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DTSTAMP:20260817T171515Z
LOCATION:Hall C\, C Block\, Level 4
DTSTART;TZID=Asia/Tokyo:20241203T090000
DTEND;TZID=Asia/Tokyo:20241203T120000
UID:siggraphasia_SIGGRAPH Asia 2024_sess223_papers_401@linklings.com
SUMMARY:Projected Walk on Spheres: A Monte Carlo Closest Point Method for 
 Surface PDEs
DESCRIPTION:Ryusuke Sugimoto, Nathan King, Toshiya Hachisuka, and Christop
 her Batty (University of Waterloo)\n\nWe present projected walk on spheres
  (PWoS), a novel pointwise and discretization-free Monte Carlo solver for 
 surface PDEs with Dirichlet boundaries, as a generalization of the walk on
  spheres method (WoS)  [Muller 1956; Sawhney and Crane 2020]. We adapt the
  recursive relationship of WoS designed for PDEs in volumetric domains to 
 a volumetric neighborhood around the surface, and at the end of each recur
 sion step, we project the sample point on the sphere back to the surface. 
 We motivate this simple modification to WoS with the theory of the closest
  point extension used in the closest point method. \nTo define the valid v
 olumetric neighborhood domain for PWoS, we develop strategies to estimate 
 the local feature size of the surface and to compute the distance to the D
 irichlet boundaries on the surface extended in their normal directions. We
  also design a mean value filtering method for PWoS to improve the method'
 s efficiency when the surface is represented as a polygonal mesh or a poin
 t cloud. Finally, we study the convergence of PWoS and demonstrate its app
 lication to graphics tasks, including diffusion curves, geodesic distance 
 computation, and wave propagation animation. We show that our method works
  with various types of surfaces, including a surface of mixed codimension.
 \n\nRegistration Category: Enhanced Access, Full Access, Full Access Suppo
 rter\n\nLanguage Format: English Language\n\n
URL:https://asia.siggraph.org/2024/program/?id=papers_401&sess=sess106
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