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The Visual Computer

, Volume 11, Issue 1, pp 52–62 | Cite as

On generating topologically consistent isosurfaces from uniform samples

  • B. K. Natarajan
Article

Abstract

A set of sample points of a function of three variables may be visualized by defining an interpolating functionf of the samples and examining isosurfaces of the formf(x, y, z)=t for various values oft. To display the isosurfaces on a graphics device, it is desirable to approximate them with piecewise triangular surfaces that (a) are geometrically good approximations, (b) are topologically consistent, and (c) consist of a small number of triangles. By topologically consistent we mean that the topology of the piecewise triangular surface matches that of the surfacef(x, y, z)=t, i.e., the interpolantf determines both the geometry and the topology of the piecewise triangular surface. In this paper we provide an efficient algorithm for the case in whichf is the piecewise trilinear interpolant; for this case existing methods fail to satisfy all three of the above conditions simultaneously.

Key words

Isosurfaces Topologically consistent Saddle points Trilinear interpolation 

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • B. K. Natarajan
    • 1
  1. 1.Hewlett-Packard LaboratoriesPalo AltoUSA

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