The synthesis of solids bounded by many faces

ABSTRACT

A technique is presented which allows a class of solid objects to be synthesized and stored using a computer. Synthesis begins with primitive solids like a cube, wedge, or cylinder. Any solid can be moved, scaled, or rotated. Solids may also be added together or subtracted. Two algorithms to perform addition are described. For practical designers, the technique has the advantage that operations are concise, readily composed, and are given in terms of easily imagined solids. Quite short sequences of operations suffice to build up complex solids bounded by many faces.

REFERENCES

• 1: Bellman, R., et al., Abstraction and patern classification. J. Math. Anal. and Applications 13 (1966), 1-7.
• 2: Braid, I.C. Designing with Volumes (2nd ed.). Cantab Press, 97 Hurst Park Ave, Cambridge, U.K., 1974.
• 3: Engeli, M., and Hrdliczka, V. EUKLID-eine Einfiihrung. Fides Rechenzentrum, Zurich, 1974.
• 4: Lang, C.A. SAL--systems assembly language. Proc. AFIPS 1969 SJCC. Vol. 38, pp. 543-555, AFIPS Press, Montvale, N.J.
• 5: William M. Newman , Robert F. Sproull, Principles of interactive computer graphics (2nd ed.), McGraw-Hill, Inc., New York, NY, 1979

INDEX TERMS

Primary 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

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

  J. Computer Applications

General Terms:
Design, Theory

Keywords:
computational geometry, computer-aided design, graphics, machined components, polyhedra, shape synthesis, three-dimensional modeling