geom.Matrix.getDeterminant() might contain a typo.

[batmuffino]

Matrix.getDeterminant() might contain a typo.

In the function

    public final double getDeterminant()
    {
        double result = 0.0;
        // Columns 2, 3, 4.
        result += this.m11 *
            (this.m22 * (this.m33 * this.m44 - this.m43 * this.m34)
                - this.m23 * (this.m32 * this.m44 - this.m42 * this.m34)
                + this.m24 * (this.m32 * this.m43 - this.m42 * this.m33));
        // Columns 1, 3, 4.
        result -= this.m12 *
            (this.m21 * (this.m33 * this.m44 - this.m43 * this.m34)
                - this.m23 * (this.m31 * this.m44 - this.m41 * this.m34)
                + this.m24 * (this.m31 * this.m43 - this.m41 * this.m33));
        // Columns 1, 2, 4.
        result += this.m13 *
            (this.m21 * (this.m32 * this.m44 - this.m42 * this.m34)
                - this.m22 * (this.m31 * this.m44 - this.m41 * this.m34)
                + this.m24 * (this.m31 * this.m42 - this.m41 * this.m32));
        // Columns 1, 2, 3.
        result -= this.m14 *
            (this.m21 * (this.m32 * this.m43 - this.m42 - this.m33)
                - this.m22 * (this.m31 * this.m43 - this.m41 * this.m33)
                + this.m23 * (this.m31 * this.m42 - this.m41 * this.m32));
        return result;
    }

The last line containing

        // Columns 1, 2, 3.
        result -= this.m14 *
            (this.m21 * (this.m32 * this.m43 - this.m42 - this.m33)
                - this.m22 * (this.m31 * this.m43 - this.m41 * this.m33)
                + this.m23 * (this.m31 * this.m42 - this.m41 * this.m32));

should probably read like the following:

        // Columns 1, 2, 3.
        result -= this.m14 *
            (this.m21 * (this.m32 * this.m43 - this.m42 * this.m33)
                - this.m22 * (this.m31 * this.m43 - this.m41 * this.m33)
                + this.m23 * (this.m31 * this.m42 - this.m41 * this.m32));

A problem causes by this is that the determinant of a Matrix is not equal to the determinant of the Matrix's transpose. This can be verified by, e.g., running the following

        Matrix m1 = new Matrix( 1, 0, 0, 1,
                                1, 1, 0, 0,
                                0, 0, 1, 0,
                                0, 0, 0, 1);

        System.out.println(m1.getDeterminant());
        System.out.println(m1.getTranspose().getDeterminant());

Found with M. Moeller while debugging some related issues and noticing that the determinant differs from apache.commons.math