A Be´zier curve builder implemented in APL2

ABSTRACT

The Be´zier representation of curves is commonly used in computer graphics. A different, less advanced way of representing a curve is that of using a polyline, i.e., a sequence of short straight lines. This paper describes a “curve builder” that converts a polyline into a sequence of one or more Be´zier curves. Part of the method is based on mathematical groundwork by Pat Beirne of Corel Systems Corporation, with extensions by the authors. The project was implemented in APL and could not otherwise have been completed with the resources and time available.

REFERENCES

• 1: I. D. Faux , M. J. Pratt, Computational Geometry for Design and Manufacture, Halsted Press, New York, NY, 1979
• 2: IBM Publishing Systems DrawMaster. Program Number 5664-388, IBM Corporation (1987).
• 3: CoreIDRAW, Corel Systems Corporation, Ottawa, Canada (1990).
• 4: Adobe Illustrator Document Format Specification. Adobe Systems Incorporated, Palo Alto, California (1989).

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Geometrical problems and computations

  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Curve, surface, solid, and object representations

General Terms:
Algorithms, Languages