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...

In this paper, parametric polynomial minimal surfaces of degree six with isothermal parameter are discussed. We firstly propose the sufficient and necessary condition of a harmonic polynomial parametric surface of degree six being a minimal surface. Then we obtain two kinds of new minimal surfaces from the condition. The new minimal surfaces have similar properties as Enneper’s minimal surface,...

A generalization of Patterson’s work (Patterson, 1985), on the invariants of the rational Bézier curves, to the case of surfaces is presented. An equation for the determination of the invariants for surfaces of degree (n, n) is derived and solved for the bi-quadratics – for which it is shown that seven independent, invariant functions exist. Explicit forms of the invariants are derived and a nu...

The Plateau–Bézier problem consists in finding the Bézier surface with minimal area from among all Bézier surfaces with prescribed border. An approximation to the solution of the Plateau–Bézier problem is obtained by replacing the area functional with the Dirichlet functional. Some comparisons between Dirichlet extremals and Bézier surfaces obtained by the use of masks related with minimal surf...

We discuss 3D Bézier curves with monotone curvature and torsion, generalizing a 2D class of curves by Y. Mineur et al. © 2006 Elsevier B.V. All rights reserved.

It is well known that the degree-raised Bernstein-Bézier coefficients of degree n of a polynomial g converge to g at the rate 1/n. In this paper we consider the polynomial An(g) of degree ≤ n interpolating the coefficients. We show how An can be viewed as an inverse to the Bernstein operator and that the derivatives An(g) (r) converge uniformly to g at the rate 1/n for all r. We also give an as...