论文信息 - Contouring a bivariate quadratic polynomial over a triangle

Contouring a bivariate quadratic polynomial over a triangle

Abstract We consider the problem of contouring a bivariate quadratic polynomial, defined as a triangular Bezier patch. The important cases where the contour has disjoint sections or is a closed curve are considered in detail. Our results lead to a simple, yet completely robust algorithm for describing contours as piecewise rational quadratic Bezier curves.

Gerald E. Farin | Andrew J. Worsey | G. Farin | A. Worsey

[1] Carl S. Petersen. Adaptive contouring of three-dimensional surfaces , 1984, Comput. Aided Geom. Des..

[2] Gerald Farin,et al. Triangular Bernstein-Bézier patches , 1986, Comput. Aided Geom. Des..

[3] Wolfgang Böhm,et al. A survey of curve and surface methods in CAGD , 1984, Comput. Aided Geom. Des..

[4] Malcolm A. Sabin,et al. Piecewise Quadratic Approximations on Triangles , 1977, TOMS.

[5] I. Faux,et al. Computational Geometry for Design and Manufacture , 1979 .

[6] Rida T. Farouki,et al. On the numerical condition of algebraic curves and surfaces 1. Implicit equations , 1988, Comput. Aided Geom. Des..

[7] C. D. Boor,et al. B-Form Basics. , 1986 .

[8] Rida T. Farouki,et al. Algorithms for polynomials in Bernstein form , 1988, Comput. Aided Geom. Des..

[9] Rida T. Farouki,et al. On the numerical condition of polynomials in Bernstein form , 1987, Comput. Aided Geom. Des..