I am confused about what our geometry representation is for arbitrary (e.g. frogs) shapes. If we don't have meshing, what is the data model that is traversed to render a frog with walk on spheres?
Thanks for the question. Grid free MC methods like WoS avoid the need for volumetric meshing (unlike say FEM), but they still require a geometric representation of the surface of the domain that you can perform distance queries on to simulate random walks. The latter could be a mesh, implicit function, nurbs patch etc., the only prerequisite is the ability to compute the distance to the surface. Volumetric meshing can often be a pretty big bottleneck, especially on complex models (such as the frog), so WoS offers a way to bypass that step for computing solutions to common PDEs. If I remember correctly, the frog model is a (surface) mesh extracted from a CT scan. You can perform distance queries fairly quickly to a surface mesh with tree based data structures such as a BVH.
@@rohansawhney1583 hi in relation to this i wanted to ask: what if i have many uniformly sampled points on the surface , i can still compute the closest distance to those, however the query point could escape the region. Maybe having sampled enough boundary points and set an large enough minimum radius could prevent this.
Thanks so much for this clear and concise explanation! Great work!
Amazing work, I learned from you at 2 Minute Papers
Really clear explanation and really interesting paper!
Absolutely amazing video! Subscribed.
Thank you! Very excited to see the applications.
nice work bro
Really awesome concept, and fantastically presented!
Do you use Blender?
I am confused about what our geometry representation is for arbitrary (e.g. frogs) shapes. If we don't have meshing, what is the data model that is traversed to render a frog with walk on spheres?
Thanks for the question. Grid free MC methods like WoS avoid the need for volumetric meshing (unlike say FEM), but they still require a geometric representation of the surface of the domain that you can perform distance queries on to simulate random walks. The latter could be a mesh, implicit function, nurbs patch etc., the only prerequisite is the ability to compute the distance to the surface. Volumetric meshing can often be a pretty big bottleneck, especially on complex models (such as the frog), so WoS offers a way to bypass that step for computing solutions to common PDEs. If I remember correctly, the frog model is a (surface) mesh extracted from a CT scan. You can perform distance queries fairly quickly to a surface mesh with tree based data structures such as a BVH.
@@rohansawhney1583 hi in relation to this i wanted to ask: what if i have many uniformly sampled points on the surface , i can still compute the closest distance to those, however the query point could escape the region. Maybe having sampled enough boundary points and set an large enough minimum radius could prevent this.
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