Topology guaranteed and error controlled curve tracing for parametric surface-surface intersection

We present a novel and efficient curve tracing method of the intersection of two parametric surfaces with error bound controlled and correct topology. Our method decomposes the 4D intersection curve in the parameter space into strongly monotonic curve segments such that their corresponding 3D curve segments in the model space are also strongly monotonic. This decomposition strategy can prevent straying or looping and maintain the 3D topology between the curve segments. Furthermore, by controlling the density of decomposition in the model space, our method can easily control the error bound of the numerical approximation of the curve segments. As a result, our method is very efficient compared to previous related work. Our experiments support our claims.