Carla/source/modules/juce_graphics/geometry/juce_AffineTransform.cpp

/*
  ==============================================================================

   This file is part of the JUCE 7 technical preview.
   Copyright (c) 2022 - Raw Material Software Limited

   You may use this code under the terms of the GPL v3
   (see www.gnu.org/licenses).

   For the technical preview this file cannot be licensed commercially.

   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