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 ...

Wang-Ball (WB) curve is one of the generalized cubic Ball basis which was first put forward in CONSURF system by Ball. Wang extended it to arbitrary odd and even degrees. An algorithmic approach to degree reduction of interval Wang-Ball curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed WB curves) associated with the original interval WB curve are obtained. Th...

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...

A design of a class of linkages is presented which are less complex than those suggested by Kapovich and Millson in the con…guration of conventional planar linkages. Conventional linkage constraints are relaxed allowing sliding joints and telescoping links. The precise number of …xed links, telescoping links, and sliding contacts is determined for this modern linkage to trace a Bézier curve of ...

In this paper we classify and derive closed formulas for geometric elements of quadrics in rational Bézier triangular form (such as the center, the conic at infinity, the vertex and the axis of paraboloids and the principal planes), using just the control vertices and the weights for the quadric patch. The results are extended also to quadric tensor product patches. Our results rely on using te...

This paper presents a multi-degree reduction approximation algorithm for a usable type of curves in Computer Aided Geometric Design, generalized Ball curves of Wang-Said type in L2-norm, which has many advantages such as explicit expression, endpoint constrains, best approximation and error prediction. The basic idea is by deriving and using the conversion formulas between the WSGB basis and th...