Self-intersections of offsets of quadratic surfaces

Part I, Explicit surfaces

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Although offset surfaces are widely used in various engineering applications, their degenerating mechanism is not well known in a quantitative manner. Offset surfaces are functionally more complex than their progenitor surfaces and may degenerate even if the progenitor surfaces are regular. Self-intersections of the offsets of regular surfaces may be induced by concave regions of surface where the positive offset distance exceeds the maximum absolute value of the negative minimum principal curvature or the absolute value of the negative offset distance exceeds the maximum value of the positive maximum principal curvature. It is well known that any regular surface can be locally approximated in the neighborhood of a point p by the explicit quadratic surface of the form r(x, y) = [x, y,1/2(αx2 + βy2)]T to the second order where -α and -βare the principal curvatures at point p. Therefore investigations of the selfintersecting mechanisms of the offsets of explicit quadratic surfaces due to differential geometry properties lead to an understanding of the self-intersecting mechanisms of offsets of regular parametric surfaces. In this paper, we develop the equations of the self-intersection curves of an offset of an explicit quadratic surface. We also develop an algorithm to detect and trace a small loop of a self-inter section curve of an offset of a regular parametric surface based on our analysis of offsets of explicit quadratic surfaces. Examples illustrate our method.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalEngineering with Computers
Volume14
Issue number1
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes

Fingerprint

Self-intersection
Principal curvature
Offset Surface
Parametric Surfaces
Absolute value
Exceed
Region of surface
Curve
Differential Geometry
Engineering Application
Trace

Keywords

  • NC machining
  • Offset
  • 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 I, Explicit surfaces. / Maekawa, Takashi.

In: Engineering with Computers, Vol. 14, No. 1, 01.01.1998, p. 1-13.

Research output: Contribution to journalArticle

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