  In this paper, we propose a stochastic geometric iterative method to
approximate the high-resolution 3D models by finite Loop subdivision surfaces.
Given an input mesh as the fitting target, the initial control mesh is
generated using the mesh simplification algorithm. Then, our method adjusts the
control mesh iteratively to make its finite Loop subdivision surface
approximates the input mesh. In each geometric iteration, we randomly select
part of points on the subdivision surface to calculate the difference vectors
and distribute the vectors to the control points. Finally, the control points
are updated by adding the weighted average of these difference vectors. We
prove the convergence of our method and verify it by demonstrating error curves
in the experiment. In addition, compared with an existing geometric iterative
method, our method has a faster fitting speed and higher fitting precision.
