This document has four purposes. it is a tutorial in parametric curve and surface representations, it describes a number of algorithms for generating both shaded and line-drawn pictures of bivariate surfaces and trivariate volumes, it explicitly gives transformations between all of the widely used curve and surface representations, and it proposes a solution to the problem of displaying the res...

We compute the singular points of a plane rational curve, parametrically given, using the implicitization matrix derived from the μ-basis of the curve. It is shown that singularity factors, which are defined and uniquely determined by the elementary divisors of the implicitization matrix, contain all the information about the singular points, such as the parameter values of the singular points ...

Morin and Goldman [Computer Aided Geometric Design 17 (2000) 813] have recently presented a remarkable new framework, based on employing Poisson series, for describing analytic functions in CAD. We compare this Poisson formulation with s-power series, modified Newton series that can be regarded as the two-point analogue of Taylor expansions. Such s-power series yield, over finite intervals, bet...

This paper presents a Computer-Aided Geometric Design (CAGD) based approach for building 3-D models which can be used for the recognition of 3-D objects for industrial machine vision applications. The objects are designed using the Alpha_1 CAGD system developed at the University of Utah. A new method is given which uses the CAGD design and allows the points on the surface of the object to be sa...

Recently, a powerful extension of neural networks. the so-called functionaI networks. has been introduced / I /. This kind of networks exhibits more versatility than neural networks so they can be successfully applied to several problems in Cotputer-Aided Geometric Design (CAGD). As an illustration, the simplest functional network representing tensor product surfaces is obtained. Then, function...

The problem of parametrizing 3D data points is fundamental for many applications in computer-aided geometric design, e.g. surface fitting, texture mapping, and remeshing. We present a new method for constructing a global parametrization of a triangulated (topologically disklike) surface over a planar region with minimal distortion. In contrast to many existing approaches which need the boundary...

A rational cubic trigonometric spline with two shape parameters which play an important role in manipulating the shape of the curve is described in this paper. Its algebraic analogue with shape parameters has been discussed. Spline is presented both in interpolatory and rational B-spline form and the properties of resulting Bsplines are also studied. Keywords— Computer aided geometric design, r...

This paper is concerned with the mathematics and formal specification of “set-like” operations for the mixed dimension cellular objects of the Djinn Application Programming Interface. The relationships between these operations and stratifications of dimensionally heterogeneous semianalytic point-sets are uncovered and formalised. Semianalytic geometry is central to the algebraic model discussed...

One of the puzzlingly hard problems in Computer Aided Geometric Design and Approximation Theory is that of finding the dimension of the spline space of C piecewise degree n polynomials over a 2D triangulation Ω. We denote such spaces by Sr n(Ω). In this note, we restrict Ω to have a special structure, namely to be unconstricted. This will allow for several exact dimension formulas.

Powar, P.L., Minimal roughness property of the Delaunay triangulation: a shorter approach, Computer Aided Geometric Design 9 (1992) 491-494. Recently Rippa (1990) has investigated an interesting result which states that “The Delaunay triangulation of the data points minimizes the roughness measure of a Piecewise Linear Interpolating Surface (PLISJ for any fixed set of function values”. This res...