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Contouring a bivariate quadratic polynomial over a triangle. (English) Zbl 0726.65014

The authors consider the problem of contouring a bivariate quadratic polynomial, defined as a triangular Bézier patch. The problem of contouring a quadratic polynomial over a triangle has been earlier considered by S. Marlow and M. J. D. Powell [A Fortran subroutine for plotting the part of a conic that is inside a given triangle. Report No.R8336, Atomic Energy Res. Establishment, Harwell, England (1976)] and the second author [Comput. Aided Geom. Des. 3, 83-127 (1986; Zbl 0633.65007)]. The algorithms given by these authors have some deficiencies.
In this paper an algorithm for solving this problem is presented which is more efficient and accurate than that of Marlow and Powell and far more robust than that of the second author. The authors use the Bernstein- Bézier form for quadratic polynomials defined over a triangle, and also for describing conic sections. Recent results show that the Bernstein basis for polynomials is more stable for numerical computations than the monomial basis.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)

Citations:

Zbl 0633.65007
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References:

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