Tracking Point-Curve Critical Distances

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Tracking Point-Curve Critical Distances
This paper presents a novel approach to continuously and robustly tracking critical (geometrically, perpendicular and/or extremal) distances from a moving plane point p ∈ R2 to a static parametrized piecewise rational curve γ(s) (s ∈ R). The approach is a combination of local marching, and the detection and computation of global topological change, both based on the differential properties of a constructed implicit surface; it does not use any global search strategy except the initialization. Implementing the mathematical idea from singularity community, we encode a particular critical distance as a point ps = (p, s) in the so-called augmented parametric space R3 = R2 × R, and the totality of point ps’s (when p moves over the whole plane R2 ) as an implicit surface I in R3 . In most situations, when p is perturbed in the plane, all of its corresponding critical distances, are only evolved, without structural change, by marching on a sectional curve on I. However, occasionally,...
Xianming Chen, Elaine Cohen, Richard F. Riesenfeld
Added 11 Jun 2010
Updated 11 Jun 2010
Type Conference
Year 2006
Where GMP
Authors Xianming Chen, Elaine Cohen, Richard F. Riesenfeld
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