THREE-DIMENSIONAL CURVES AND SURFACES FOR RAPID COMPUTER DISPLAY

Abstract

Rational parameteric polynomial functions of second degree or higher provide a class of curves including all conic sections. They can be generated by an iterative process easily implemented in software or hardware. The numerical accuracy of the process is analyzed. Algorithms for the specification, display, and modification of the curve are presented. Such curves are represented in a homogeneous coordinate formulation convenient for computer applications. Three- dimensional surfaces composed of such curves are similarly convenient to use. Without recourse to trigonometric functions, such classical surfaces as spheres and toroids can be readily described. The ease with which translation, rotation and projective transformations can be applied is exhibited. In particular, we do not perform such transformations on the points of the surface to be displayed--upwards of several thousand--but rather upon the rather small set of numbers in a 4 x 4 x 4 tensor that represents the surface. These surfaces are intended to be used in an interactive, freeform computer-aided design system. In this direction we discuss the enforcing of continuity conditions and possible data structures for representing the surfaces.

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Document Details

Document Type
Technical Report
Publication Date
Apr 30, 1969
Accession Number
AD0696176

Entities

People

  • Theodore M. Lee

Organizations

  • Harvard University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Computer Graphics
  • Computer Programming
  • Computer Programs
  • Computer-Aided Design
  • Computers
  • Converters
  • Equations
  • Geometry
  • Human-Machine Interaction
  • Information Science
  • Language
  • Statistical Analysis
  • Three Dimensional
  • Two Dimensional
  • Vector Spaces

Readers

  • Approximation Theory.
  • Database Systems and Applications
  • Graph Algorithms and Convex Optimization.