Lifting curve parameterization methods to isosurfaces Original Research Article

We describe a new technique for the parameterization of surfaces which applies to the isosurfaces produced by the marching cubes algorithm. The technique is motivated by methods of parameterization for curves including the centripetal and chord length methods. The technique for extending the concept of curve parameterization to an isosurface parameterization is based upon the 4*-network which is a collection of three mutually orthogonal planar polygons lying on and intersecting at the vertices of the marching cubes isosurface. Several examples from geometric modeling, and medical imaging analysis are included.