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DTSTAMP:20250110T023312Z
LOCATION:Hall B5 (1)\, B Block\, Level 5
DTSTART;TZID=Asia/Tokyo:20241205T144500
DTEND;TZID=Asia/Tokyo:20241205T145900
UID:siggraphasia_SIGGRAPH Asia 2024_sess133_papers_209@linklings.com
SUMMARY:GauWN: Gaussian-smoothed Winding Number and its Derivatives
DESCRIPTION:Technical Papers\n\nHaoran Sun (State Key Laboratory of CAD&CG
 , Zhejiang University); Jingkai Wang (State Key Laboratory of CAD&CG, Zhej
 iang University; Shanghai Jiao Tong University); and Hujun Bao and Jin Hua
 ng (State Key Laboratory of CAD&CG, Zhejiang University)\n\nFor a fixed po
 lygon, one can easily determine whether a point is inside or\noutside it u
 sing the winding number. However, deforming a given polygon\nbased on a se
 t of points with expected inside/outside labeling is much more\ndifficult.
  It asks the winding number to be differentiable with respect to loca-\nti
 ons of the inside/outside test point and the polygon vertices. We propose 
 a\nmethod to address this even for a possibly intersected 2D polygon throu
 gh\nGaussian kernel convolution. Our method can be applied to various prob
 -\nlems such as resolving embedding issues (e.g., intersections), editing 
 curves\nusing an in-out brush, and offsetting curves with feature preserva
 tion.\nIt may seem difficult to compute the value and derivatives of this 
 smoothed\nwinding number (GauWN) efficiently, but the cost is only 4 to 6 
 times that of\nthe vanilla one. To achieve this efficiency, we employ two 
 key strategies: 1)\nFor value computation, we extend the divergence theore
 m to handle self-\nintersected cases and transform the convolution into a 
 line integral that can\nbe computed efficiently. 2) For derivatives, we ut
 ilize local decomposition to\nfind a line integral form and leverage the r
 adial symmetry and orthogonal\nseparability of the Gaussian kernel. With t
 his differentiable winding number,\nwe can solve the aforementioned proble
 ms efficiently by formulating them\nto involve both the explicit boundary 
 and its implicit field. Surprisingly,\nthere is no need to create a backgr
 ound mesh despite the involvement of an\nimplicit field, making our method
  easy to apply.\n\nRegistration Category: Full Access, Full Access Support
 er\n\nLanguage Format: English Language\n\nSession Chair: Mirela Ben-Chen 
 (Technion – Israel Institute of Technology)
URL:https://asia.siggraph.org/2024/program/?id=papers_209&sess=sess133
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