Efficient Point Projection to Freeform Curves and Surfaces

We present an efficient algorithm for projecting a given point to its closest point on a family of freeform C1-continuous curves and surfaces. The algorithm is based on an efficient culling technique that eliminates redundant curves and surfaces which obviously contain no projection from the given p...

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Bibliographic Details
Published inAdvances in Geometric Modeling and Processing pp. 192 - 205
Main Authors Oh, Young-Taek, Kim, Yong-Joon, Lee, Jieun, Kim, Myung-Soo, Elber, Gershon
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Curve Segment
Distance Function
Point Projection
Query Point
Voronoi Cell
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Summary:We present an efficient algorithm for projecting a given point to its closest point on a family of freeform C1-continuous curves and surfaces. The algorithm is based on an efficient culling technique that eliminates redundant curves and surfaces which obviously contain no projection from the given point. Based on this scheme, we can reduce the whole computation to considerably smaller subproblems, which are then solved using a numerical method. In several experimental results, we demonstrate the effectiveness of the proposed approach.
ISBN:3642134106
9783642134104
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-13411-1_13