Isosurface construction in any dimension using Convex Hulls

IEEE Transactions on Visualization and Computer Graphics
Praveen BhaniramkaRoger Crawfis

Abstract

We present an algorithm for constructing isosurfaces in any dimension. The input to the algorithm is a set of scalar values in a d-dimensional regular grid of (topological) hypercubes. The output is a set of (d-1)-dimensional simplices forming a piecewise linear approximation to the isosurface. The algorithm constructs the isosurface piecewise within each hypercube in the grid using the convex hull of an appropriate set of points. We prove that our algorithm correctly produces a triangulation of a (d-1)-manifold with boundary. In dimensions three and four, lookup tables with 2(8) and 2(16) entries, respectively, can be used to speed the algorithm's running time. In three dimensions, this gives the popular Marching Cubes algorithm. We discuss applications of four-dimensional isosurface construction to time varying isosurfaces, interval volumes, and morphing.

Citations

Jan 13, 2009·Cognitive Processing·Alexander Klippel
May 10, 2008·IEEE Transactions on Visualization and Computer Graphics·Federico Ponchio, Kai Hormann
Nov 8, 2008·IEEE Transactions on Visualization and Computer Graphics·Carlos A DietrichCláudio T Silva
Oct 17, 2009·IEEE Transactions on Visualization and Computer Graphics·Tiago EtieneCláudio T Silva
Oct 27, 2010·IEEE Transactions on Visualization and Computer Graphics·Marc Khoury, Rephael Wenger
Jan 16, 2010·IEEE Transactions on Visualization and Computer Graphics·Peer-Timo BremerJohn B Bell
Sep 15, 2007·Journal of Neurophysiology·Andrey V Olypher, Ronald L Calabrese

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