Accession Number : ADA306831

Title :   Serious Putty: Topological Design for Variational Curves and Surfaces.

Descriptive Note : Doctoral thesis,

Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE

Personal Author(s) : Welch, William

PDF Url : ADA306831

Report Date : 01 DEC 1995

Pagination or Media Count : 132

Abstract : In this work we develop a new approach to designing curves and free-form surfaces on a computer. It is inspired by a style of pencil-and-paper design used for sculptured surfaces, in which the designer specifies the shapes of important curves (character lines) and indicates surfaces that pass through them smoothly, with no unnecessary bulges or wiggles (that is, the surfaces are fair). Unlike previous modeling approaches based on the notion of character lines, this approach allows surfaces to be cut apart and smoothly joined along arbitrary curves, so that the designer can build up complex shapes and topologies from simpler ones. Further, the surfaces are infinitely stretchy, so that the designer may add unlimited amounts of detail simply by indicating more control points and curves. Finally, portions of the surface may be made to copy externally controlled shape tools. This allows the designer to mix free-form and structured shapes within a single composite surface model of arbitrary topology. This kind of conceptually simple shape description (give me a fair surface bordered by these curves that passes through those curves while touching that point) may be precisely interpreted as a functional minimization problem in the calculus of variations (give me the surface coordinate function that maximizes this fairness integral subject to those geometric constraints). The modeler described here represents curves and surfaces implicitly, as the solutions of such variational minimization problems. As the designer interacts directly with a surface, the modeler interprets these actions as changing the variational shape specification.

Descriptors :   *COMPUTER AIDED DESIGN, *COMPUTER GRAPHICS, MATHEMATICAL MODELS, ALGORITHMS, SURFACE ANALYSIS, OPTIMIZATION, PARAMETRIC ANALYSIS, QUEUEING THEORY, REAL TIME, SHAPE, THESES, MESH, NONPARAMETRIC STATISTICS, THREE DIMENSIONAL, FINITE DIFFERENCE THEORY, CURVATURE, TOPOLOGY, INTERPOLATION, SAMPLING, CONVERGENCE, INTERACTIVE GRAPHICS, CONTROL THEORY, APPLIED MATHEMATICS, DESIGN CRITERIA, DYNAMIC PROGRAMMING, ITERATIONS, CALCULUS OF VARIATIONS, CURVES(GEOMETRY), STRUCTURED PROGRAMMING, TRIANGULATION, OBJECT ORIENTED PROGRAMMING, SMOOTHING(MATHEMATICS).

Subject Categories : Computer Programming and Software
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE