This paper discusses the application of orthogonal collocation on finite elements (OCFE) method using quadratic and cubic B-spline basis functions partial differential equations. Collocation is performed at Gaussian points to obtain an optimal solution, hence name collocation. The used solve various cases Burgers’ equations, including modified equation. KdV–Burgers’ equation considered as a tes...

2 The Calculus of Variations 2 2.1 Functionals of f and f ′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Functionals of f , f ′, and f ′′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Cubic Splines and Green’s Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Euler-Lagrange Equations for Multi...

In this paper we disprove the belief widespread within the computer graphics community that Catmull-Clark subdivision surfaces cannot be evaluated directly without explicitly subdividing. We show that the surface and all its derivatives can be evaluated in terms of a set of eigenbasis functions which depend only on the subdivision scheme and we derive analytical expressions for these basis func...

In the note, we prove that additive Schwarz type preconditioner is applicable to the nested finite dimensional subspaces generated by Hermite cubic splines for the second order elliptic problem. It is shown that the preconditioned system is well conditioned.

Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve P and produce sequences of vertices fj and bj respectively. We proposed to analyze a subdivision scheme Js that blends the rules of these two refinement methods to produce vertices of the form vj=(1–s)fj+sbj. Iterative applications of Js yield a...

A method of generating cubic blending spline curves based on weighted trigonometric and hyperbolic polynomial is presented in this paper. The curves inherit nearly all properties of cubic B-splines and enjoy some other advantageous properties for modeling. They can represent some conics and some transcendental curves exactly. Here weight coefficients are also shape parameters, which are called ...

We construct a suitable normalized B-spline representation for C-continuous quintic Powell-Sabin splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction is based on the determination of a set of triangles that must contain a specific set of points. We are able to define control points and cubic control polynomials which are t...

In this paper we present an efficient contour tracking algorithm which can track 2D silhouettes of multiple objects in extended image sequences captured by a static camera. We represent contours using cubic B-splines, and our tracking algorithm is based on tracking a lower dimensional shape-space. The tracker is coupled with a multiple model filtering algorithm which caters for objects that mov...