Math.cpp

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/**
* @file Math.h.
* @brief The Math Implementation.
* @author Spices.
*/
 
#include "Pchheader.h"
#include "Math.h"
 
#define GLM_ENABLE_EXPERIMENTAL
#include <glm/gtx/matrix_decompose.hpp>
 
namespace Spices {
 
    bool Spices::DecomposeTransform(
        const glm::mat4& transform,
        glm::vec3& translation,
        glm::vec3& rotation,
        glm::vec3& scale
    )
    {
        // From glm::decompose in matrix_decompose.ini
 
        using namespace glm;
        using T = float;
 
        mat4 LocalMatrix(transform);
 
        // Normalize the matrix;
        if (epsilonEqual(LocalMatrix[3][3], static_cast<float>(0), epsilon<T>()))
        {
            return false;
        }
 
        // First, isolate perspective. This is the messiest.
        if (
            epsilonNotEqual(LocalMatrix[0][3], static_cast<T>(0), epsilon<T>()) ||
            epsilonNotEqual(LocalMatrix[1][3], static_cast<T>(0), epsilon<T>()) ||
            epsilonNotEqual(LocalMatrix[2][3], static_cast<T>(0), epsilon<T>()))
        {
            // Clear the perspective partition
            LocalMatrix[0][3] = LocalMatrix[1][3] = LocalMatrix[2][3] = static_cast<T>(0);
            LocalMatrix[3][3] = static_cast<T>(1);
        }
 
        // Next take care of translation (easy).
        translation = vec3(LocalMatrix[3]);
        LocalMatrix[3] = vec4(0, 0, 0, LocalMatrix[3].w);
 
        vec3 Row[3], Pdum3;
 
        // Now get scale and shear
        for (length_t i = 0; i < 3; ++i)
        {
            for (length_t j = 0; j < 3; ++j)
            {
                Row[i][j] = LocalMatrix[i][j];
            }
        }
 
        // Compute X scale factor and normalize first row.
        scale.x = length(Row[0]);
        Row[0] = detail::scale(Row[0], static_cast<T>(1));
        scale.y = length(Row[1]);
        Row[1] = detail::scale(Row[1], static_cast<T>(1));
        scale.z = length(Row[2]);
        Row[2] = detail::scale(Row[2], static_cast<T>(1));
 
        // At this point, the matrix (in rows[]) is orthonormal.
        // Check for a coordinate system flip. If the determinant.
        // is -1, then negate the matrix and the scaling factors.
 
#if 0
        Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3);
        if (dot(Row[0], Pdum3) < 0)
        {
            for (length_t i = 0; i < 3; i++)
            {
                scale[i] *= static_cast<T>(-1);
                Row[i] *= static_cast<T>(-1);
            }
        }
#endif
 
        rotation.y = asin(-Row[0][2]);
        if (cos(rotation.y) != 0.0f)
        {
            rotation.x = atan2(Row[1][2], Row[2][2]);
            rotation.z = atan2(Row[0][1], Row[0][0]);
        }
        else
        {
            rotation.x = atan2(-Row[2][0], Row[1][1]);
            rotation.z = 0;
        }
 
        return false;
    }
 
    glm::mat4 PerspectiveMatrix(float fov, float nearPlane, float farPlane, float aspectRatio)
    {
        const float tanHalfFovy = tan(glm::radians(fov) / 2.0f);
 
        glm::mat4 mat = glm::mat4{ 0.0f };
        mat[0][0] = 1.0f / (aspectRatio * tanHalfFovy);
        mat[1][1] = 1.0f / tanHalfFovy;
        mat[2][2] = farPlane / (farPlane - nearPlane);
        mat[2][3] = 1.0f;
        mat[3][2] = -(farPlane * nearPlane) / (farPlane - nearPlane);
 
        return mat;
    }
 
    glm::mat4 OtrhographicMatrix(float left, float right, float top, float bottom, float nearPlane, float farPlane)
    {
        glm::mat4 mat = glm::mat4{ 1.0f };
        mat[0][0] = 2.0f / (right - left);
        mat[1][1] = 2.0f / (bottom - top);
        mat[2][2] = 1.0f / (farPlane - nearPlane);
        mat[3][0] = -(right + left) / (right - left);
        mat[3][1] = -(bottom + top) / (bottom - top);
        mat[3][2] = -nearPlane / (farPlane - nearPlane);
 
        return mat;
    }
 
    glm::mat4 PerspectiveMatrixInverseZ(float fov, float nearPlane, float aspectRatio)
    {
        const float tanHalfFovy = tan(glm::radians(fov) / 2.0f);
 
        glm::mat4 mat = glm::mat4{ 0.0f };
        mat[0][0] = 1.0f / (aspectRatio * tanHalfFovy);
        mat[1][1] = 1.0f / tanHalfFovy;
        mat[2][2] = 0.0f;
        mat[2][3] = 1.0f;
        mat[3][2] = nearPlane;
 
        return mat;
    }
}