In this paper, we propose a new efficient topology estimation algorithm to construct a multiresolution polygonal mesh from measured three-dimensional (3-D) range data. The topology estimation problem is defined under the constraints of cognition, compactness, and regularity, and the algorithm is designed to be applied to either a cloud of points or a dense mesh. The proposed algorithm initially segments the range data into a finite number of Voronoi patches using the K-means clustering algorithm. Each patch is then approximated by an appropriate polygonal and eventually a triangular mesh model. In order to improve the equiangularity of the mesh, we employ a dynamic mesh model, in which the mesh finds its equilibrium state adaptively, according to the equiangularity constraint. Experimental results demonstrate that satisfactory equiangular triangular mesh models can be constructed rapidly at various resolutions, while yielding tolerable modeling error.