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DTSTAMP:20260817T171532Z
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:Haoran Sun (State Key Laboratory of CAD&CG, Zhejiang Universit
 y); Jingkai Wang (State Key Laboratory of CAD&CG, Zhejiang University; Sha
 nghai Jiao Tong University); and Hujun Bao and Jin Huang (State Key Labora
 tory of CAD&CG, Zhejiang University)\n\nFor a fixed polygon, one can easil
 y determine whether a point is inside or\noutside it using the winding num
 ber. However, deforming a given polygon\nbased on a set of points with exp
 ected inside/outside labeling is much more\ndifficult. It asks the winding
  number to be differentiable with respect to loca-\ntions of the inside/ou
 tside test point and the polygon vertices. We propose a\nmethod to address
  this even for a possibly intersected 2D polygon through\nGaussian kernel 
 convolution. Our method can be applied to various prob-\nlems such as reso
 lving embedding issues (e.g., intersections), editing curves\nusing an in-
 out brush, and offsetting curves with feature preservation.\nIt may seem d
 ifficult to compute the value and derivatives of this smoothed\nwinding nu
 mber (GauWN) efficiently, but the cost is only 4 to 6 times that of\nthe v
 anilla one. To achieve this efficiency, we employ two key strategies: 1)\n
 For value computation, we extend the divergence theorem to handle self-\ni
 ntersected cases and transform the convolution into a line integral that c
 an\nbe computed efficiently. 2) For derivatives, we utilize local decompos
 ition to\nfind a line integral form and leverage the radial symmetry and o
 rthogonal\nseparability of the Gaussian kernel. With this differentiable w
 inding number,\nwe can solve the aforementioned problems efficiently by fo
 rmulating them\nto involve both the explicit boundary and its implicit fie
 ld. Surprisingly,\nthere is no need to create a background mesh despite th
 e involvement of an\nimplicit field, making our method easy to apply.\n\nR
 egistration Category: Full Access, Full Access Supporter\n\nLanguage Forma
 t: English Language\n\nSession Chair: Mirela Ben-Chen (Technion – Israel I
 nstitute of Technology)\n\n
URL:https://asia.siggraph.org/2024/program/?id=papers_209&sess=sess133
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