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Advisor(s)
Abstract(s)
In computer graphics, most algorithms for sampling implicit surfaces
use a 2-points numerical method. If the surface-describing
function evaluates positive at the first point and negative at the second
one, we can say that the surface is located somewhere between
them. Surfaces detected this way are called sign-variant implicit
surfaces. However, 2-points numerical methods may fail to detect
and sample the surface because the functions of many implicit surfaces
evaluate either positive or negative everywhere around them.
These surfaces are here called sign-invariant implicit surfaces. In
this paper, instead of using a 2-points numerical method, we use a
1-point numerical method to guarantee that our algorithm detects
and samples both sign-variant and sign-invariant surface components
or branches correctly. This algorithm follows a continuation
approach to tessellate implicit surfaces, so that it applies symbolic
factorization to decompose the function expression into symbolic
components, sampling then each symbolic function component separately.
This ensures that our algorithm detects, samples, and triangulates
most components of implicit surfaces.
Description
Keywords
Implicit surfaces Polygonization Symbolic factorization Numerical methods.