Method and system for generating polygon meshes approximating surfaces using iteration for mesh vertex positions

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.