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

Takashi Maekawa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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
Issue number1
Publication statusPublished - 1998 Jan 1
Externally publishedYes


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

ASJC Scopus subject areas

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


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