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BEGIN:VEVENT
DTSTAMP:20250110T023309Z
LOCATION:Hall B5 (1)\, B Block\, Level 5
DTSTART;TZID=Asia/Tokyo:20241203T145600
DTEND;TZID=Asia/Tokyo:20241203T150800
UID:siggraphasia_SIGGRAPH Asia 2024_sess106_papers_401@linklings.com
SUMMARY:Projected Walk on Spheres: A Monte Carlo Closest Point Method for 
 Surface PDEs
DESCRIPTION:Technical Papers\n\nRyusuke Sugimoto, Nathan King, Toshiya Hac
 hisuka, and Christopher Batty (University of Waterloo)\n\nWe present proje
 cted walk on spheres (PWoS), a novel pointwise and discretization-free Mon
 te Carlo solver for surface PDEs with Dirichlet boundaries, as a generaliz
 ation of the walk on spheres method (WoS)  [Muller 1956; Sawhney and Crane
  2020]. We adapt the recursive relationship of WoS designed for PDEs in vo
 lumetric domains to a volumetric neighborhood around the surface, and at t
 he end of each recursion step, we project the sample point on the sphere b
 ack to the surface. We motivate this simple modification to WoS with the t
 heory of the closest point extension used in the closest point method. \nT
 o define the valid volumetric neighborhood domain for PWoS, we develop str
 ategies to estimate the local feature size of the surface and to compute t
 he distance to the Dirichlet boundaries on the surface extended in their n
 ormal directions. We also design a mean value filtering method for PWoS to
  improve the method's efficiency when the surface is represented as a poly
 gonal mesh or a point cloud. Finally, we study the convergence of PWoS and
  demonstrate its application to graphics tasks, including diffusion curves
 , geodesic distance computation, and wave propagation animation. We show t
 hat our method works with various types of surfaces, including a surface o
 f mixed codimension.\n\nRegistration Category: Full Access, Full Access Su
 pporter\n\nLanguage Format: English Language\n\nSession Chair: Yonghao Yue
  (Aoyama Gakuin University)
URL:https://asia.siggraph.org/2024/program/?id=papers_401&sess=sess106
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