += 1 else : zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D if ( c1 & 0x08 ) == 0 : wsv_ext0 = wsb wsv_ext1 = wsb - 1 dw_ext0 = dw0 - SQUISH_CONSTANT_4D dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D else : wsv_ext0 = wsv_ext1 = wsb + 1 dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D # One contribution is a _permutation of (0,0,0,2) based on the smaller-sided po xsv_ext2 = xsb ysv_ext2 = ysb zsv_ext2 = zsb wsv_ext2 = wsb dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D if ( c2 & 0x01 ) != 0 : xsv_ext2 += 2 dx_ext2 -= 2 elif ( c2 & 0x02 ) != 0 : ysv_ext2 += 2 dy_ext2 -= 2 elif ( c2 & 0x04 ) != 0 : zsv_ext2 += 2 dz_ext2 -= 2 else : wsv_ext2 += 2 dw_ext2 -= 2 # Contribution (1,0,0,0) dx1 = dx0 - 1 - SQUISH_CONSTANT_4D dy1 = dy0 - 0 - SQUISH_CONSTANT_4D dz1 = dz0 - 0 - SQUISH_CONSTANT_4D dw1 = dw0 - 0 - SQUISH_CONSTANT_4D attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1 if attn1 > 0 : attn1 *= attn1 value += attn1 * attn1 * extrapolate ( xsb + 1 , ysb + 0 , zsb + 0 , wsb + 0 , dx1 , dy1 , dz1 , dw1 ) # Contribution (0,1,0,0) dx2 = dx0 - 0 - SQUISH_CONSTANT_4D dy2 = dy0 - 1 - SQUISH_CONSTANT_4D dz2 = dz1 dw2 = dw1 attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2 if attn2 > 0 : attn2 *= attn2 value += attn2 * attn2 * extrapolate ( xsb + 0 , ysb + 1 , zsb + 0 , wsb + 0 , dx2 , dy2 , dz2 , dw2 ) # Contribution (0,0,1,0) dx3 = dx2 dy3 = dy1 dz3 = dz0 - 1 - SQUISH_CONSTANT_4D dw3 = dw1 attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3 if attn3 > 0 : attn3 *= attn3 value += attn3 * attn3 * extrapolate ( xsb + 0 , ysb + 0 , zsb + 1 , wsb + 0 , dx3 , dy3 , dz3 , dw3 ) # Contribution (0,0,0,1) dx4 = dx2 dy4 = dy1 dz4 = dz1 dw4 = dw0 - 1 - SQUISH_CONSTANT_4D attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4 if attn4 > 0 : attn4 *= attn4 value += attn4 * attn4 * extrapolate ( xsb + 0 , ysb + 0 , zsb + 0 , wsb + 1 , dx4 , dy4 , dz4 , dw4 ) # Contribution (1,1,0,0) dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5 if attn5 > 0 : attn5 *= attn5 value += attn5 * attn5 * extrapolate ( xsb + 1 , ysb + 1 , zsb + 0 , wsb + 0 , dx5 , dy5 , dz5 , dw5 ) # Contribution (1,0,1,0) dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6 if attn6 > 0 : attn6 *= attn6 value += attn6 * attn6 * extrapolate ( xsb + 1 , ysb + 0 , zsb + 1 , wsb + 0 , dx6 , dy6 , dz6 , dw6 ) # Contribution (1,0,0,1) dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7 if attn7 > 0 : attn7 *= attn7 value += attn7 * attn7 * extrapolate ( xsb + 1 , ysb + 0 , zsb + 0 , wsb + 1 , dx7 , dy7 , dz7 , dw7 ) # Contribution (0,1,1,0) dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8 if attn8 > 0 : attn8 *= attn8 value += attn8 * attn8 * extrapolate ( xsb + 0 , ysb + 1 , zsb + 1 , wsb + 0 , dx8 , dy8 , dz8 , dw8 ) # Contribution (0,1,0,1) dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9 if attn9 > 0 : attn9 *= attn9 value += attn9 * attn9 * extrapolate ( xsb + 0 , ysb + 1 , zsb + 0 , wsb + 1 , dx9 , dy9 , dz9 , dw9 ) # Contribution (0,0,1,1) dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10 if attn10 > 0 : attn10 *= attn10 value += attn10 * attn10 * extrapolate ( xsb + 0 , ysb + 0 , zsb + 1 , wsb + 1 , dx10 , dy10 , dz10 , dw10 ) else : # We're inside the second dispentachoron (Rectified 4-Simplex) a_is_bigger_side = True b_is_bigger_side = True # Decide between (0,0,1,1) and (1,1,0,0) if xins + yins < zins + wins : a_score = xins + yins a_po = 0x0C else : a_score = zins + wins a_po = 0x03 # Decide between (0,1,0,1) and (1,0,1,0) if xins + zins < yins + wins : b_score = xins + zins b_po = 0x0A else : b_score = yins + wins b_po = 0x05 # Closer between (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer. if xins + wins < yins + zins : score = xins + wins if a_score <= b_score and score < b_score : b_score = score b_po = 0x06 elif a_score > b_score and score < a_score : a_score = score a_po = 0x06 else : score = yins + zins if a_score <= b_score and score < b_score : b_score = score b_po = 0x09 elif a_score > b_score and score < a_score : a_score = score a_po = 0x09 # Decide if (0,1,1,1) is closer. p1 = 3 - in_sum + xins if a_score <= b_score and p1 < b_score : b_score = p1 b_po = 0x0E b_is_bigger_side = False elif a_score > b_score and p1 < a_score : a_score = p1 a_po = 0x0E a_is_bigger_side = False # Decide if (1,0,1,1) is closer. p2 = 3 - in_sum + yins if a_score <= b_score and p2 < b_score : b_score = p2 b_po = 0x0D b_is_bigger_side = False elif a_score > b_score and p2 < a_score : a_score = p2 a_po = 0x0D a_is_bigger_side = False # Decide if (1,1,0,1) is closer. p3 = 3 - in_sum + zins if a_score <= b_score and p3 < b_score : b_score = p3 b_po = 0x0B b_is_bigger_side = False elif a_score > b_score and p3 < a_score : a_score = p3 a_po = 0x0B a_is_bigger_side = False # Decide if (1,1,1,0) is closer. p4 = 3 - in_sum + wins if a_score <= b_score and p4 < b_score : b_po = 0x07 b_is_bigger_side = False elif a_score > b_score and p4 < a_score : a_po = 0x07 a_is_bigger_side = False # Where each of the two closest pos are determines how the extra three vertices are calculated. if a_is_bigger_side == b_is_bigger_side : if a_is_bigger_side : # Both closest pos on the bigger side c1 = ( a_po & b_po ) c2 = ( a_po | b_po ) # Two contributions are _permutations of (0,0,0,1) and (0,0,0,2) based on c1 xsv_ext0 = xsv_ext1 = xsb ysv_ext0 = ysv_ext1 = ysb zsv_ext0 = zsv_ext1 = zsb wsv_ext0 = wsv_ext1 = wsb dx_ext0 = dx0 - SQUISH_CONSTANT_4D dy_ext0 = dy0 - SQUISH_CONSTANT_4D dz_ext0 = dz0 - SQUISH_CONSTANT_4D dw_ext0 = dw0 - SQUISH_CONSTANT_4D dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_4D dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_4D dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - 2 * SQUISH_CONSTANT_4D if ( c1 & 0x01 ) != 0 : xsv_ext0 += 1 dx_ext0 -= 1 xsv_ext1 += 2 dx_ext1 -= 2 elif ( c1 & 0x02 ) != 0 : ysv_ext0 += 1 dy_ext0 -= 1 ysv_ext1 += 2 dy_ext1 -= 2 elif ( c1 & 0x04 ) != 0 : zsv_ext0 += 1 dz_ext0 -= 1 zsv_ext1 += 2 dz_ext1 -= 2 else : wsv_ext0 += 1 dw_ext0 -= 1 wsv_ext1 += 2 dw_ext1 -= 2 # One contribution is a _permutation of (1,1,1,-1) based on c2 xsv_ext2 = xsb + 1 ysv_ext2 = ysb + 1 zsv_ext2 = zsb + 1 wsv_ext2 = wsb + 1 dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D if ( c2 & 0x01 ) == 0 : xsv_ext2 -= 2 dx_ext2 += 2 elif ( c2 & 0x02 ) == 0 : ysv_ext2 -= 2 dy_ext2 += 2 elif ( c2 & 0x04 ) == 0 : zsv_ext2 -= 2 dz_ext2 += 2 else : wsv_ext2 -= 2 dw_ext2 += 2 else : # Both closest pos on the smaller side # One of the two extra pos is (1,1,1,1) xsv_ext2 = xsb + 1 ysv_ext2 = ysb + 1 zsv_ext2 = zsb + 1 wsv_ext2 = wsb + 1 dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D # Other two pos are based on the shared axes. c = ( a_po & b_po ) if ( c & 0x01 ) != 0 : xsv_ext0 = xsb + 2 xsv_ext1 = xsb + 1 dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D else : xsv_ext0 = xsv_ext1 = xsb dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D if ( c & 0x02 ) != 0 : ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D if ( c & 0x01 ) == 0 : ysv_ext0 += 1 dy_ext0 -= 1 else : ysv_ext1 += 1 dy_ext1 -= 1 else : ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D if ( c & 0x04 ) != 0 : zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D if ( c & 0x03 ) == 0 : zsv_ext0 += 1 dz_ext0 -= 1 else : zsv_ext1 += 1 dz_ext1 -= 1 else : zsv_ext0 = zsv_ext1 = zsb dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D if ( c & 0x08 ) != 0 : wsv_ext0 = wsb + 1 wsv_ext1 = wsb + 2 dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D else : wsv_ext0 = wsv_ext1 = wsb dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D else : # One po on each "side" if a_is_bigger_side : c1 = a_po c2 = b_po else : c1 = b_po c2 = a_po # Two contributions are the bigger-sided po with each 1 replaced with 2. if ( c1 & 0x01 ) != 0 : xsv_ext0 = xsb + 2 xsv_ext1 = xsb + 1 dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D else : xsv_ext0 = xsv_ext1 = xsb dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D if ( c1 & 0x02 ) != 0 : ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D if ( c1 & 0x01 ) == 0 : ysv_ext0 += 1 dy_ext0 -= 1 else : ysv_ext1 += 1 dy_ext1 -= 1 else : ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D if ( c1 & 0x04 ) != 0 : zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D if ( c1 & 0x03 ) == 0 : zsv_ext0 += 1 dz_ext0 -= 1 else : zsv_ext1 += 1 dz_ext1 -= 1 else : zsv_ext0 = zsv_ext1 = zsb dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D if ( c1 & 0x08 ) != 0 : wsv_ext0 = wsb + 1 wsv_ext1 = wsb + 2 dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D else : wsv_ext0 = wsv_ext1 = wsb dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D # One contribution is a _permutation of (1,1,1,-1) based on the smaller-sided po xsv_ext2 = xsb + 1 ysv_ext2 = ysb + 1 zsv_ext2 = zsb + 1 wsv_ext2 = wsb + 1 dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D if ( c2 & 0x01 ) == 0 : xsv_ext2 -= 2 dx_ext2 += 2 elif ( c2 & 0x02 ) == 0 : ysv_ext2 -= 2 dy_ext2 += 2 elif ( c2 & 0x04 ) == 0 : zsv_ext2 -= 2 dz_ext2 += 2 else : wsv_ext2 -= 2 dw_ext2 += 2 # Contribution (1,1,1,0) dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D dw4 = dw0 - 3 * SQUISH_CONSTANT_4D attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4 if attn4 > 0 : attn4 *= attn4 value += attn4 * attn4 * extrapolate ( xsb + 1 , ysb + 1 , zsb + 1 , wsb + 0 , dx4 , dy4 , dz4 , dw4 ) # Contribution (1,1,0,1) dx3 = dx4 dy3 = dy4 dz3 = dz0 - 3 * SQUISH_CONSTANT_4D dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3 if attn3 > 0 : attn3 *= attn3 value += attn3 * attn3 * extrapolate ( xsb + 1 , ysb + 1 , zsb + 0 , wsb + 1 , dx3 , dy3 , dz3 , dw3 ) # Contribution (1,0,1,1) dx2 = dx4 dy2 = dy0 - 3 * SQUISH_CONSTANT_4D dz2 = dz4 dw2 = dw3 attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2 if attn2 > 0 : attn2 *= attn2 value += attn2 * attn2 * extrapolate ( xsb + 1 , ysb + 0 , zsb + 1 , wsb + 1 , dx2 , dy2 , dz2 , dw2 ) # Contribution (0,1,1,1) dx1 = dx0 - 3 * SQUISH_CONSTANT_4D dz1 = dz4 dy1 = dy4 dw1 = dw3 attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1 if attn1 > 0 : attn1 *= attn1 value += attn1 * attn1 * extrapolate ( xsb + 0 , ysb + 1 , zsb + 1 , wsb + 1 , dx1 , dy1 , dz1 , dw1 ) # Contribution (1,1,0,0) dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5 if attn5 > 0 : attn5 *= attn5 value += attn5 * attn5 * extrapolate ( xsb + 1 , ysb + 1 , zsb + 0 , wsb + 0 , dx5 , dy5 , dz5 , dw5 ) # Contribution (1,0,1,0) dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6 if attn6 > 0 : attn6 *= attn6 value += attn6 * attn6 * extrapolate ( xsb + 1 , ysb + 0 , zsb + 1 , wsb + 0 , dx6 , dy6 , dz6 , dw6 ) # Contribution (1,0,0,1) dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7 if attn7 > 0 : attn7 *= attn7 value += attn7 * attn7 * extrapolate ( xsb + 1 , ysb + 0 , zsb + 0 , wsb + 1 , dx7 , dy7 , dz7 , dw7 ) # Contribution (0,1,1,0) dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8 if attn8 > 0 : attn8 *= attn8 value += attn8 * attn8 * extrapolate ( xsb + 0 , ysb + 1 , zsb + 1 , wsb + 0 , dx8 , dy8 , dz8 , dw8 ) # Contribution (0,1,0,1) dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9 if attn9 > 0 : attn9 *= attn9 value += attn9 * attn9 * extrapolate ( xsb + 0 , ysb + 1 , zsb + 0 , wsb + 1 , dx9 , dy9 , dz9 , dw9 ) # Contribution (0,0,1,1) dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10 if attn10 > 0 : attn10 *= attn10 value += attn10 * attn10 * extrapolate ( xsb + 0 , ysb + 0 , zsb + 1 , wsb + 1 , dx10 , dy10 , dz10 , dw10 ) # First extra vertex attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 - dw_ext0 * dw_ext0 if attn_ext0 > 0 : attn_ext0 *= attn_ext0 value += attn_ext0 * attn_ext0 * extrapolate ( xsv_ext0 , ysv_ext0 , zsv_ext0 , wsv_ext0 , dx_ext0 , dy_ext0 , dz_ext0 , dw_ext0 ) # Second extra vertex attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 - dw_ext1 * dw_ext1 if attn_ext1 > 0 : attn_ext1 *= attn_ext1 value += attn_ext1 * attn_ext1 * extrapolate ( xsv_ext1 , ysv_ext1 , zsv_ext1 , wsv_ext1 , dx_ext1 , dy_ext1 , dz_ext1 , dw_ext1 ) # Third extra vertex attn_ext2 = 2 - dx_ext2 * dx_ext2 - dy_ext2 * dy_ext2 - dz_ext2 * dz_ext2 - dw_ext2 * dw_ext2 if attn_ext2 > 0 : attn_ext2 *= attn_ext2 value += attn_ext2 * attn_ext2 * extrapolate ( xsv_ext2 , ysv_ext2 , zsv_ext2 , wsv_ext2 , dx_ext2 , dy_ext2 , dz_ext2 , dw_ext2 ) return value / NORM_CONSTANT_4D
Generate 4D OpenSimplex noise from X,Y,Z,W coordinates.
Generate 4D OpenSimplex noise from X Y Z W coordinates .