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A Uniform Subdivision Method for Triangular Bezier Patches

Kenneth I. Joy

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Abstract

A subdivision method for Bezier triangles is presented that parallels the development of Lane-Riesenfeld for Bezier Curves. The method is developed from the mathematical description of the patch, and the resulting algorithm does not require evaluation of the blending functions. This method subdivides the triangle uniformly so that the lengths of the sides of the subtriangles are uniformly reduced. This method is a member of the class of methods first presented by Goldman, which contain subdivision methods that arise from degenerate subdivision of Bezier tetrahedra. It is shown that a certain method is a natural extension of the Lane-Riesenfeld results for Bezier curves.

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A subdivision method for Bezier triangles is presented that parallels the development of Lane-Riesenfeld for Bezier Curves. The method is developed from the mathematical description of the patch, and the resulting algorithm does not require evaluation of the blending functions. This method subdivides the triangle uniformly so that the lengths of the sides of the subtriangles are uniformly reduced. This method is a member of the class of methods first presented by Goldman, which contain subdivision methods that arise from degenerate subdivision of Bezier tetrahedra. It is shown that a certain method is a natural extension of the Lane-Riesenfeld results for Bezier curves.

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Available abstract

A subdivision method for Bezier triangles is presented that parallels the development of Lane-Riesenfeld for Bezier Curves. The method is developed from the mathematical description of the patch, and the resulting algorithm does not require evaluation of the blending functions. This method subdivides the triangle uniformly so that the lengths of the sides of the subtriangles are uniformly reduced. This method is a member of the class of methods first presented by Goldman, which contain subdivision methods that arise from degenerate subdivision of Bezier tetrahedra. It is shown that a certain method is a natural extension of the Lane-Riesenfeld results for Bezier curves.

Key concepts: Subdivision, Bézier curve, Mathematics, Class (philosophy), Computer science, Geometry, Algorithm, Combinatorics

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