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[SNU CSE Seminar/2020-01-21] Minkowski sum of pipe surfaces as a special type of skinning

2020-01-17l 조회수 3228


일자 : 2020년 1월 21일(화) 오후 2-4시
장소 : 302동 309-1호

제목 : Minkowski sum of pipe surfaces as a special type of skinning

연사 : Professor Roland Kunkli
(University of Debrecen, Hungary)

Abstract
The Minkowski sum of two objects has many applications in engineering, such as robot motion planning, collision detection, or NC machining; therefore, in recent years, numerous papers have been published on the topic of analyzing and computing it in the case of different two- and three-dimensional shapes. In most cases, the goal is obtaining the boundary of the Minkowski sum, which has an important relationship with the convolution of the considered objects. Generally, the computation is time-consuming as a result of trimming and the complexity of input shapes; but because of specialized applications that use moving objects, there is a growing demand for algorithms that can solve the problem in real-time.

Lots of research works deal with input models represented by polygonal meshes and provide outputs in this form as well. Nevertheless, in the case of some special groups of surfaces, the exact parametrization of the convolution surface exists, and by trimming it, we can obtain the Minkowski sum boundary as well. In this talk, we will present our results in analyzing the Minkowski sum boundary of pipe surfaces, which also belong to this latter mentioned group. The mentioned outcomes were motivated by a more general goal, computing the Minkowski sum of two parametrized skinning surfaces made by our previously published sphere-based algorithm.

After showing the exact parametrization of the convolution patches of general pipe surfaces, we will discuss the problem of common tangents and a possible solution to their exact calculation when the spines are circular arcs. We will also demonstrate our upgraded, grid-based trimming solution, with which we can run our algorithm in real-time when one object is static, and the other one is rotating around an arbitrary axis. At the end of the presentation, we will show a general approach that can help to create the Minkowski boundary of more general skinning surfaces as well.


문의: 3D Modeling and Processing Lab. (880-1840)

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