text: //
  // Copyright (c) 2008-2017 the Urho3D project.
  //
  // 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 CLAIM, DAMAGES OR OTHER
  // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
  // THE SOFTWARE.
  //
  
  #include "../Precompiled.h"
  
  #include "../Math/Matrix3x4.h"
  #include "../Math/Matrix4.h"
  
  #include <cstdio>
  
  #include "../DebugNew.h"
  
  namespace Atomic
  {
  
  const Matrix4 Matrix4::ZERO(
      0.0f, 0.0f, 0.0f, 0.0f,
      0.0f, 0.0f, 0.0f, 0.0f,
      0.0f, 0.0f, 0.0f, 0.0f,
      0.0f, 0.0f, 0.0f, 0.0f);
  
  const Matrix4 Matrix4::IDENTITY;
  
  Matrix4 Matrix4::operator *(const Matrix3x4& rhs) const
  {
      return Matrix4(
          m00_ * rhs.m00_ + m01_ * rhs.m10_ + m02_ * rhs.m20_,
          m00_ * rhs.m01_ + m01_ * rhs.m11_ + m02_ * rhs.m21_,
          m00_ * rhs.m02_ + m01_ * rhs.m12_ + m02_ * rhs.m22_,
          m00_ * rhs.m03_ + m01_ * rhs.m13_ + m02_ * rhs.m23_ + m03_,
          m10_ * rhs.m00_ + m11_ * rhs.m10_ + m12_ * rhs.m20_,
          m10_ * rhs.m01_ + m11_ * rhs.m11_ + m12_ * rhs.m21_,
          m10_ * rhs.m02_ + m11_ * rhs.m12_ + m12_ * rhs.m22_,
          m10_ * rhs.m03_ + m11_ * rhs.m13_ + m12_ * rhs.m23_ + m13_,
          m20_ * rhs.m00_ + m21_ * rhs.m10_ + m22_ * rhs.m20_,
          m20_ * rhs.m01_ + m21_ * rhs.m11_ + m22_ * rhs.m21_,
          m20_ * rhs.m02_ + m21_ * rhs.m12_ + m22_ * rhs.m22_,
          m20_ * rhs.m03_ + m21_ * rhs.m13_ + m22_ * rhs.m23_ + m23_,
          m30_ * rhs.m00_ + m31_ * rhs.m10_ + m32_ * rhs.m20_,
          m30_ * rhs.m01_ + m31_ * rhs.m11_ + m32_ * rhs.m21_,
          m30_ * rhs.m02_ + m31_ * rhs.m12_ + m32_ * rhs.m22_,
          m30_ * rhs.m03_ + m31_ * rhs.m13_ + m32_ * rhs.m23_ + m33_
      );
  }
  
  void Matrix4::Decompose(Vector3& translation, Quaternion& rotation, Vector3& scale) const
  {
      translation.x_ = m03_;
      translation.y_ = m13_;
      translation.z_ = m23_;
  
      scale.x_ = sqrtf(m00_ * m00_ + m10_ * m10_ + m20_ * m20_);
      scale.y_ = sqrtf(m01_ * m01_ + m11_ * m11_ + m21_ * m21_);
      scale.z_ = sqrtf(m02_ * m02_ + m12_ * m12_ + m22_ * m22_);
  
      Vector3 invScale(1.0f / scale.x_, 1.0f / scale.y_, 1.0f / scale.z_);
      rotation = Quaternion(ToMatrix3().Scaled(invScale));
  }
  
  Matrix4 Matrix4::Inverse() const
  {
      float v0 = m20_ * m31_ - m21_ * m30_;
      float v1 = m20_ * m32_ - m22_ * m30_;
      float v2 = m20_ * m33_ - m23_ * m30_;
      float v3 = m21_ * m32_ - m22_ * m31_;
      float v4 = m21_ * m33_ - m23_ * m31_;
      float v5 = m22_ * m33_ - m23_ * m32_;
  
      float i00 = (v5 * m11_ - v4 * m12_ + v3 * m13_);
      float i10 = -(v5 * m10_ - v2 * m12_ + v1 * m13_);
      float i20 = (v4 * m10_ - v2 * m11_ + v0 * m13_);
      float i30 = -(v3 * m10_ - v1 * m11_ + v0 * m12_);
  
      float invDet = 1.0f / (i00 * m00_ + i10 * m01_ + i20 * m02_ + i30 * m03_);
  
      i00 *= invDet;
      i10 *= invDet;
      i20 *= invDet;
      i30 *= invDet;
  
      float i01 = -(v5 * m01_ - v4 * m02_ + v3 * m03_) * invDet;
      float i11 = (v5 * m00_ - v2 * m02_ + v1 * m03_) * invDet;
      float i21 = -(v4 * m00_ - v2 * m01_ + v0 * m03_) * invDet;
      float i31 = (v3 * m00_ - v1 * m01_ + v0 * m02_) * invDet;
  
      v0 = m10_ * m31_ - m11_ * m30_;
      v1 = m10_ * m32_ - m12_ * m30_;
      v2 = m10_ * m33_ - m13_ * m30_;
      v3 = m11_ * m32_ - m12_ * m31_;
      v4 = m11_ * m33_ - m13_ * m31_;
      v5 = m12_ * m33_ - m13_ * m32_;
  
      float i02 = (v5 * m01_ - v4 * m02_ + v3 * m03_) * invDet;
      float i12 = -(v5 * m00_ - v2 * m02_ + v1 * m03_) * invDet;
      float i22 = (v4 * m00_ - v2 * m01_ + v0 * m03_) * invDet;
      float i32 = -(v3 * m00_ - v1 * m01_ + v0 * m02_) * invDet;
  
      v0 = m21_ * m10_ - m20_ * m11_;
      v1 = m22_ * m10_ - m20_ * m12_;
      v2 = m23_ * m10_ - m20_ * m13_;
      v3 = m22_ * m11_ - m21_ * m12_;
      v4 = m23_ * m11_ - m21_ * m13_;
      v5 = m23_ * m12_ - m22_ * m13_;
  
      float i03 = -(v5 * m01_ - v4 * m02_ + v3 * m03_) * invDet;
      float i13 = (v5 * m00_ - v2 * m02_ + v1 * m03_) * invDet;
      float i23 = -(v4 * m00_ - v2 * m01_ + v0 * m03_) * invDet;
      float i33 = (v3 * m00_ - v1 * m01_ + v0 * m02_) * invDet;
  
      return Matrix4(
          i00, i01, i02, i03,
          i10, i11, i12, i13,
          i20, i21, i22, i23,
          i30, i31, i32, i33);
  }
  
  String Matrix4::ToString() const
  {
      char tempBuffer[MATRIX_CONVERSION_BUFFER_LENGTH];
      sprintf(tempBuffer, "%g %g %g %g %g %g %g %g %g %g %g %g %g %g %g %g", m00_, m01_, m02_, m03_, m10_, m11_, m12_, m13_, m20_,
          m21_, m22_, m23_, m30_, m31_, m32_, m33_);
      return String(tempBuffer);
  }
  
  }
  