Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
A polygonal approximation to direct scalar volume rendering
VVS '90 Proceedings of the 1990 workshop on Volume visualization
Octrees for faster isosurface generation
ACM Transactions on Graphics (TOG)
Distance approximations for rasterizing implicit curves
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
Medical Imaging: Surface Mapping Brain Function on 3D Models
IEEE Computer Graphics and Applications
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A-patches are a form of representation of an algebraic curve or surface over a simplex. The A-patch conditions can be used as the basis for an adaptive subdivision style marching tetrahedra algorithm whose advantage is that it guarantees that we do not miss features of the algebraic: singularities are localized, and in regions around nearby multiple sheets, the subdivision process continues until the sheets are separated. Unfortunately, the A-patch single sheet conditions are too strict: for some algebraics, the subdivision process converges slowly or fails to converge. In this paper, I give an additional single sheet condition for curves that allows for convergence of this process. I also give additional conditions for surfaces that trades off some of the single sheet guarantees for improved convergence.