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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>
Continuous Collision Detection for Ellipsoids
Yi-King Choi,Jung-Woo Chang,Wenping Wang,Myung-Soo Kim,Elber, G. IEEE 2009 IEEE transactions on visualization and computer gr Vol.15 No.2
<P>We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition described in terms of the signs of roots of the characteristic equation of two ellipsoids. Then we derive a time-dependent characteristic equation for two moving ellipsoids, which enables us to develop a real-time algorithm for computing the time intervals in which two moving ellipsoids collide. The effectiveness of our approach is demonstrated with several practical examples.</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>
Lensink, Marc F.,Velankar, Sameer,Kryshtafovych, Andriy,Huang, Shen‐,You,Schneidman‐,Duhovny, Dina,Sali, Andrej,Segura, Joan,Fernandez‐,Fuentes, Narcis,Viswanath, Shruthi,Elber, Ron John Wiley and Sons Inc. 2016 Proteins Vol.84 No.-
<P><B>ABSTRACT</B></P><P>We present the results for CAPRI Round 30, the first joint CASP‐CAPRI experiment, which brought together experts from the protein structure prediction and protein–protein docking communities. The Round comprised 25 targets from amongst those submitted for the CASP11 prediction experiment of 2014. The targets included mostly homodimers, a few homotetramers, and two heterodimers, and comprised protein chains that could readily be modeled using templates from the Protein Data Bank. On average 24 CAPRI groups and 7 CASP groups submitted docking predictions for each target, and 12 CAPRI groups per target participated in the CAPRI scoring experiment. In total more than 9500 models were assessed against the 3D structures of the corresponding target complexes. Results show that the prediction of homodimer assemblies by homology modeling techniques and docking calculations is quite successful for targets featuring large enough subunit interfaces to represent stable associations. Targets with ambiguous or inaccurate oligomeric state assignments, often featuring crystal contact‐sized interfaces, represented a confounding factor. For those, a much poorer prediction performance was achieved, while nonetheless often providing helpful clues on the correct oligomeric state of the protein. The prediction performance was very poor for genuine tetrameric targets, where the inaccuracy of the homology‐built subunit models and the smaller pair‐wise interfaces severely limited the ability to derive the correct assembly mode. Our analysis also shows that docking procedures tend to perform better than standard homology modeling techniques and that highly accurate models of the protein components are not always required to identify their association modes with acceptable accuracy. Proteins 2016; 84(Suppl 1):323–348. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.</P>