This paper presents a kinematic model of the human arm in which the workspace of the elbow is modeled as a triangular B ezier spline surface. It is also explained how this model is used for solving forward and inverse kinematics in computer animation systems. In order to solve inverse kinematics problems, it is necessary to nd a curve on the surface modeling the elbow workspace. This curve is o...

A scheme is described for interactively modifying the shape of convexity preserving planar interpolating curves. An initial curve is obtained by patching together rational cubic and straight line segments. This scheme has, in general, geometric continuity of order 2(G continuity) and preserves the local convexity of the data. A method for interactively modifying such curves, while maintaining t...

In this paper, we construct a family of Bernstein functions using class rational parametrization. The new basis on an index $\alpha \in {\left(-\infty \, , 0 \right)}\cup {\left(1 +\infty\right)}$, and for given degree $k\in \mathbb{N}^*$, these are with numerator denominator polynomials k. All the classical properties as positivity, partition unity hold they constitute approximation continuous...

Il existe de nombreux algorithmes de calcul pour l'enveloppe convexe d'un polygone simple. Il existe aussi des propositions d'algorithmes calculant, a l'aide de quelques primitives assez complexes, l'enveloppe convexe d'objets born es non pas par des segments de droite, mais par des courbes planes suusament lisses et convexes par morceaux. Les r esultats fournis par les algorithmes actuels sont...

We introduce control curves for trigonometric splines and show that they have properties similar to those for classical polynomial splines. In particular, we discuss knot insertion algorithms, and show that as more and more knots are inserted into a trigonometric spline, the associated control curves converge to the spline. In addition, we establish a convex-hull property and a variation-dimini...

abstract We present a uniied framework for most of the known and a few new evaluation algorithms for multivariate polynomials expressed in a wide variety of bases including the B ezier, multinomial (or Taylor), Lagrange and Newton bases. This uniication is achieved by considering evaluation algorithms for multivariate polynomials expressed in terms of L-bases, a class of bases that include the ...

The computational complexity of general change of basis algorithms from one bivariate polynomial basis of degree n to another bivariate polynomial basis of degree n using matrix multiplication is O(n 4). Applying blossoming and duality, we derive change of basis algorithms with computational complexity O(n 3) between two important classes of polynomial bases used for representing surfaces in CA...

The main preoccupations of research in computer-aided geometric design have been on shape-speciication techniques for polynomial curves and surfaces, and on the continuity between segments or patches. When modelling with such techniques, curves and surfaces can be compressed or expanded arbitrarily. There has been relatively little work on interacting with direct spatial properties of curves an...

We discuss strategies for comparisons of nonperturbative QCD predictions parton distribution functions (PDFs) with high-energy experiments in the region large partonic momentum fractions $x$. Analytic functional forms PDFs cannot be uniquely determined solely based on discrete experimental measurements because a mathematical property mimicry PDF parametrizations that we prove using representati...