Abstract: Generating polygon meshes that approximate surfaces using iteration for mesh vertex positions. In some implementations, a method includes receiving input data that represents a surface distinguishing a volume, where a voxel grid includes the surface. Particular voxels of the voxel grid are identified, which the surface intersects. A surface-approximating mesh is generated including polygons defined by vertices in the particular voxels. Generating the mesh includes determining approximate positions of a subset of the vertices in a subset of the particular voxels, based on interpolation of locations in the voxel subset where the surface intersects the voxel subset. Errors between approximate voxel values (based on the approximate positions) and assigned voxel values of the particular voxels (based on the input data) are determined, and the approximate position of at least one vertex of the subset of the vertices is adjusted using a successive over-relaxation technique to reduce the errors.

Abstract: Generating polygon meshes that approximate surfaces using root-finding and iteration for mesh vertex positions. In some implementations, a method includes receiving input data that represents a surface that distinguishes an inside and an outside of a volume. A voxel grid that includes the surface is determined, the voxel grid including a plurality of voxels. Particular voxels of the voxel grid are identified, which the surface intersects. A mesh is generated that approximates the surface, the mesh including a plurality of polygons that are defined by vertices in the particular voxels. 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.

Abstract: Generating polygon meshes that approximate surfaces using iteration for mesh vertex positions. In some implementations, a method includes receiving input data that represents a surface distinguishing a volume, where a voxel grid includes the surface. Particular voxels of the voxel grid are identified, which the surface intersects. A surface-approximating mesh is generated including polygons defined by vertices in the particular voxels. Generating the mesh includes determining approximate positions of a subset of the vertices in a subset of the particular voxels, based on interpolation of locations in the voxel subset where the surface intersects the voxel subset. Errors between approximate voxel values (based on the approximate positions) and assigned voxel values of the particular voxels (based on the input data) are determined, and the approximate position of at least one vertex of the subset of the vertices is adjusted using a successive over-relaxation technique to reduce the errors.