Pyramid Algorithms for Multisided Bezier Patches

In Chapter 5 we studied three-sided and four-sided Bezier patches built using dynamic programming procedures based upon three-term and four-term recurrence relations. In this chapter we are going to study Bezier patches with an arbitrary number of sides. Three-sided and four-sided patches are typically used for free-form design; multisided patches are commonly required when it is necessary to fill n-sided holes.

Our approach to multisided patches will be similar to our approach to three-sided and four-sided patches: we shall build dynamic programming procedures—pyramid algorithms—based upon special recurrence relations. By now we have a good deal of experience with generating useful ...

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