With steer-by-wire, suspension and steering systems are no longer governed by purely mechanical criteria but must instead be designed according to mechatronic considerations. This paper demonstrates an approach to steer-bywire suspension design in which geometric design variables are chosen to render the tire reaction torque about the steer axis highly predictable. This predictability, in turn,...

Given a parameterization of an algebraic rational curve in a projective space of arbitrary dimension, we introduce and study a new implicit representation of this curve which consists in the locus where the rank of a single matrix drops. Then, we illustrate the advantages of this representation by addressing several important problems of Computer Aided Geometric Design: The point-on-curve and i...

This paper studies geometric design of developable composite Bézier surfaces from two boundary curves. The number of degrees of freedom (DOF) is characterized for the surface design by deriving and counting the developability constraints imposed on the surface control points. With a first boundary curve freely chosen, ð2m þ 3Þ, ðm þ 4Þ, and five DOFs are available for a second boundary curve of...

We present a new algorithm in order to compute the multidimensional residue of a polynomial map based on a perturbation argument and the Generalized Transformation Law. Then we use it for studying some fundamental problems in Computer Aided Geometric Design.

Given an algebraic plane curve C defined by a rational parametrization P(t), we present formulae for the computation of the degree of C, and the multiplicity of a point. Using the results presented in [Sendra, J.R., Winkler, F., 2001. Tracing index of rational curve parametrizations. Computer Aided Geometric Design 18 (8), 771–795], the formulae simply involve the computation of the degree of a...

DeVore, R.A., B. Jawerth and B.J. Lucier, Surface compression, Computer Aided Geometric Design 9 (1992) 219-239. We propose wavelet decompositions as a technique for compressing the number of a control parameters of surfaces that arise in Computer-Aided Geometric Design. In addition, we give a specific numerical algorithm for surface compression based on wavelet decompositions of surfaces into ...

In this survey, we will show some connections between several mathematical problems such as extrapolation, linear systems, totally positive matrices and computer-aided geometric design, with elimination techniques as the common tool to deal with all of them. c © 2000 Elsevier Science B.V. All rights reserved.

DP curves, which possess the shape-preserving property and linear complexity evaluation algorithm, occupy a significantly important place in computer aided geometric design. Thus to do the research on the DP curves algorithms has a positive meaning. Aphirukmatakun et al. presented a degree elevation algorithm of DP curves based on the transformation between the DP basis and power basis. At the ...

Lachance. M.A. and A.J. Schwartz. Four point parabolic interpolation, Computer Aided Geometric Design 8 (1991) 143-149. We show that four points in the plane may be interpolated by one or two parabolas or possibly by no parabola, depending on the configuration of points. We provide methods for distinguishing the cases and constructing the parabolas.

A number of applications in computer-aided manufacturing, CAD, and computer-aided geometric design ask for triangulating pieces of material with defects. These tasks are known collectively as constrained triangulations. Recently, a powerful architecture called the reconng-urable mesh has been proposed: in essence, a reconngurable mesh consists of a mesh-connected architecture augmented by a dyn...