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Efficient convex hull computation for planar freeform curves
Kim, Yong-Joon,Lee, Jieun,Kim, Myung-Soo,Elber, Gershon Elsevier 2011 Computers & graphics Vol.35 No.3
<P><B>Abstract</B></P><P>We present an efficient real-time algorithm for computing the precise convex hulls of planar freeform curves. For this purpose, the planar curves are initially approximated with <I>G</I><SUP>1</SUP>-biarcs within a given error bound ε in a preprocessing step. The algorithm is based on an efficient construction of approximate convex hulls using circular arcs. The majority of redundant curve segments can be eliminated using simple geometric tests on circular arcs. In several experimental results, we demonstrate the effectiveness of the proposed approach, which shows the performance improvement in the range of 200–300 times speed up compared with the previous results (Elber et al., 2001) <ce:cross-ref refid='bib8'>[8]</ce:cross-ref>.</P> <P><B>Graphical abstract</B></P><P><ce:figure id='f0050'></ce:figure></P><P><B>Highlights</B></P><P>► We present an efficient real-time algorithm for computing the precise convex hulls for planar freeform curves with <I>G</I><SUP>1</SUP>-biarc approximation. ► The algorithm is based on an efficient construction of approximate convex hulls using circular arcs. ► The majority of redundant curve segments can be eliminated using simple geometric tests on circular arcs.</P>
Trimming offset surface self-intersections around near-singular regions
Hong, Q Youn,Park, Youngjin,Kim, Myung-Soo,Elber, Gershon Elsevier 2019 Computers & graphics Vol.82 No.-
<P><B>Abstract</B></P> <P>We present a new method for offset surface trimming that eliminates redundant parts of an offset surface that are closer than the offset distance to the original surface. The proposed approach deals with numerical instability around near-singular regions of an offset surface using the concept of offset trimming regions in the parameter space and carrying out numerical computations based on the regularity and intrinsic properties of the given input surface. In particular, we replace the self-intersection of an offset surface (which can be unstable around near-singular regions) by computation on the original input surface (and its derivatives) only, and also by the intersection of osculating tori that can be constructed in a highly stable way by offsetting the osculating tori of the given input regular surface. We demonstrate the effectiveness of our approach using non-trivial test examples of offset surface trimming, including some examples from the previous publications for the purpose of comparison.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A new algorithm for offset surface trimming that eliminates redundant parts of an offset surface that are closer than the offset distance to the original surface. </LI> <LI> A new approach that can deal with numerical instability around near-singular regions of an offset surface. </LI> <LI> A unique approach that can handle offset trimming without using offset surface. </LI> </UL> </P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>