US 12,141,921 B2
Method and system for generating polygon meshes approximating surfaces using root-finding and iteration for mesh vertex positions
Alen Ladavac, Zagreb (HR); and Morgan Samuel McGuire, Waterloo (CA)
Assigned to Roblox Corporation, San Mateo, CA (US)
Filed by Roblox Corporation, San Mateo, CA (US)
Filed on Jun. 2, 2022, as Appl. No. 17/831,310.
Prior Publication US 2023/0394767 A1, Dec. 7, 2023
This patent is subject to a terminal disclaimer.
Int. Cl. G06T 17/20 (2006.01)
CPC G06T 17/205 (2013.01) [G06T 2200/04 (2013.01)] 18 Claims
OG exemplary drawing
 
1. A computer-implemented method comprising:
receiving, by one or more processors, input data that represents a surface that distinguishes an inside and an outside of a volume;
determining, by the one or more processors, a voxel grid that includes the surface, wherein the voxel grid includes a plurality of voxels;
identifying, by the one or more processors, particular voxels of the voxel grid which the surface intersects; and
generating, by the one or more processors, a mesh that approximates the surface, the mesh including a plurality of polygons that are defined by vertices of the mesh in the particular voxels, wherein generating the mesh includes determining positions of the vertices using a root-finding technique that finds roots of a surface function that describes the surface, wherein the root-finding technique includes, for each vertex of the vertices:
determining an approximate position of the vertex based on a root of the surface function determined based on a derivative of the surface function;
determining an error between the approximate position and the surface; and
determining a new approximate position of the vertex within an associated voxel to reduce the error.