In this paper, we give several simple methods for drawing a whole rational surface (without base points) as several Bézier patches. The first two methods apply to surfaces specified by triangular control nets and partition the real projective plane RP into four and six triangles respectively. The third method applies to surfaces specified by rectangular control nets and partitions the torus RP ...

Strip approximation with Bézier patches in conical form for design and manufacturing of developable materials Chih-Hsing Chu a , Charlie C.L. Wang b & Chi-Rung Tsai a a Department of Industrial Engineering and Engineering Management , National Tsing Hua University , Hsinchu, Taiwan b Department of Mechanical and Automation Engineering , The Chinese University of Hong Kong , Shatin N.T., Hong Ko...

The aim of this article is to focus on the investigation of such rationally parametrized hypersurfaces which admit rational convolution (RC) generally, or in some special cases. Examples of such hypersurfaces are presented and their properties are discussed. We also aim to examine links between well-known curves and surfaces (PH/PN or LN) and general objects defined and explored in this article...

The stretching energy functional and the bending energy functional are widely used for approximating the solution of the Plateau-Béizer Problem. This paper presents another two simple methods by using the extended stretching energy functional and the extended bending energy functional. The resulting surface obtained by the new methods will have a smaller area. Comparisons are made with both the...

We study polynomial solutions in the Bézier form of the wave equation in dimensions one and two. We explicitly determine which control points of the Bézier solution at two different times fix the solution.

Resumen. La simulación en tiempo real de multitudes ha sido relevante en aplicaciones relacionadas a la planificación urbana, evacuaciones, entrenamiento para el control de multitudes y entretenimiento. Problemas fundamentales como la navegación de agentes y evasión de colisiones deben ser resueltos eficientemente para obtener una simulación interactiva. Este trabajo propone un método integrado...

Article history: Received 9 March 2007 Received in revised form 16 June 2008 Accepted 20 October 2008 Available online 1 November 2008

In this paper, we introduce a method for the application of Bézier curve algorithms to lookup-table-based interpolations, particularly for the use of timing, power, and noise analysis in integrated circuit design. Bézier curves can replace conventional piecewise linear functions for accuracy enhancement. Selecting control points with physical implications and forcing curves to pass through samp...

In this paper we show that the best constrained degree reduction of a given Bézier curve f of degree from n to m with Cα−1-continuity at the boundary in L2-norm is equivalent to the best weighted Euclidean approximation of the vector of Bernstein–Bézier (BB) coefficients of f from the vector of degree raised BB coefficients of polynomials of degree m with Cα−1-continuity at the boundary.  2003...

Said-Ball curves and surfaces are extensively applied in the realm of geometric modeling. Their appearance is only decided by control points, which produces a great deal inconvenience for shape design sophisticated products. To overcome this defect, we construct novel kind quartic generalized (QGS-Ball, short) surfaces, contain multiple parameters, global local can be easily modified via parame...