affine_inverse.hpp

#ifndef PASTELMATH_AFFINE_INVERSE_HPP
#define PASTELMATH_AFFINE_INVERSE_HPP

#include "pastel/math/affine/affine_inverse.h"

namespace Pastel
{

    template <typename Real>
    AffineTransformation<Real> inverse(
        const AffineTransformation<Real>& that)
    {
        // (forall x)
        //
        // C(Ax + b) + d = x
        // <=>
        // CAx + (Cb + d) - x = 0
        // <=>
        // (CA - I)x + (Cb + d) = 0
        // <=>
        // CA - I = 0 and Cb + d = 0
        // <=>
        // C = A^{-1} and d = -A^{-1}b

        // Compute C = A^{-1}.
        Matrix<Real> inverseMatrix(
            inverse(that.matrix()));

        // Compute d = -A^{-1}b.
        Vector<Real> inverseTranslation =
            -inverseMatrix * that.translation();

        AffineTransformation<Real> result(
            std::move(inverseMatrix),
            std::move(inverseTranslation));

        return result;
    }

    template <typename Real>
    AffineTransformation<Real> orthogonalInverse(
        const AffineTransformation<Real>& that)
    {
        // C = A^{-1} = A^T and
        // d = -A^{-1}b = -A^T b

        AffineTransformation<Real> result(
            transpose(that.matrix()),
            -transpose(that.matrix()) * that.translation());

        return result;
    }

}

#endif