#include "matrix.h"

Matrix

Matrix::get_inverted() const {

	Real d = det();

	if (equal(d, 0)) {

		// try to make back transform for X-axis

		if (equal(m02, 0) && equal(m10, 0) && equal(m11, 0) && equal(m12, 0) && equal(m22, 1)) {

			d = axis_x().lensqr();

			if (d > precision) {

				d = 1.0/d;

				return Matrix(

				    d*m00,                 0, 0,

				    d*m01,                 0, 0,

				   -d*(m20*m00 + m21*m01), 0, 1 );

			}

		}

		// try to make back transform for Y-axis

		if (equal(m00, 0) && equal(m01, 0) && equal(m02, 0) && equal(m12, 0) && equal(m22, 1)) {

			d = axis_y().lensqr();

			if (d > precision) {

				d = 1/d;

				return Matrix(

				    0,  d*m10,                 0,

					0,  d*m11,                 0,

					0, -d*(m20*m10 + m21*m11), 1 );

			}

		}

		// give up

		return Matrix( 0, 0, 0,

					   0, 0, 0,

					   0, 0, 0 );

	}

	// proper inversion

	Real p = 1/d, m = -p;

	return Matrix(

		p*(m11*m22 - m12*m21), // row0

		m*(m01*m22 - m02*m21),

		p*(m01*m12 - m02*m11),

		m*(m10*m22 - m12*m20), // row1

		p*(m00*m22 - m02*m20),

		m*(m00*m12 - m02*m10),

		p*(m10*m21 - m11*m20), // row2

		m*(m00*m21 - m01*m20),

		p*(m00*m11 - m01*m10) );

}