Self-intersections of offsets of quadratic surfaces: Part II, Implicit surfaces

Takashi Maekawa

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The paper investigates self-intersections of offsets of implicit quadratic surfaces. The quadratic surfaces are the simplest curved objects, referred to as quadrics, and are widely used in mechanical design. In an earlier paper, we have investigated the self-intersections of offsets of explicit quadratic surfaces, such as elliptic paraboloid, hyperbolic paraboloid and parabolic cylinder, since not only are they used in mechanical design, but also any regular surface can be locally approximated by such explicit quadratic surfaces. In this paper, we investigate the rest of the quadrics whose offsets may degenerate, i.e. the implicit quadratic-surfaces (ellipsoid, hyperboloid, elliptic cone, elliptic cylinder and hyperbolic cylinder). We found that self-intersection curves of offsets of all the implicit quadratic surfaces are planar implicit conics and their corresponding curve on the progenitor surface can be expressed as the intersection curve between an ellipsoid, whose semi-axes are proportional to the offset distance, and the implicit quadratic surfaces themselves.

Original languageEnglish
Pages (from-to)14-22
Number of pages9
JournalEngineering with Computers
Volume14
Issue number1
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes

Fingerprint

Implicit Surfaces
Self-intersection
Mechanical Design
Quadric
Ellipsoid
Curve
Hyperbolic paraboloid
Cones
Cone
Intersection
Directly proportional

Keywords

  • NC machining
  • Offset surfaces
  • Self-intersections
  • Trimmed offset

ASJC Scopus subject areas

  • Software
  • Modelling and Simulation
  • Engineering(all)
  • Computer Science Applications

Cite this

Self-intersections of offsets of quadratic surfaces : Part II, Implicit surfaces. / Maekawa, Takashi.

In: Engineering with Computers, Vol. 14, No. 1, 01.01.1998, p. 14-22.

Research output: Contribution to journalArticle

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