Geometric approaches to nonplanar quadric surface intersection curves

ABSTRACT

Quadric surfaces occur frequently in the design of discrete piece parts in mechanical CAD/CAM. Solid modeling systems based on quadric surfaces must be able to represent intersection curves parametrically and in a fashion that allows the underlying surfaces to be partitioned. An algebraic approach originally developed by Levin meets these needs but is numerically sensitive and based on solutions to fourth-degree polynomial equations. In this paper we develop geometric approaches that are robust and efficient, and do not require solutions to polynomials of degree higher than 2.

REFERENCES

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INDEX TERMS

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

Additional Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Geometric algorithms, languages, and systems

  J. Computer Applications
  J.6 COMPUTER-AIDED ENGINEERING
      Subjects: Computer-aided design (CAD)

General Terms:
Algorithms, Performance, Reliability