Bézier Curves and Surface Patches on Quadrics

Bezier curves, Bezier spline curves, Bezier tensor product patches and triangular patches on quadrics (sphere, hyperboloid of one or two sheets, paraboloid) are constructed with the help of quadratic maps ϕ i . The maps transform integral Bezier curves and patches from a parameter space ( u, v, w ) to rational Bezier curves and patches on quadrics. Curves of degree n in ( u, v, w )-space lead to Bezier curves of degree 2 n. Tensor product patches of degree ( n, m ) in ( u, v, w )-space lead to degree (2 n , 2 m ) while triangular patches of degree n in ( u, v, w )-space lead to triangular patches of degree 2 n.