Critical Points of Polynomial Metaballs

Proc. Implicit Surfaces '98, June 1998, pp. 69-76

Maintaining a triangle mesh on a changing implicit surface provides an amortized method for efficiently polygonizing an implicit surface animation. Such maintenance requires special attention to the triangular mesh, including mesh reconnection when the implicit surface changes topological type, and optimization to ensure the triangles are well shaped. For added efficiency, piecewise polynomial metaballs are often used, but introduce special problems in finding the critical points necessary to determine topological type.

There are numerous details important to implementing such techniques on piecewise polynomial metaballs. Two new metaball kernels are compared with an existing kernel for finding and classifying critical points. Interval versions of metaball kernels and their derivatives are derived to ease implementation. A simplified technique for searching for critical points is given, along with modifications that cause the search to avoid regions of degenerate critical points surrounding piecewise polynomial metaballs. Recent methods for maintaining an optimal mesh on a changing surface are compared. Dynamic surfaces
pose new problems to existing meshing optimizations and specific solutions are developed and presented.

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