Bézier Surfaces with Orthogonal Iso-parameter Curves

The representation of Bézier surfaces greatly affects the results of rendering and tessellation applications. To improve the orthogonality of surface iso-parameter curves, the constraints and their corresponding construction method of surfaces with orthogonal iso-parameter curves are given in this paper. The only rational bilinear surface with orthogonal iso-parameter curves is a rectangle. For Bézier surfaces of degree 2 × 2, we derive the explicit orthogonality condition of their control points, by using which a scheme to construct surfaces with orthogonal iso-parameter curves is then presented. Also the possible extension of the construction scheme for Bézier surfaces of any degree is discussed. Examples are given to show the performance of our algorithm for rendering and tessellation applications.