Complexity of computing nice viewpoints of objects in space

Godfried T. Toussaint

Research output: Contribution to journalConference articlepeer-review


A polyhedral object in 3-dimensional space is often well represented by a set of points and line segments that act as its features. By a nice viewpoint of an object we mean a projective view in which all (or most) of the features of the object, relevant for some task, are clearly visible. Such a view is often called a non-degenerate view or projection. In this paper we are concerned with computing non-degenerate orthogonal and perspective projections of sets of points and line segments (objects) in 3-dimensional space. We outline the areas in which such problems arise, discuss recent research on the computational complexity of these problems, illustrate the fundamental ideas used in the design of algorithms for computing non-degenerate projections, and provide pointers to the literature where the results can be found.

Original languageEnglish (US)
Pages (from-to)1-11
Number of pages11
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2000
EventVision Geometry IX - San Diego, CA, USA
Duration: Jul 30 2000Jul 31 2000

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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