Applying original and existing theoretical results, we propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the non-negative normalized B-basis of an arbitrary extended Chebyshev (EC) space that comprises the constants and can be identified with the solution space of a user-defined constant...

A technique is described for constructing three-dimensional vector graphics representations of planar regions bounded by cubic Bézier curves, such as smooth glyphs. It relies on a novel algorithm for compactly partitioning planar Bézier regions into nondegenerate Coons patches. New optimizations are also described for Bézier inside–outside tests and the computation of global bounds of direction...

The present paper proposes a new method for calculating the Gcontinuous o set curve to a cubic B ezier curve, based on the Hermite approximation technique. This method is improved by preliminary curvature estimation and is intended for use in cpu-time sensitive CAGD applications.

In this study, we have examined how to find any 5th order Bézier curve with its known first, second and third derivatives, which are the 4th order, cubic quadratic curves, respectively, based on control points of given derivatives. Also give an example

This paper presents a new approach and methodology to solve the second-order one-dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual finite difference scheme is used to discretize the time derivative. The cubic trigonometric B-spline basis functions are utilized as an interpolating function...

In this paper we describe a system, BOOLE, that generates the boundary representations (B-reps) of solids given as a CSG expression in the form of trimmed B ezier patches. The systemmakes use of techniques from computational geometry, numerical linear algebra and symbolic computation to generate the B-reps. Given two solids, the system rst computes the intersection curve between the two solids ...

We are concerned with the problem of visualizing interconnections in railroad systems. The real-world systems we have to deal with contain connections of thousands of trains. To visualize such a system from a given set of time tables a so-called train graph is used. It contains a vertex for each station met by any train, and one edge between every pair of vertices connected by some train runnin...

Manipulation of control points is a standard procedure in B-spline surface patch design. Unfortunately, this tool alone is not suucient to achieve certain goals such as removing gaps among patches. In this paper, we introduce another approach for removing gaps but maintaining the geometrical smoothness condition. The only requirement is to sacriice the true B-spline representation along the bou...