text: /*************************************************************************/
  /*  camera_matrix.cpp                                                    */
  /*************************************************************************/
  /*                       This file is part of:                           */
  /*                           GODOT ENGINE                                */
  /*                      https://godotengine.org                          */
  /*************************************************************************/
  /* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur.                 */
  /* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md).   */
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  /*************************************************************************/
  
  #include "camera_matrix.h"
  
  #include "core/math/math_funcs.h"
  #include "core/print_string.h"
  
  void CameraMatrix::set_identity() {
  
  	for (int i = 0; i < 4; i++) {
  
  		for (int j = 0; j < 4; j++) {
  
  			matrix[i][j] = (i == j) ? 1 : 0;
  		}
  	}
  }
  
  void CameraMatrix::set_zero() {
  
  	for (int i = 0; i < 4; i++) {
  
  		for (int j = 0; j < 4; j++) {
  
  			matrix[i][j] = 0;
  		}
  	}
  }
  
  Plane CameraMatrix::xform4(const Plane &p_vec4) const {
  
  	Plane ret;
  
  	ret.normal.x = matrix[0][0] * p_vec4.normal.x + matrix[1][0] * p_vec4.normal.y + matrix[2][0] * p_vec4.normal.z + matrix[3][0] * p_vec4.distance;
  	ret.normal.y = matrix[0][1] * p_vec4.normal.x + matrix[1][1] * p_vec4.normal.y + matrix[2][1] * p_vec4.normal.z + matrix[3][1] * p_vec4.distance;
  	ret.normal.z = matrix[0][2] * p_vec4.normal.x + matrix[1][2] * p_vec4.normal.y + matrix[2][2] * p_vec4.normal.z + matrix[3][2] * p_vec4.distance;
  	ret.distance = matrix[0][3] * p_vec4.normal.x + matrix[1][3] * p_vec4.normal.y + matrix[2][3] * p_vec4.normal.z + matrix[3][3] * p_vec4.distance;
  	return ret;
  }
  
  void CameraMatrix::set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov) {
  
  	if (p_flip_fov) {
  		p_fovy_degrees = get_fovy(p_fovy_degrees, 1.0 / p_aspect);
  	}
  
  	real_t sine, cotangent, deltaZ;
  	real_t radians = p_fovy_degrees / 2.0 * Math_PI / 180.0;
  
  	deltaZ = p_z_far - p_z_near;
  	sine = Math::sin(radians);
  
  	if ((deltaZ == 0) || (sine == 0) || (p_aspect == 0)) {
  		return;
  	}
  	cotangent = Math::cos(radians) / sine;
  
  	set_identity();
  
  	matrix[0][0] = cotangent / p_aspect;
  	matrix[1][1] = cotangent;
  	matrix[2][2] = -(p_z_far + p_z_near) / deltaZ;
  	matrix[2][3] = -1;
  	matrix[3][2] = -2 * p_z_near * p_z_far / deltaZ;
  	matrix[3][3] = 0;
  }
  
  void CameraMatrix::set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov, int p_eye, real_t p_intraocular_dist, real_t p_convergence_dist) {
  	if (p_flip_fov) {
  		p_fovy_degrees = get_fovy(p_fovy_degrees, 1.0 / p_aspect);
  	}
  
  	real_t left, right, modeltranslation, ymax, xmax, frustumshift;
  
  	ymax = p_z_near * tan(p_fovy_degrees * Math_PI / 360.0f);
  	xmax = ymax * p_aspect;
  	frustumshift = (p_intraocular_dist / 2.0) * p_z_near / p_convergence_dist;
  
  	switch (p_eye) {
  		case 1: { // left eye
  			left = -xmax + frustumshift;
  			right = xmax + frustumshift;
  			modeltranslation = p_intraocular_dist / 2.0;
  		}; break;
  		case 2: { // right eye
  			left = -xmax - frustumshift;
  			right = xmax - frustumshift;
  			modeltranslation = -p_intraocular_dist / 2.0;
  		}; break;
  		default: { // mono, should give the same result as set_perspective(p_fovy_degrees,p_aspect,p_z_near,p_z_far,p_flip_fov)
  			left = -xmax;
  			right = xmax;
  			modeltranslation = 0.0;
  		}; break;
  	};
  
  	set_frustum(left, right, -ymax, ymax, p_z_near, p_z_far);
  
  	// translate matrix by (modeltranslation, 0.0, 0.0)
  	CameraMatrix cm;
  	cm.set_identity();
  	cm.matrix[3][0] = modeltranslation;
  	*this = *this * cm;
  }
  
  void CameraMatrix::set_for_hmd(int p_eye, real_t p_aspect, real_t p_intraocular_dist, real_t p_display_width, real_t p_display_to_lens, real_t p_oversample, real_t p_z_near, real_t p_z_far) {
  	// we first calculate our base frustum on our values without taking our lens magnification into account.
  	real_t f1 = (p_intraocular_dist * 0.5) / p_display_to_lens;
  	real_t f2 = ((p_display_width - p_intraocular_dist) * 0.5) / p_display_to_lens;
  	real_t f3 = (p_display_width / 4.0) / p_display_to_lens;
  
  	// now we apply our oversample factor to increase our FOV. how much we oversample is always a balance we strike between performance and how much
  	// we're willing to sacrifice in FOV.
  	real_t add = ((f1 + f2) * (p_oversample - 1.0)) / 2.0;
  	f1 += add;
  	f2 += add;
  	f3 *= p_oversample;
  
  	// always apply KEEP_WIDTH aspect ratio
  	f3 /= p_aspect;
  
  	switch (p_eye) {
  		case 1: { // left eye
  			set_frustum(-f2 * p_z_near, f1 * p_z_near, -f3 * p_z_near, f3 * p_z_near, p_z_near, p_z_far);
  		}; break;
  		case 2: { // right eye
  			set_frustum(-f1 * p_z_near, f2 * p_z_near, -f3 * p_z_near, f3 * p_z_near, p_z_near, p_z_far);
  		}; break;
  		default: { // mono, does not apply here!
  		}; break;
  	};
  };
  
  void CameraMatrix::set_orthogonal(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_znear, real_t p_zfar) {
  
  	set_identity();
  
  	matrix[0][0] = 2.0 / (p_right - p_left);
  	matrix[3][0] = -((p_right + p_left) / (p_right - p_left));
  	matrix[1][1] = 2.0 / (p_top - p_bottom);
  	matrix[3][1] = -((p_top + p_bottom) / (p_top - p_bottom));
  	matrix[2][2] = -2.0 / (p_zfar - p_znear);
  	matrix[3][2] = -((p_zfar + p_znear) / (p_zfar - p_znear));
  	matrix[3][3] = 1.0;
  }
  
  void CameraMatrix::set_orthogonal(real_t p_size, real_t p_aspect, real_t p_znear, real_t p_zfar, bool p_flip_fov) {
  
  	if (!p_flip_fov) {
  		p_size *= p_aspect;
  	}
  
  	set_orthogonal(-p_size / 2, +p_size / 2, -p_size / p_aspect / 2, +p_size / p_aspect / 2, p_znear, p_zfar);
  }
  
  void CameraMatrix::set_frustum(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_near, real_t p_far) {
  
  	ERR_FAIL_COND(p_right <= p_left);
  	ERR_FAIL_COND(p_top <= p_bottom);
  	ERR_FAIL_COND(p_far <= p_near);
  
  	real_t *te = &matrix[0][0];
  	real_t x = 2 * p_near / (p_right - p_left);
  	real_t y = 2 * p_near / (p_top - p_bottom);
  
  	real_t a = (p_right + p_left) / (p_right - p_left);
  	real_t b = (p_top + p_bottom) / (p_top - p_bottom);
  	real_t c = -(p_far + p_near) / (p_far - p_near);
  	real_t d = -2 * p_far * p_near / (p_far - p_near);
  
  	te[0] = x;
  	te[1] = 0;
  	te[2] = 0;
  	te[3] = 0;
  	te[4] = 0;
  	te[5] = y;
  	te[6] = 0;
  	te[7] = 0;
  	te[8] = a;
  	te[9] = b;
  	te[10] = c;
  	te[11] = -1;
  	te[12] = 0;
  	te[13] = 0;
  	te[14] = d;
  	te[15] = 0;
  }
  
  void CameraMatrix::set_frustum(real_t p_size, real_t p_aspect, Vector2 p_offset, real_t p_near, real_t p_far, bool p_flip_fov) {
  	if (!p_flip_fov) {
  		p_size *= p_aspect;
  	}
  
  	set_frustum(-p_size / 2 + p_offset.x, +p_size / 2 + p_offset.x, -p_size / p_aspect / 2 + p_offset.y, +p_size / p_aspect / 2 + p_offset.y, p_near, p_far);
  }
  
  real_t CameraMatrix::get_z_far() const {
  
  	const real_t *matrix = (const real_t *)this->matrix;
  	Plane new_plane = Plane(matrix[3] - matrix[2],
  			matrix[7] - matrix[6],
  			matrix[11] - matrix[10],
  			matrix[15] - matrix[14]);
  
  	new_plane.normal = -new_plane.normal;
  	new_plane.normalize();
  
  	return new_plane.distance;
  }
  real_t CameraMatrix::get_z_near() const {
  
  	const real_t *matrix = (const real_t *)this->matrix;
  	Plane new_plane = Plane(matrix[3] + matrix[2],
  			matrix[7] + matrix[6],
  			matrix[11] + matrix[10],
  			-matrix[15] - matrix[14]);
  
  	new_plane.normalize();
  	return new_plane.distance;
  }
  
  Vector2 CameraMatrix::get_viewport_half_extents() const {
  
  	const real_t *matrix = (const real_t *)this->matrix;
  	///////--- Near Plane ---///////
  	Plane near_plane = Plane(matrix[3] + matrix[2],
  			matrix[7] + matrix[6],
  			matrix[11] + matrix[10],
  			-matrix[15] - matrix[14]);
  	near_plane.normalize();
  
  	///////--- Right Plane ---///////
  	Plane right_plane = Plane(matrix[3] - matrix[0],
  			matrix[7] - matrix[4],
  			matrix[11] - matrix[8],
  			-matrix[15] + matrix[12]);
  	right_plane.normalize();
  
  	Plane top_plane = Plane(matrix[3] - matrix[1],
  			matrix[7] - matrix[5],
  			matrix[11] - matrix[9],
  			-matrix[15] + matrix[13]);
  	top_plane.normalize();
  
  	Vector3 res;
  	near_plane.intersect_3(right_plane, top_plane, &res);
  
  	return Vector2(res.x, res.y);
  }
  
  void CameraMatrix::get_far_plane_size(real_t &r_width, real_t &r_height) const {
  
  	const real_t *matrix = (const real_t *)this->matrix;
  	///////--- Far Plane ---///////
  	Plane far_plane = Plane(matrix[3] - matrix[2],
  			matrix[7] - matrix[6],
  			matrix[11] - matrix[10],
  			-matrix[15] + matrix[14]);
  	far_plane.normalize();
  
  	///////--- Right Plane ---///////
  	Plane right_plane = Plane(matrix[3] - matrix[0],
  			matrix[7] - matrix[4],
  			matrix[11] - matrix[8],
  			-matrix[15] + matrix[12]);
  	right_plane.normalize();
  
  	Plane top_plane = Plane(matrix[3] - matrix[1],
  			matrix[7] - matrix[5],
  			matrix[11] - matrix[9],
  			-matrix[15] + matrix[13]);
  	top_plane.normalize();
  
  	Vector3 res;
  	far_plane.intersect_3(right_plane, top_plane, &res);
  
  	r_width = res.x;
  	r_height = res.y;
  }
  
  bool CameraMatrix::get_endpoints(const Transform &p_transform, Vector3 *p_8points) const {
  
  	Vector<Plane> planes = get_projection_planes(Transform());
  	const Planes intersections[8][3] = {
  		{ PLANE_FAR, PLANE_LEFT, PLANE_TOP },
  		{ PLANE_FAR, PLANE_LEFT, PLANE_BOTTOM },
  		{ PLANE_FAR, PLANE_RIGHT, PLANE_TOP },
  		{ PLANE_FAR, PLANE_RIGHT, PLANE_BOTTOM },
  		{ PLANE_NEAR, PLANE_LEFT, PLANE_TOP },
  		{ PLANE_NEAR, PLANE_LEFT, PLANE_BOTTOM },
  		{ PLANE_NEAR, PLANE_RIGHT, PLANE_TOP },
  		{ PLANE_NEAR, PLANE_RIGHT, PLANE_BOTTOM },
  	};
  
  	for (int i = 0; i < 8; i++) {
  
  		Vector3 point;
  		bool res = planes[intersections[i][0]].intersect_3(planes[intersections[i][1]], planes[intersections[i][2]], &point);
  		ERR_FAIL_COND_V(!res, false);
  		p_8points[i] = p_transform.xform(point);
  	}
  
  	return true;
  }
  
  Vector<Plane> CameraMatrix::get_projection_planes(const Transform &p_transform) const {
  
  	/** Fast Plane Extraction from combined modelview/projection matrices.
  	 * References:
  	 * https://web.archive.org/web/20011221205252/http://www.markmorley.com/opengl/frustumculling.html
  	 * https://web.archive.org/web/20061020020112/http://www2.ravensoft.com/users/ggribb/plane%20extraction.pdf
  	 */
  
  	Vector<Plane> planes;
  
  	const real_t *matrix = (const real_t *)this->matrix;
  
  	Plane new_plane;
  
  	///////--- Near Plane ---///////
  	new_plane = Plane(matrix[3] + matrix[2],
  			matrix[7] + matrix[6],
  			matrix[11] + matrix[10],
  			matrix[15] + matrix[14]);
  
  	new_plane.normal = -new_plane.normal;
  	new_plane.normalize();
  
  	planes.push_back(p_transform.xform(new_plane));
  
  	///////--- Far Plane ---///////
  	new_plane = Plane(matrix[3] - matrix[2],
  			matrix[7] - matrix[6],
  			matrix[11] - matrix[10],
  			matrix[15] - matrix[14]);
  
  	new_plane.normal = -new_plane.normal;
  	new_plane.normalize();
  
  	planes.push_back(p_transform.xform(new_plane));
  
  	///////--- Left Plane ---///////
  	new_plane = Plane(matrix[3] + matrix[0],
  			matrix[7] + matrix[4],
  			matrix[11] + matrix[8],
  			matrix[15] + matrix[12]);
  
  	new_plane.normal = -new_plane.normal;
  	new_plane.normalize();
  
  	planes.push_back(p_transform.xform(new_plane));
  
  	///////--- Top Plane ---///////
  	new_plane = Plane(matrix[3] - matrix[1],
  			matrix[7] - matrix[5],
  			matrix[11] - matrix[9],
  			matrix[15] - matrix[13]);
  
  	new_plane.normal = -new_plane.normal;
  	new_plane.normalize();
  
  	planes.push_back(p_transform.xform(new_plane));
  
  	///////--- Right Plane ---///////
  	new_plane = Plane(matrix[3] - matrix[0],
  			matrix[7] - matrix[4],
  			matrix[11] - matrix[8],
  			matrix[15] - matrix[12]);
  
  	new_plane.normal = -new_plane.normal;
  	new_plane.normalize();
  
  	planes.push_back(p_transform.xform(new_plane));
  
  	///////--- Bottom Plane ---///////
  	new_plane = Plane(matrix[3] + matrix[1],
  			matrix[7] + matrix[5],
  			matrix[11] + matrix[9],
  			matrix[15] + matrix[13]);
  
  	new_plane.normal = -new_plane.normal;
  	new_plane.normalize();
  
  	planes.push_back(p_transform.xform(new_plane));
  
  	return planes;
  }
  
  CameraMatrix CameraMatrix::inverse() const {
  
  	CameraMatrix cm = *this;
  	cm.invert();
  	return cm;
  }
  
  void CameraMatrix::invert() {
  
  	int i, j, k;
  	int pvt_i[4], pvt_j[4]; /* Locations of pivot matrix */
  	real_t pvt_val; /* Value of current pivot element */
  	real_t hold; /* Temporary storage */
  	real_t determinat; /* Determinant */
  
  	determinat = 1.0;
  	for (k = 0; k < 4; k++) {
  		/** Locate k'th pivot element **/
  		pvt_val = matrix[k][k]; /** Initialize for search **/
  		pvt_i[k] = k;
  		pvt_j[k] = k;
  		for (i = k; i < 4; i++) {
  			for (j = k; j < 4; j++) {
  				if (Math::absd(matrix[i][j]) > Math::absd(pvt_val)) {
  					pvt_i[k] = i;
  					pvt_j[k] = j;
  					pvt_val = matrix[i][j];
  				}
  			}
  		}
  
  		/** Product of pivots, gives determinant when finished **/
  		determinat *= pvt_val;
  		if (Math::absd(determinat) < 1e-7) {
  			return; //(false);  /** Matrix is singular (zero determinant). **/
  		}
  
  		/** "Interchange" rows (with sign change stuff) **/
  		i = pvt_i[k];
  		if (i != k) { /** If rows are different **/
  			for (j = 0; j < 4; j++) {
  				hold = -matrix[k][j];
  				matrix[k][j] = matrix[i][j];
  				matrix[i][j] = hold;
  			}
  		}
  
  		/** "Interchange" columns **/
  		j = pvt_j[k];
  		if (j != k) { /** If columns are different **/
  			for (i = 0; i < 4; i++) {
  				hold = -matrix[i][k];
  				matrix[i][k] = matrix[i][j];
  				matrix[i][j] = hold;
  			}
  		}
  
  		/** Divide column by minus pivot value **/
  		for (i = 0; i < 4; i++) {
  			if (i != k) matrix[i][k] /= (-pvt_val);
  		}
  
  		/** Reduce the matrix **/
  		for (i = 0; i < 4; i++) {
  			hold = matrix[i][k];
  			for (j = 0; j < 4; j++) {
  				if (i != k && j != k) matrix[i][j] += hold * matrix[k][j];
  			}
  		}
  
  		/** Divide row by pivot **/
  		for (j = 0; j < 4; j++) {
  			if (j != k) matrix[k][j] /= pvt_val;
  		}
  
  		/** Replace pivot by reciprocal (at last we can touch it). **/
  		matrix[k][k] = 1.0 / pvt_val;
  	}
  
  	/* That was most of the work, one final pass of row/column interchange */
  	/* to finish */
  	for (k = 4 - 2; k >= 0; k--) { /* Don't need to work with 1 by 1 corner*/
  		i = pvt_j[k]; /* Rows to swap correspond to pivot COLUMN */
  		if (i != k) { /* If rows are different */
  			for (j = 0; j < 4; j++) {
  				hold = matrix[k][j];
  				matrix[k][j] = -matrix[i][j];
  				matrix[i][j] = hold;
  			}
  		}
  
  		j = pvt_i[k]; /* Columns to swap correspond to pivot ROW */
  		if (j != k) /* If columns are different */
  			for (i = 0; i < 4; i++) {
  				hold = matrix[i][k];
  				matrix[i][k] = -matrix[i][j];
  				matrix[i][j] = hold;
  			}
  	}
  }
  
  void CameraMatrix::flip_y() {
  	for (int i = 0; i < 4; i++) {
  		matrix[1][i] = -matrix[1][i];
  	}
  }
  
  CameraMatrix::CameraMatrix() {
  
  	set_identity();
  }
  
  CameraMatrix CameraMatrix::operator*(const CameraMatrix &p_matrix) const {
  
  	CameraMatrix new_matrix;
  
  	for (int j = 0; j < 4; j++) {
  		for (int i = 0; i < 4; i++) {
  			real_t ab = 0;
  			for (int k = 0; k < 4; k++)
  				ab += matrix[k][i] * p_matrix.matrix[j][k];
  			new_matrix.matrix[j][i] = ab;
  		}
  	}
  
  	return new_matrix;
  }
  
  void CameraMatrix::set_depth_correction(bool p_flip_y) {
  
  	real_t *m = &matrix[0][0];
  
  	m[0] = 1;
  	m[1] = 0.0;
  	m[2] = 0.0;
  	m[3] = 0.0;
  	m[4] = 0.0;
  	m[5] = p_flip_y ? -1 : 1;
  	m[6] = 0.0;
  	m[7] = 0.0;
  	m[8] = 0.0;
  	m[9] = 0.0;
  	m[10] = 0.5;
  	m[11] = 0.0;
  	m[12] = 0.0;
  	m[13] = 0.0;
  	m[14] = 0.5;
  	m[15] = 1.0;
  }
  
  void CameraMatrix::set_light_bias() {
  
  	real_t *m = &matrix[0][0];
  
  	m[0] = 0.5;
  	m[1] = 0.0;
  	m[2] = 0.0;
  	m[3] = 0.0;
  	m[4] = 0.0;
  	m[5] = 0.5;
  	m[6] = 0.0;
  	m[7] = 0.0;
  	m[8] = 0.0;
  	m[9] = 0.0;
  	m[10] = 0.5;
  	m[11] = 0.0;
  	m[12] = 0.5;
  	m[13] = 0.5;
  	m[14] = 0.5;
  	m[15] = 1.0;
  }
  
  void CameraMatrix::set_light_atlas_rect(const Rect2 &p_rect) {
  
  	real_t *m = &matrix[0][0];
  
  	m[0] = p_rect.size.width;
  	m[1] = 0.0;
  	m[2] = 0.0;
  	m[3] = 0.0;
  	m[4] = 0.0;
  	m[5] = p_rect.size.height;
  	m[6] = 0.0;
  	m[7] = 0.0;
  	m[8] = 0.0;
  	m[9] = 0.0;
  	m[10] = 1.0;
  	m[11] = 0.0;
  	m[12] = p_rect.position.x;
  	m[13] = p_rect.position.y;
  	m[14] = 0.0;
  	m[15] = 1.0;
  }
  
  CameraMatrix::operator String() const {
  
  	String str;
  	for (int i = 0; i < 4; i++)
  		for (int j = 0; j < 4; j++)
  			str += String((j > 0) ? ", " : "\n") + rtos(matrix[i][j]);
  
  	return str;
  }
  
  real_t CameraMatrix::get_aspect() const {
  
  	Vector2 vp_he = get_viewport_half_extents();
  	return vp_he.x / vp_he.y;
  }
  
  int CameraMatrix::get_pixels_per_meter(int p_for_pixel_width) const {
  
  	Vector3 result = xform(Vector3(1, 0, -1));
  
  	return int((result.x * 0.5 + 0.5) * p_for_pixel_width);
  }
  
  bool CameraMatrix::is_orthogonal() const {
  
  	return matrix[3][3] == 1.0;
  }
  
  real_t CameraMatrix::get_fov() const {
  	const real_t *matrix = (const real_t *)this->matrix;
  
  	Plane right_plane = Plane(matrix[3] - matrix[0],
  			matrix[7] - matrix[4],
  			matrix[11] - matrix[8],
  			-matrix[15] + matrix[12]);
  	right_plane.normalize();
  
  	if ((matrix[8] == 0) && (matrix[9] == 0)) {
  		return Math::rad2deg(Math::acos(Math::abs(right_plane.normal.x))) * 2.0;
  	} else {
  		// our frustum is asymmetrical need to calculate the left planes angle separately..
  		Plane left_plane = Plane(matrix[3] + matrix[0],
  				matrix[7] + matrix[4],
  				matrix[11] + matrix[8],
  				matrix[15] + matrix[12]);
  		left_plane.normalize();
  
  		return Math::rad2deg(Math::acos(Math::abs(left_plane.normal.x))) + Math::rad2deg(Math::acos(Math::abs(right_plane.normal.x)));
  	}
  }
  
  void CameraMatrix::make_scale(const Vector3 &p_scale) {
  
  	set_identity();
  	matrix[0][0] = p_scale.x;
  	matrix[1][1] = p_scale.y;
  	matrix[2][2] = p_scale.z;
  }
  
  void CameraMatrix::scale_translate_to_fit(const AABB &p_aabb) {
  
  	Vector3 min = p_aabb.position;
  	Vector3 max = p_aabb.position + p_aabb.size;
  
  	matrix[0][0] = 2 / (max.x - min.x);
  	matrix[1][0] = 0;
  	matrix[2][0] = 0;
  	matrix[3][0] = -(max.x + min.x) / (max.x - min.x);
  
  	matrix[0][1] = 0;
  	matrix[1][1] = 2 / (max.y - min.y);
  	matrix[2][1] = 0;
  	matrix[3][1] = -(max.y + min.y) / (max.y - min.y);
  
  	matrix[0][2] = 0;
  	matrix[1][2] = 0;
  	matrix[2][2] = 2 / (max.z - min.z);
  	matrix[3][2] = -(max.z + min.z) / (max.z - min.z);
  
  	matrix[0][3] = 0;
  	matrix[1][3] = 0;
  	matrix[2][3] = 0;
  	matrix[3][3] = 1;
  }
  
  CameraMatrix::operator Transform() const {
  
  	Transform tr;
  	const real_t *m = &matrix[0][0];
  
  	tr.basis.elements[0][0] = m[0];
  	tr.basis.elements[1][0] = m[1];
  	tr.basis.elements[2][0] = m[2];
  
  	tr.basis.elements[0][1] = m[4];
  	tr.basis.elements[1][1] = m[5];
  	tr.basis.elements[2][1] = m[6];
  
  	tr.basis.elements[0][2] = m[8];
  	tr.basis.elements[1][2] = m[9];
  	tr.basis.elements[2][2] = m[10];
  
  	tr.origin.x = m[12];
  	tr.origin.y = m[13];
  	tr.origin.z = m[14];
  
  	return tr;
  }
  
  CameraMatrix::CameraMatrix(const Transform &p_transform) {
  
  	const Transform &tr = p_transform;
  	real_t *m = &matrix[0][0];
  
  	m[0] = tr.basis.elements[0][0];
  	m[1] = tr.basis.elements[1][0];
  	m[2] = tr.basis.elements[2][0];
  	m[3] = 0.0;
  	m[4] = tr.basis.elements[0][1];
  	m[5] = tr.basis.elements[1][1];
  	m[6] = tr.basis.elements[2][1];
  	m[7] = 0.0;
  	m[8] = tr.basis.elements[0][2];
  	m[9] = tr.basis.elements[1][2];
  	m[10] = tr.basis.elements[2][2];
  	m[11] = 0.0;
  	m[12] = tr.origin.x;
  	m[13] = tr.origin.y;
  	m[14] = tr.origin.z;
  	m[15] = 1.0;
  }
  
  CameraMatrix::~CameraMatrix() {
  }
  