Dynamic Mesh Optimization with Curvature Dependent Subdivision for Polygonized Implicit Surfaces with Sharp Features

Converting from implicit surfaces into polygons and further optimization are a preprocessing step in rendering implicit surfaces for visualization and other uses. This paper describes a simple method for accurate polygonization of implicit surfaces with sharp features. First, an initial coarse mesh is generated by traditional Marching Cubes (MC) method, Then the mesh is used to approximate the implicit surface with simultaneous control of mesh vertex positions, regularity and normals. The refined mesh finally converges to a limit mesh which represents a high quality approximation of the implicit surface. To reconstruct small surface features, the optimization process combines with a curvature dependent mesh adaptive subdivision. For analyzing how close the refined mesh approximates the implicit surface, two error metrics are applied. One measures the deviations of the mesh vertices from the implicit surface, while the other measures the deviations of the mesh normals from the implicit surface.