Implicit modeling from polygon soup using convolution

We present a novel method for creating implicit surfaces from polygonal models. The implicit function is defined by convolving a kernel with the triangles in the polygonal model. By adopting a piecewise quartic polynomial kernel function with a finite support, we derive a convolution model that has a closed-form solution, and thus can be efficiently evaluated. The user only needs to specify an effective radius of influence to generate an implicit surface of desired closeness to the polygonal model. The resulting implicit surface is fast to evaluate, not requiring accumulating evaluation results using any hierarchical data structure, and can be efficiently ray-traced to reveal the detailed features.