Loop Subdivision Surface Fitting by Geometric Algorithms

This paper describes a method to approximate point sets by Loop subdivision surfaces based on geometric algorithms. We assume that the data points are given in triangular mesh of arbitrary topological type. The initial control mesh of the Loop subdivision surface is obtained by simplifying the input triangular mesh using QEM algorithm. Our algorithm iteratively updates the control mesh in a global manner based on a simple point-surface distance computation followed by translations of the control vertices along the displacement vectors. The main advantages of our approach compared to existing surface fitting methods are simplicity, speed, and generality. Computational results show that our algorithm runs at least six times faster than current state-of-the-art subdivision fitting methods. We demonstrate our technique with a variety of complex examples.