The Application of Total Positivity to Computer Aided Curve and Surface Design,
Abstract
Of particular importance in an interactive curve and surface design system is the interface to the user. The mathematical model employed in the system must be sufficiently flexible for interaction between designer and machine to converge to a satisfactory result. The mathematical theory of Total Positivity is combined with the interactive techniques of Bezier and Riesenfeld in developing new methods of shape representation which retain the valuable variation-diminishing and convex hull properties of Bernstein and B-spline approximation, while providing improvements in the interactive interface to the user. Specifically, extending the Bezier notion of using a polygon to describe a smooth curve, methods of assigning a weight to each vertex which will control the amount of local fit to the polygon of polygonal net are provided. Thus, the designer can cause cusps and flats easily by manipulating the tension at each vertex. Further, the generalization from curves to surfaces can be done with rectilinear data or triangular data. Illustrations are provided from an experimental implementation of the newly constructed models as a demonstration of their feasibility and utility in computer aided curve and surface design. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1977
- Accession Number
- ADA052656
Entities
People
- J. M. Lane
- R. F. Riesenfeld
Organizations
- University of Utah