بسمه تعالی
روز هندسه محاسباتی و هندسه معماری
دوشنبه ۳ اسفند ۱۳۹۴
دانشکده ریاضی- دانشگاه یزد
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برنامه سخنرانیها (امکان تغییر برنامه وجود دارد)د |
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چکیده |
عنوان |
سخنران |
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| Many of today’s most striking buildings are nontraditional freeform shapes. While the digital design of freeform geometry with current modeling tools is well understood, the actual fabrication on the architectural scale is a big challenge, but also a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in the emerging field of Architectural Geometry, elaborate on important relations to contemporary research in Geometry and Computer Graphics, and illustrate the transfer of mathematical research into the architectural practice at hand of selected projects. | Architectural Geometry | ساعت ۹ الی ۱۰ |
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| We consider a number of motion planning reconfiguration problems that involve n degrees-of-freedom. Several open problems will be mentioned. | Reconfiguration problems in motion planning | ساعت ۱۰ الی ۱۱ |
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پذیرایی |
ساعت ۱۱ الی ۲۰: ۱۱ |
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| We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay triangulation; the second finds the Delaunay triangulation, given a compressed quadtree. Both algorithms run in deterministic linear time on a pointer machine. Our work builds on and extends previous results by Krznaric and Levcopolous and Buchin and Mulzer. Our main tool for the second algorithm is the well-separated pair decomposition (WSPD), a structure that has been used previously to find Euclidean minimum spanning trees in higher dimensions. We show that knowing the WSPD (and a quadtree) suffices to compute a planar EMST in linear time. With the EMST at hand, we can find the Delaunay triangulation in linear time. As a corollary, we obtain deterministic versions of many previous algorithms related to Delaunay triangulations, such as splitting planar Delaunay triangulations, preprocessing imprecise points for faster Delaunay computation, and transdichotomous Delaunay triangulations. | Triangulating the Square: Quadtrees and Delaunay Triangulations are Equivalent | ساعت ۲۰: ۱۱ الی ۱۰: ۱۲ |
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