Isosurface Polygonization using Hyperbolic Arcs to Resolve Topological Ambiguity Problems

Pasko A. A., Pilyugin V. V., Pokrovskiy V. N.,
"Geometric modeling in the analysis of trivariate functions",
Computers and Graphics, vol.12, Nos.3/4, 1988, pp.457-465.
Electronic version: scanned, PDF (3.6Mb)

It is an English translation of
Pasko A. A., Pilyugin V. V., Pokrovskiy V. N., Using computer geometry for analysis of functions of three variables, Communications of Joint Institute of Nuclear Research, JINR P10-86-310, Dubna, Russia, 1986, 10 p. (in Russian).
Electronic version: PDF (298K) scanned by the SPIRES HEP project (U. Stanford).


An algorithm of polygonization of an isosurface of a function of three variables is presented. Trilinear interpolation inside a cell and bilinear interpolation on a cell face are used for the hyperbolic arcs detection at faces of a cubic cell and for the construction of the edges connectivity graph to resolve topological ambiguities.

a b
c d

Algorithm of isosurface polygonization using hyperbolic arcs:
a) subdivision of a bounding box into rectangular cells;
b) example of surface patches inside a cell with hyperbolic arc boundaries on the cell faces;
c) cycles in the connectivity graph corresponding to surface patches in the cell;
d) topological ambiguity case of four intersection points of cell face edges with the isosurface is resolved using hyperbolic arcs (resulting from the trilinear interpolation inside the cell and the bilinear interpolation on the cell face).

This algorithm is implemented in the HyperFun Polygonizer.
See examples of polygonized isosurfaces at the HyperFun Gallery.

See the related topics:
Sharp Features of Polygonized Implicit Surfaces
Surface and Volume Discretization of Functionally Based Heterogeneous Objects
Trimmimg Implicit Surfaces

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