Convex hulls of piecewise-smooth Jordan curves
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Cited by (35)
Precise convex hull computation for freeform models using a hierarchical Gauss map and a Coons bounding volume hierarchy
2014, CAD Computer Aided DesignCitation Excerpt :Early convex hull algorithms considered only discrete objects such as points, lines, polygons, or polyhedra [1]. Theoretical algorithms (with no implementation) have been designed for planar curves [5–7]. Practical algorithms with full implementation were developed in [2,8,4].
Efficient convex hull computation for planar freeform curves
2011, Computers and Graphics (Pergamon)Citation Excerpt :Early algorithms considered only discrete objects such as points, lines, polygons, or polyhedra [3,5,10,11,17–19]. Some theoretical algorithms were developed for planar curved regions [4,6,20]; however, they assumed certain curve operations which are difficult to implement in an efficient and robust way. In particular, the algorithms are based on rather expensive curve operations such as common tangent computation for pairs of curve segments.
A smooth, obstacle-avoiding curve
2006, Computers and Graphics (Pergamon)Citation Excerpt :A polygonal obstacle can be treated efficiently by representing it by the vertices of its convex hull. Even an obstacle with curved sides can be bounded by a convex polygon (see Fig. 6 and [15]). There is probably no general algorithm to find the “best” bounding convex polygon, but individual cases are often treated easily.
The convex hull of rational plane curves
2001, Graphical Models3-D localization and feature recovering through CAD-based stable pose calculation
2001, Pattern Recognition Letters
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Some of this work was done while A. A. Schäffer was a summer employee of AT & T Bell Laboratories; during the academic year his work is funded by a National Science Foundation Graduate Fellowship and by National Science Foundation Grant NSFDCR 83-00984.