BezierSurf


Entity/Object	Variable	Description
integer		Version.
Boolean		1 if the surface is rational, 0 if it is polynomial (nonrational).
integer	p	Degree in the first parameter.
integer	q	Degree in the second parameter.
double[q+1][p+1][k]	Pw	The surface control points. If the surface is rational, these are given in homogeneous coordinates and k = 4. If the surface is polynomial, these are given in Cartesian coordinates and k = 3. The value of p must be greater than or equal to the value of q.

Description

A rectangular rational Bézier surface of degree p-by-q is described by

where

and

are the Bernstein basis functions of degree p and q, respectively, as described in the entry of BezierCurve. This surface description is called rectangular because the parameter domain is rectangular; that is, the two parameters s and t can vary freely in given intervals. The homogeneous control points Pw[j][i] used in the serialization of a rational surface have the components:

A polynomial surface has all weights equal to 1.