# Isosurface construction in any dimension using Convex Hulls.IEEE Trans Vis Comput Graph. 2004 Mar-Apr; 10(2):130-41.IT

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.

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*IEEE Transactions On Visualization and Computer Graphics,*vol. 10, no. 2, 2004, pp. 130-41.

*IEEE Trans Vis Comput Graph*. 2004;10(2):130-41.

*IEEE Transactions On Visualization and Computer Graphics*,

*10*(2), 130-41.

*IEEE Trans Vis Comput Graph.*2004 Mar-Apr;10(2):130-41. PubMed PMID: 15384638.