Non-manifold implicit surfaces based on discontinuous implicitization and polygonization

Implicit surfaces in 3D geometric modeling are limited to two manifolds because the corresponding implicit fields are usually defined by real-valued functions which bisect space into interior and exterior. We present a novel method of modeling non-manifold surfaces by implicit representation. Our method allows discontinuity of the field function and assesses the special meaning of the locus where the function is not differentiable. The enhancement can yield a non-manifold surface with such features as holes and boundaries. The discontinuous field function also enables multiple classification of the field, which makes it possible to represent branches and intersections of the implicit surfaces. The implicit field is polygonized by the algorithm based on the marching cubes algorithm, which is extended to treat discontinuous fields correctly. We also describe an efficient implementation of converting a surface model into a set of discrete samples of field function, and finally present the result of the non-manifold surfaces reproduced by our method.