Pii: S0010-4485(98)00052-9
نویسندگان
چکیده
Presented in this paper is a new intersection algorithm between planar Bézier curves. The algorithm, named the cocktail algorithm, mixes and matches the merits of existing intersection algorithms appropriately. In the proposed approach, curves are approximated by a number of rational quadratic Bézier curve segments according to the shape characteristics of the curve. Then, the rational quadratic Bézier curve approximations are intersected using the implicitization method to produce the seeds of the numerical process. Experimental results reveal that the performance of the cocktail algorithm is superior to others for the curves with degrees higher than cubic. For cubic curves, however, the cocktail algorithm is slightly slower than the implicitization method with a hard coded resultant, but faster than others. q 1999 Elsevier Science Ltd. All rights reserved
منابع مشابه
Pii: S0010-4485(98)00066-9
This paper presents algorithms for computing offsets of NURBS curves and surfaces. The basic approach consists of four steps: (1) recognition of special curves and surfaces; (2) sampling the offset curve or surface based on bounds on second derivatives; (3) interpolating these points; and (4) removing all unwanted knots using the offset tolerance. The method provides a good handle on error cont...
متن کاملApproximation of developable surfaces with cone spline surfaces
Developable surfaces are modelled with pieces of right circular cones. These cone spline surfaces are well-suited for applications: They possess degree two parametric and implicit representations. Bending sequences and the development can be explicitly computed and the offsets are of the same type. The algorithms are based on elementary analytic and constructive geometry. There appear interesti...
متن کاملThe intersection of two ruled surfaces
This paper presents an eecient and robust algorithm that computes the intersection curve of two ruled surfaces. The surface intersection problem is reformulated as a zero-set nding problem for a bivariate function, which is also equivalent to the construction of an implicit curve in the plane. Each connected component of the surface intersection curve corresponds to a connected component in the...
متن کاملBisector curves of planar rational curves
This paper presents a simple and robust method for computing the bisector of two planar rational curves. We represent the correspondence between the foot points on two planar rational curves C1(t) and C2(r) as an implicit curve F(t; r) = 0, where F(t; r) is a bivariate polynomial B-spline function. Given two rational curves of degree m in the xy-plane, the curve F(t; r) = 0 has degree 4m 2, whi...
متن کاملPii: S0010-4485(98)00065-7
This paper presents a simple and robust method for computing the bisector of two planar rational curves. We represent the correspondence between the foot points on two planar rational curves C1ðtÞ and C2ðrÞ as an implicit curve F(t,r) 1⁄4 0, where F(t,r) is a bivariate polynomial B-spline function. Given two rational curves of degree m in the xy-plane, the curve F(t,r) 1⁄4 0 has degree 4m 1 2, ...
متن کامل