In this paper, we introduce a wavelet method for the description, approximation, analysis and simulation of optical surfaces. We describe the new method and show results of several numerical experiments for relevant applications in optics. We focus on three main aspects. First, we describe a highly accurate representation of smooth optical surfaces in terms of a B-spline quasi-interpolant. This...

Jonathan C. Carr1, Andrew H. Gee1, Richard W. Prager1 & Kevin J. Dalton2 1Dept. of Engineering, University of Cambridge, Cambridge, UK. Email: [email protected] 2Dept. Obstetrics & Gynaecology, University of Cambridge, Cambridge, UK. ABSTRACT A 3D B-spline quasi-interpolant is used to extract smooth iso-value surfaces from volume data. In this technique discretization and partial voluming arti...

.This paper is concerned with the range restricted interpolation of 'data on rectangular grids. The interpolant is constrained to lie on the same side of the constraint surface as the data. Sufficient non-negativity conditions on the Bezier ordinates are derived to ensure the non-negativity of a bicubic Bezier patch. The method modifies Bezier ordinates locally to fulfill the sufficient non-neg...

We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data using C(2) rational cubic spline. It involves three families of shape paramete...

It is an important fact that general families of Chebyshev and L-splines can be locally represented, i.e. there exists a basis of B-splines which spans the entire space. We develop a special technique to calculate with 4 order Chebyshev splines of minimum deficiency on nonuniform meshes, which leads to a numerically stable algorithm, at least in case one special Hermite interpolant can be const...

taking, for each fixed t, the k divided difference of g(s) := gk(s; t) at ti, . . . ti+k in the usual manner even when some or all of the tj ’s coincide. I leave unresolved any possible ambiguity when t = tj for some j, and concern myself only with left and right limits at such a point; i.e., I replace each t = tj by the “two points” tj and t + j . As is well known, Nik > 0 on (ti, ti+k), and N...

Fractal methodology provides a general frame for the understanding of real-world phenomena. In particular, the classical methods of real-data interpolation can be generalized by means of fractal techniques. In this paper, we describe a procedure for the construction of smooth fractal functions, with the help of Hermite osculatory polynomials. As a consequence of the process, we generalize any s...

The fact that the Darboux frame is rotation–minimizing along lines of curvature of a smooth surface is invoked to construct rational surface patches whose boundary curves are lines of curvature. For given patch corner points and associated frames defining the surface normals and principal directions, the patch boundaries are constructed as quintic RRMF curves, i.e., spatial Pythagorean–hodograp...

We present a new perspective on the Floater–Hormann interpolant. This interpolant is rational of degree (n, d), reproduces polynomials of degree d, and has no real poles. By casting the evaluation of this interpolant as a pyramid algorithm, we first demonstrate a close relation to Neville’s algorithm. We then derive an O(nd) algorithm for computing the barycentric weights of the Floater–Hormann...

An automatic lips detection and tracking system based on watershed segmentation and H approach is presented. For some of the lips detection systems, skin/non-skin detection is a prerequisite step to localise the face region and the lips region is then detected from the face region. In this paper, a direct lips detection technique using watershed segmentation without needing preliminary face loc...