Bisector Surface of Rational Space
نویسندگان
چکیده
Given a point and a rational curve in the plane, their bisector curve is rational 2]. However, in general, the bisector of two rational curves in the plane is not rational 3]. Given a point and a rational space curve, this paper shows that the bisector surface is a rational ruled surface. Moreover, given two rational space curves, we show that the bisector surface is rational (except for the degenerate case in which the two curves are coplanar).
منابع مشابه
Geometric Properties of Bisector Surfaces
This paper studies algebraic and geometric properties of curve–curve, curve– surface, and surface–surface bisectors. The computation is in general difficult since the bisector is determined by solving a system of nonlinear equations. Geometric considerations will help us to determine several distinguished curve and surface pairs which possess elementary computable bisectors. Emphasis is on lowd...
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 کاملPrecise Voronoi Cell Extraction of Free-Form Planar Piecewise C1-Continuous Closed Rational Curves
We present an algorithm for generating Voronoi cells for a set of planar piecewise C1-continuous closed rational curves, which is precise up to machine precision. The algorithm starts with the symbolically generated bisectors for pairs of C1-continuous curve segments (C(t),Ci(r)). The bisectors are represented implicitly in the tr-parameter space. Then, they are properly trimmed after being spl...
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 کاملPlanar Bisector CurvesBased on Developable
This paper presents an algorithm to compute the bisector curve of two planar paramet-ric curves. We reduce the problem of computing a bisector curve to that of intersecting two developable surfaces. Given an input curve C (t) = (x(t); y(t)), the corresponding developable surface D C(t) is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the parabol...
متن کامل