Two methods to generate tensor-product Bézier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of ∆4−→x = 0 with prescribed boundary and adjacent to the boundary control points of a n× n Bézier surface. The second one is based on the nonhomog...

Graphics systems usually have primitives for rendering straight-line segments, circles, Bézier curves and surfaces. However, they do not have generalized primitives for implicit curves and surfaces. This is so because current algorithms have serious difficulties in dealing with differential singularities (e.g. self-intersections). This paper is about a generic algorithm capable of rendering any...

A quadratic Bézier spline with G-continuity is given to approximate a planar parametric curve. In its construction, the parametric curve is first divided into several segments. A rational quadratic Bézier curve is then applied to approximate each segment and recursive subdivision for the segment may be used if the approximation error is out of the given range. With this method, we not only keep...

In this paper we present two path planning algorithms based on Bézier curves for autonomous vehicles with waypoints and corridor constraints. Bézier curves have useful properties for the path generation problem. The paper describes how the algorithms apply these properties to generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bézier curve ...

Door passing is the basic capability of an intelligent wheelchair. This paper presents a novel approach to address the door passing issue using Bézier curve based trajectory planning. The planed path consists of two segments: one from corridor to door and the other from door to the goal position. For each segment, an optimal Bézier curve is generated as a reference trajectory for an intelligent...

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 quadrati...

This paper deals with the problem of multi-degree reduction of a composite Bézier curve with the parametric continuity constraints at the endpoints of the segments. We present a novel method which is based on the idea of using constrained dual Bernstein polynomials to compute the control points of the reduced composite curve. In contrast to other methods, ours minimizes the L2-error for the who...

We prove that if an nth degree rational Bézier curve has a singular point, then it belongs to the two (n− 1)th degree rational Bézier curves defined in the (n− 1)th step of the de Casteljau algorithm. Moreover, both curves are tangent at the singular point. A procedure to construct Bézier curves with singularities of any order is given.  2001 Elsevier Science B.V. All rights reserved.

In this paper, we propose a novel adaptive mesh fitting algorithm that fits a triangular model with G1 smoothly stitching bi-quintic Bézier patches. Our algorithm first segments the input mesh into a set of quadrilateral patches, whose boundaries form a quadrangle mesh. For each boundary of each quadrilateral patch, we construct a normal curve and a boundary-fitting curve, which fit the normal ...

Abstract—We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach t...