Determination and classification of triangular quadric patches Original Research Article

A method for determining, if a given rational triangular Bézier patch of degree 2 lies on a quadric surface, and if so, for establishing the quadricʹs affine type, is presented. First, the question whether the patch is a quadric patch is solved by means of the related Veronese surface in five-dimensional projective space. Once established that the patch lies on a quadric the Gaussian curvature in one of the corner points of the patch is used for a rough classification yielding the projective type of the quadric. Then, the quadricʹs affine type is obtained by means of the quadricʹs intersection with the plane at infinity. An easy algorithm for the method is finally presented, together with several examples.