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| from sympy.core.containers import Tuple | |
| from sympy.core.numbers import (Rational, pi) | |
| from sympy.core.singleton import S | |
| from sympy.core.symbol import (Symbol, symbols) | |
| from sympy.functions.elementary.hyperbolic import asinh | |
| from sympy.functions.elementary.miscellaneous import sqrt | |
| from sympy.geometry import Curve, Line, Point, Ellipse, Ray, Segment, Circle, Polygon, RegularPolygon | |
| from sympy.testing.pytest import raises, slow | |
| def test_curve(): | |
| x = Symbol('x', real=True) | |
| s = Symbol('s') | |
| z = Symbol('z') | |
| # this curve is independent of the indicated parameter | |
| c = Curve([2*s, s**2], (z, 0, 2)) | |
| assert c.parameter == z | |
| assert c.functions == (2*s, s**2) | |
| assert c.arbitrary_point() == Point(2*s, s**2) | |
| assert c.arbitrary_point(z) == Point(2*s, s**2) | |
| # this is how it is normally used | |
| c = Curve([2*s, s**2], (s, 0, 2)) | |
| assert c.parameter == s | |
| assert c.functions == (2*s, s**2) | |
| t = Symbol('t') | |
| # the t returned as assumptions | |
| assert c.arbitrary_point() != Point(2*t, t**2) | |
| t = Symbol('t', real=True) | |
| # now t has the same assumptions so the test passes | |
| assert c.arbitrary_point() == Point(2*t, t**2) | |
| assert c.arbitrary_point(z) == Point(2*z, z**2) | |
| assert c.arbitrary_point(c.parameter) == Point(2*s, s**2) | |
| assert c.arbitrary_point(None) == Point(2*s, s**2) | |
| assert c.plot_interval() == [t, 0, 2] | |
| assert c.plot_interval(z) == [z, 0, 2] | |
| assert Curve([x, x], (x, 0, 1)).rotate(pi/2) == Curve([-x, x], (x, 0, 1)) | |
| assert Curve([x, x], (x, 0, 1)).rotate(pi/2, (1, 2)).scale(2, 3).translate( | |
| 1, 3).arbitrary_point(s) == \ | |
| Line((0, 0), (1, 1)).rotate(pi/2, (1, 2)).scale(2, 3).translate( | |
| 1, 3).arbitrary_point(s) == \ | |
| Point(-2*s + 7, 3*s + 6) | |
| raises(ValueError, lambda: Curve((s), (s, 1, 2))) | |
| raises(ValueError, lambda: Curve((x, x * 2), (1, x))) | |
| raises(ValueError, lambda: Curve((s, s + t), (s, 1, 2)).arbitrary_point()) | |
| raises(ValueError, lambda: Curve((s, s + t), (t, 1, 2)).arbitrary_point(s)) | |
| def test_free_symbols(): | |
| a, b, c, d, e, f, s = symbols('a:f,s') | |
| assert Point(a, b).free_symbols == {a, b} | |
| assert Line((a, b), (c, d)).free_symbols == {a, b, c, d} | |
| assert Ray((a, b), (c, d)).free_symbols == {a, b, c, d} | |
| assert Ray((a, b), angle=c).free_symbols == {a, b, c} | |
| assert Segment((a, b), (c, d)).free_symbols == {a, b, c, d} | |
| assert Line((a, b), slope=c).free_symbols == {a, b, c} | |
| assert Curve((a*s, b*s), (s, c, d)).free_symbols == {a, b, c, d} | |
| assert Ellipse((a, b), c, d).free_symbols == {a, b, c, d} | |
| assert Ellipse((a, b), c, eccentricity=d).free_symbols == \ | |
| {a, b, c, d} | |
| assert Ellipse((a, b), vradius=c, eccentricity=d).free_symbols == \ | |
| {a, b, c, d} | |
| assert Circle((a, b), c).free_symbols == {a, b, c} | |
| assert Circle((a, b), (c, d), (e, f)).free_symbols == \ | |
| {e, d, c, b, f, a} | |
| assert Polygon((a, b), (c, d), (e, f)).free_symbols == \ | |
| {e, b, d, f, a, c} | |
| assert RegularPolygon((a, b), c, d, e).free_symbols == {e, a, b, c, d} | |
| def test_transform(): | |
| x = Symbol('x', real=True) | |
| y = Symbol('y', real=True) | |
| c = Curve((x, x**2), (x, 0, 1)) | |
| cout = Curve((2*x - 4, 3*x**2 - 10), (x, 0, 1)) | |
| pts = [Point(0, 0), Point(S.Half, Rational(1, 4)), Point(1, 1)] | |
| pts_out = [Point(-4, -10), Point(-3, Rational(-37, 4)), Point(-2, -7)] | |
| assert c.scale(2, 3, (4, 5)) == cout | |
| assert [c.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts | |
| assert [cout.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts_out | |
| assert Curve((x + y, 3*x), (x, 0, 1)).subs(y, S.Half) == \ | |
| Curve((x + S.Half, 3*x), (x, 0, 1)) | |
| assert Curve((x, 3*x), (x, 0, 1)).translate(4, 5) == \ | |
| Curve((x + 4, 3*x + 5), (x, 0, 1)) | |
| def test_length(): | |
| t = Symbol('t', real=True) | |
| c1 = Curve((t, 0), (t, 0, 1)) | |
| assert c1.length == 1 | |
| c2 = Curve((t, t), (t, 0, 1)) | |
| assert c2.length == sqrt(2) | |
| c3 = Curve((t ** 2, t), (t, 2, 5)) | |
| assert c3.length == -sqrt(17) - asinh(4) / 4 + asinh(10) / 4 + 5 * sqrt(101) / 2 | |
| def test_parameter_value(): | |
| t = Symbol('t') | |
| C = Curve([2*t, t**2], (t, 0, 2)) | |
| assert C.parameter_value((2, 1), t) == {t: 1} | |
| raises(ValueError, lambda: C.parameter_value((2, 0), t)) | |
| def test_issue_17997(): | |
| t, s = symbols('t s') | |
| c = Curve((t, t**2), (t, 0, 10)) | |
| p = Curve([2*s, s**2], (s, 0, 2)) | |
| assert c(2) == Point(2, 4) | |
| assert p(1) == Point(2, 1) | |