Muto::Math Namespace Reference

Contains mathematical utility functions for the Vesper engine. More...

Functions
bool	DecomposeTransform (const glm::mat4 &transform, glm::vec3 &translation, glm::vec3 &rotation, glm::vec3 &scale)
	Decomposes a transformation matrix into its translation, rotation, and scale components.

Detailed Description

Contains mathematical utility functions for the Vesper engine.

Function Documentation

DecomposeTransform()

bool Muto::Math::DecomposeTransform	(	const glm::mat4 &	transform,
		glm::vec3 &	translation,
		glm::vec3 &	rotation,
		glm::vec3 &	scale
	)

Decomposes a transformation matrix into its translation, rotation, and scale components.

    {
        // From glm::decompose in matrix_decompose.inl
 
        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) {
            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 true;
    }