- Author:
- Brian A. Barsky
This tutorial describes parametric Bernstein/Bezier curves and parametric tensor-product Bernstein/Bezier surfaces. The parametric representation is described, the Bezier curves are discussed. The single Bezier curve is extended to a composite Bezier curve using parametric continuity. then the more general geometric continuity is defined, first for order two (G2), and then for arbitrary order n (Gn). Composite Bezier curves are stitched together with G1 and G2 continuity using constraints on the control vertices and using geometric constructions. The subdivision of Bezier curves is then derived along with a discussion of the associated geometric construction, the deCasseljau Algorithm, and Rafness testing. Then, the Bezier curve is generalized to a tensor-product surface. Finally, the rational Bezier curve and rational tensor-product surface are discussed.
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