text: /*************************************************************************/
  /*  transform.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).   */
  /*                                                                       */
  /* Permission is hereby granted, free of charge, to any person obtaining */
  /* a copy of this software and associated documentation files (the       */
  /* "Software"), to deal in the Software without restriction, including   */
  /* without limitation the rights to use, copy, modify, merge, publish,   */
  /* distribute, sublicense, and/or sell copies of the Software, and to    */
  /* permit persons to whom the Software is furnished to do so, subject to */
  /* the following conditions:                                             */
  /*                                                                       */
  /* The above copyright notice and this permission notice shall be        */
  /* included in all copies or substantial portions of the Software.       */
  /*                                                                       */
  /* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
  /* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
  /* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
  /* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
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  /* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
  /*************************************************************************/
  
  #include "transform.h"
  
  #include "core/math/math_funcs.h"
  #include "core/os/copymem.h"
  #include "core/print_string.h"
  
  void Transform::affine_invert() {
  
  	basis.invert();
  	origin = basis.xform(-origin);
  }
  
  Transform Transform::affine_inverse() const {
  
  	Transform ret = *this;
  	ret.affine_invert();
  	return ret;
  }
  
  void Transform::invert() {
  
  	basis.transpose();
  	origin = basis.xform(-origin);
  }
  
  Transform Transform::inverse() const {
  	// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
  	// Transform::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
  	Transform ret = *this;
  	ret.invert();
  	return ret;
  }
  
  void Transform::rotate(const Vector3 &p_axis, real_t p_phi) {
  
  	*this = rotated(p_axis, p_phi);
  }
  
  Transform Transform::rotated(const Vector3 &p_axis, real_t p_phi) const {
  
  	return Transform(Basis(p_axis, p_phi), Vector3()) * (*this);
  }
  
  void Transform::rotate_basis(const Vector3 &p_axis, real_t p_phi) {
  
  	basis.rotate(p_axis, p_phi);
  }
  
  Transform Transform::looking_at(const Vector3 &p_target, const Vector3 &p_up) const {
  
  	Transform t = *this;
  	t.set_look_at(origin, p_target, p_up);
  	return t;
  }
  
  void Transform::set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up) {
  #ifdef MATH_CHECKS
  	ERR_FAIL_COND(p_eye == p_target);
  	ERR_FAIL_COND(p_up.length() == 0);
  #endif
  	// Reference: MESA source code
  	Vector3 v_x, v_y, v_z;
  
  	/* Make rotation matrix */
  
  	/* Z vector */
  	v_z = p_eye - p_target;
  
  	v_z.normalize();
  
  	v_y = p_up;
  
  	v_x = v_y.cross(v_z);
  #ifdef MATH_CHECKS
  	ERR_FAIL_COND(v_x.length() == 0);
  #endif
  
  	/* Recompute Y = Z cross X */
  	v_y = v_z.cross(v_x);
  
  	v_x.normalize();
  	v_y.normalize();
  
  	basis.set(v_x, v_y, v_z);
  
  	origin = p_eye;
  }
  
  Transform Transform::interpolate_with(const Transform &p_transform, real_t p_c) const {
  
  	/* not sure if very "efficient" but good enough? */
  
  	Vector3 src_scale = basis.get_scale();
  	Quat src_rot = basis.get_rotation_quat();
  	Vector3 src_loc = origin;
  
  	Vector3 dst_scale = p_transform.basis.get_scale();
  	Quat dst_rot = p_transform.basis.get_rotation_quat();
  	Vector3 dst_loc = p_transform.origin;
  
  	Transform interp;
  	interp.basis.set_quat_scale(src_rot.slerp(dst_rot, p_c).normalized(), src_scale.lerp(dst_scale, p_c));
  	interp.origin = src_loc.lerp(dst_loc, p_c);
  
  	return interp;
  }
  
  void Transform::scale(const Vector3 &p_scale) {
  
  	basis.scale(p_scale);
  	origin *= p_scale;
  }
  
  Transform Transform::scaled(const Vector3 &p_scale) const {
  
  	Transform t = *this;
  	t.scale(p_scale);
  	return t;
  }
  
  void Transform::scale_basis(const Vector3 &p_scale) {
  
  	basis.scale(p_scale);
  }
  
  void Transform::translate(real_t p_tx, real_t p_ty, real_t p_tz) {
  	translate(Vector3(p_tx, p_ty, p_tz));
  }
  void Transform::translate(const Vector3 &p_translation) {
  
  	for (int i = 0; i < 3; i++) {
  		origin[i] += basis[i].dot(p_translation);
  	}
  }
  
  Transform Transform::translated(const Vector3 &p_translation) const {
  
  	Transform t = *this;
  	t.translate(p_translation);
  	return t;
  }
  
  void Transform::orthonormalize() {
  
  	basis.orthonormalize();
  }
  
  Transform Transform::orthonormalized() const {
  
  	Transform _copy = *this;
  	_copy.orthonormalize();
  	return _copy;
  }
  
  bool Transform::is_equal_approx(const Transform &p_transform) const {
  
  	return basis.is_equal_approx(p_transform.basis) && origin.is_equal_approx(p_transform.origin);
  }
  
  bool Transform::operator==(const Transform &p_transform) const {
  
  	return (basis == p_transform.basis && origin == p_transform.origin);
  }
  bool Transform::operator!=(const Transform &p_transform) const {
  
  	return (basis != p_transform.basis || origin != p_transform.origin);
  }
  
  void Transform::operator*=(const Transform &p_transform) {
  
  	origin = xform(p_transform.origin);
  	basis *= p_transform.basis;
  }
  
  Transform Transform::operator*(const Transform &p_transform) const {
  
  	Transform t = *this;
  	t *= p_transform;
  	return t;
  }
  
  Transform::operator String() const {
  
  	return basis.operator String() + " - " + origin.operator String();
  }
  
  Transform::Transform(const Basis &p_basis, const Vector3 &p_origin) :
  		basis(p_basis),
  		origin(p_origin) {
  }
  
  Transform::Transform(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t ox, real_t oy, real_t oz) {
  	basis = Basis(xx, xy, xz, yx, yy, yz, zx, zy, zz);
  	origin = Vector3(ox, oy, oz);
  }
  