text: /*
    ==============================================================================
  
     This file is part of the JUCE library.
     Copyright (c) 2022 - Raw Material Software Limited
  
     JUCE is an open source library subject to commercial or open-source
     licensing.
  
     By using JUCE, you agree to the terms of both the JUCE 7 End-User License
     Agreement and JUCE Privacy Policy.
  
     End User License Agreement: www.juce.com/juce-7-licence
     Privacy Policy: www.juce.com/juce-privacy-policy
  
     Or: You may also use this code under the terms of the GPL v3 (see
     www.gnu.org/licenses).
  
     JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
     EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
     DISCLAIMED.
  
    ==============================================================================
  */
  
  namespace juce
  {
  
  AffineTransform::AffineTransform (float m00, float m01, float m02,
                                    float m10, float m11, float m12) noexcept
   :  mat00 (m00), mat01 (m01), mat02 (m02),
      mat10 (m10), mat11 (m11), mat12 (m12)
  {
  }
  
  bool AffineTransform::operator== (const AffineTransform& other) const noexcept
  {
      return mat00 == other.mat00
          && mat01 == other.mat01
          && mat02 == other.mat02
          && mat10 == other.mat10
          && mat11 == other.mat11
          && mat12 == other.mat12;
  }
  
  bool AffineTransform::operator!= (const AffineTransform& other) const noexcept
  {
      return ! operator== (other);
  }
  
  //==============================================================================
  bool AffineTransform::isIdentity() const noexcept
  {
      return mat01 == 0.0f
          && mat02 == 0.0f
          && mat10 == 0.0f
          && mat12 == 0.0f
          && mat00 == 1.0f
          && mat11 == 1.0f;
  }
  
  const AffineTransform AffineTransform::identity (1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f);
  
  //==============================================================================
  AffineTransform AffineTransform::followedBy (const AffineTransform& other) const noexcept
  {
      return { other.mat00 * mat00 + other.mat01 * mat10,
               other.mat00 * mat01 + other.mat01 * mat11,
               other.mat00 * mat02 + other.mat01 * mat12 + other.mat02,
               other.mat10 * mat00 + other.mat11 * mat10,
               other.mat10 * mat01 + other.mat11 * mat11,
               other.mat10 * mat02 + other.mat11 * mat12 + other.mat12 };
  }
  
  AffineTransform AffineTransform::translated (float dx, float dy) const noexcept
  {
      return { mat00, mat01, mat02 + dx,
               mat10, mat11, mat12 + dy };
  }
  
  AffineTransform AffineTransform::translation (float dx, float dy) noexcept
  {
      return { 1.0f, 0.0f, dx,
               0.0f, 1.0f, dy };
  }
  
  AffineTransform AffineTransform::withAbsoluteTranslation (float tx, float ty) const noexcept
  {
      return { mat00, mat01, tx,
               mat10, mat11, ty };
  }
  
  AffineTransform AffineTransform::rotated (float rad) const noexcept
  {
      auto cosRad = std::cos (rad);
      auto sinRad = std::sin (rad);
  
      return { cosRad * mat00 - sinRad * mat10,
               cosRad * mat01 - sinRad * mat11,
               cosRad * mat02 - sinRad * mat12,
               sinRad * mat00 + cosRad * mat10,
               sinRad * mat01 + cosRad * mat11,
               sinRad * mat02 + cosRad * mat12 };
  }
  
  AffineTransform AffineTransform::rotation (float rad) noexcept
  {
      auto cosRad = std::cos (rad);
      auto sinRad = std::sin (rad);
  
      return { cosRad, -sinRad, 0,
               sinRad,  cosRad, 0 };
  }
  
  AffineTransform AffineTransform::rotation (float rad, float pivotX, float pivotY) noexcept
  {
      auto cosRad = std::cos (rad);
      auto sinRad = std::sin (rad);
  
      return { cosRad, -sinRad, -cosRad * pivotX +  sinRad * pivotY + pivotX,
               sinRad,  cosRad, -sinRad * pivotX + -cosRad * pivotY + pivotY };
  }
  
  AffineTransform AffineTransform::rotated (float angle, float pivotX, float pivotY) const noexcept
  {
      return followedBy (rotation (angle, pivotX, pivotY));
  }
  
  AffineTransform AffineTransform::scaled (float factorX, float factorY) const noexcept
  {
      return { factorX * mat00, factorX * mat01, factorX * mat02,
               factorY * mat10, factorY * mat11, factorY * mat12 };
  }
  
  AffineTransform AffineTransform::scaled (float factor) const noexcept
  {
      return { factor * mat00, factor * mat01, factor * mat02,
               factor * mat10, factor * mat11, factor * mat12 };
  }
  
  AffineTransform AffineTransform::scale (float factorX, float factorY) noexcept
  {
      return { factorX, 0, 0, 0, factorY, 0 };
  }
  
  AffineTransform AffineTransform::scale (float factor) noexcept
  {
      return { factor, 0, 0, 0, factor, 0 };
  }
  
  AffineTransform AffineTransform::scaled (float factorX, float factorY,
                                           float pivotX, float pivotY) const noexcept
  {
      return { factorX * mat00, factorX * mat01, factorX * mat02 + pivotX * (1.0f - factorX),
               factorY * mat10, factorY * mat11, factorY * mat12 + pivotY * (1.0f - factorY) };
  }
  
  AffineTransform AffineTransform::scale (float factorX, float factorY,
                                          float pivotX, float pivotY) noexcept
  {
      return { factorX, 0, pivotX * (1.0f - factorX),
               0, factorY, pivotY * (1.0f - factorY) };
  }
  
  AffineTransform AffineTransform::shear (float shearX, float shearY) noexcept
  {
      return { 1.0f,   shearX, 0,
               shearY, 1.0f,   0 };
  }
  
  AffineTransform AffineTransform::sheared (float shearX, float shearY) const noexcept
  {
      return { mat00 + shearX * mat10,
               mat01 + shearX * mat11,
               mat02 + shearX * mat12,
               mat10 + shearY * mat00,
               mat11 + shearY * mat01,
               mat12 + shearY * mat02 };
  }
  
  AffineTransform AffineTransform::verticalFlip (float height) noexcept
  {
      return { 1.0f,  0.0f, 0.0f,
               0.0f, -1.0f, height };
  }
  
  AffineTransform AffineTransform::inverted() const noexcept
  {
      double determinant = getDeterminant();
  
      if (! approximatelyEqual (determinant, 0.0))
      {
          determinant = 1.0 / determinant;
  
          auto dst00 = (float) ( mat11 * determinant);
          auto dst10 = (float) (-mat10 * determinant);
          auto dst01 = (float) (-mat01 * determinant);
          auto dst11 = (float) ( mat00 * determinant);
  
          return { dst00, dst01, -mat02 * dst00 - mat12 * dst01,
                   dst10, dst11, -mat02 * dst10 - mat12 * dst11 };
      }
  
      // singularity..
      return *this;
  }
  
  bool AffineTransform::isSingularity() const noexcept
  {
      return (mat00 * mat11 - mat10 * mat01) == 0.0f;
  }
  
  AffineTransform AffineTransform::fromTargetPoints (float x00, float y00,
                                                     float x10, float y10,
                                                     float x01, float y01) noexcept
  {
      return { x10 - x00, x01 - x00, x00,
               y10 - y00, y01 - y00, y00 };
  }
  
  AffineTransform AffineTransform::fromTargetPoints (float sx1, float sy1, float tx1, float ty1,
                                                     float sx2, float sy2, float tx2, float ty2,
                                                     float sx3, float sy3, float tx3, float ty3) noexcept
  {
      return fromTargetPoints (sx1, sy1, sx2, sy2, sx3, sy3)
              .inverted()
              .followedBy (fromTargetPoints (tx1, ty1, tx2, ty2, tx3, ty3));
  }
  
  bool AffineTransform::isOnlyTranslation() const noexcept
  {
      return mat01 == 0.0f
          && mat10 == 0.0f
          && mat00 == 1.0f
          && mat11 == 1.0f;
  }
  
  float AffineTransform::getDeterminant() const noexcept
  {
      return (mat00 * mat11) - (mat01 * mat10);
  }
  
  float AffineTransform::getScaleFactor() const noexcept
  {
      return (std::abs (mat00) + std::abs (mat11)) / 2.0f;
  }
  
  
  //==============================================================================
  //==============================================================================
  #if JUCE_UNIT_TESTS
  
  class AffineTransformTests  : public UnitTest
  {
  public:
      AffineTransformTests()
          : UnitTest ("AffineTransform", UnitTestCategories::maths)
      {}
  
      void runTest() override
      {
          beginTest ("Determinant");
          {
              constexpr float scale1 = 1.5f, scale2 = 1.3f;
  
              auto transform = AffineTransform::scale (scale1)
                                               .followedBy (AffineTransform::rotation (degreesToRadians (72.0f)))
                                               .followedBy (AffineTransform::translation (100.0f, 20.0f))
                                               .followedBy (AffineTransform::scale (scale2));
  
              expect (approximatelyEqual (std::sqrt (std::abs (transform.getDeterminant())), scale1 * scale2));
          }
      }
  };
  
  static AffineTransformTests timeTests;
  
  #endif
  
  } // namespace juce
  