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VOL. 26 | 1991 Some topical variational geometry problems in computer graphics
G. N. Newsam

Editor(s) Gerd Dziuk, Gerhard Huisken, John Hutchinson

Abstract

Smooth interpolation of arbitrary curves and surfaces is a major problem in computer graphics. There are very successful variational formulations of similar problems in smooth interpolation of arbitrary functions; these have given rise to the (linear) theory of splines. However, there appears to be as yet no equivalent useful formulation of the general problem, so present computer graphics algorithms for cunres and surfaces use somewhat ad hoc extensions of the linear results based on parametric representations of splines and surface patches. The paper briefly describes the present state of affairs in the hope that variational geometers will pick up on some of these unsolved problems and develop a coherent theory of smooth interpolation of arbitrary geometrical objects. If such a theory can be developed, it may possibly revolutionize computer graphics.

Information

Published: 1 January 1991
First available in Project Euclid: 18 November 2014

zbMATH: 0743.41010
MathSciNet: MR1139038

Rights: Copyright © 1991, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.

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