An Intuitive Approach To Geometric Continuity For Parametric Curves And Surfaces
Download An Intuitive Approach To Geometric Continuity For Parametric Curves And Surfaces PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get An Intuitive Approach To Geometric Continuity For Parametric Curves And Surfaces book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces
This report defines the nth order geometric continuity for parametric curves and surfaces, and derived the Beta constraints that are necessary and sufficient for it. Derivation of the Beta constraints is based on a simple principle of reparametrisation in conjunction with the univariate chain rule for curves, and the bivariate chain rule for surfaces. This approach uncovers the connection between geometric continuity for curves and geometric continuity for surfaces, provides new insight into the nature of geometric continuity in general, and allows the determination of the Beta constraints with less effort than previously required. Use of the Beta constraints for G to the nth power continuity allows the introduction of n shape parameters for curves, and n (n +3) shape functions for surfaces. The shape parameters and shape functions may be used to modify the shape of a geometrically continuous curve or surface, respectively. However, geometric continuity is only appropriate for applications where rate aspects of the parametrisations are unimportant since discontinuities in rate are allowed. (Reprints).
Computation of Curves and Surfaces
Author: Wolfgang Dahmen
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Assembled here is a collection of articles presented at a NATO ADVANCED STU DY INSTITUTE held at Puerto de la Cruz, Tenerife, Spain during the period of July 10th to 21st, 1989. In addition to the editors of these proceedings Professor Larry L. Schumaker from Vanderbilt University, Nashville, Tennessee, served as a member of the international organizing committee. The contents of the contribu tions fall within the heading of COMPUTATION OF CURVES AND SURFACES and therefore address mathematical and computational issues pertaining to the dis play, modeling, interrogation and representation of complex geometrical objects in various scientific and technical environments. As is the intent of the NATO ASI program the meeting was two weeks in length and the body of the scientific activities was organized around prominent experts. Each of them presented lectures on his current research activity. We were fortunate to have sixteen distinguished invited speakers representing nine NATO countries: W. Bohm (Federal Republic of Germany), C. de Boor (USA), C.K. Chui (USA), W. Dahmen (Federal Republic of Germany), F. Fontanella (Italy), M. Gasca (Spain), R. Goldman (Canada), T.N.T. Goodman (UK), J.A. Gregory (UK), C. Hoffman (USA), J. Hoschek (Federal Republic of Germany), A. Le Mehaute (France), T. Lyche (Norway), C.A. Micchelli (USA), 1.1. Schumaker (USA), C. Traas (The Netherlands). The audience consisted of both young researchers as well as established scientists from twelve NATO countries and several non-NATO countries.
An Introduction to Splines for Use in Computer Graphics and Geometric Modeling
As the field of computer graphics develops, techniques for modeling complex curves and surfaces are increasingly important. A major technique is the use of parametric splines in which a curve is defined by piecing together a succession of curve segments, and surfaces are defined by stitching together a mosaic of surface patches. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling discusses the use of splines from the point of view of the computer scientist. Assuming only a background in beginning calculus, the authors present the material using many examples and illustrations with the goal of building the reader's intuition. Based on courses given at the University of California, Berkeley, and the University of Waterloo, as well as numerous ACM Siggraph tutorials, the book includes the most recent advances in computer-aided geometric modeling and design to make spline modeling techniques generally accessible to the computer graphics and geometric modeling communities.