This paper develops a new approach to surface modeling and reconstruction which overcomes some important limitations of existing surface representation methods, such as their tendency to impose restrictive assumptions about object topology. The approach features two components. The first is a dynamic, self-organizing, oriented particle system which discovers topological and geometric surface structure implicit in visual data. The oriented particles evolve according to Newtonian mechanics and interact through long-range attraction forces, short-range repulsion forces, co-planarity, co-normality, and co-circularity forces. The second component is an efficient triangulation scheme which connects the particles into a continuous global surface model that is consistent with the inferred structure. We develop a flexible surface reconstruction algorithm that can compute complete, detailed, viewpoint invariant geometric surface descriptions of objects with arbitrary topology. We apply our algorithms to 3-D medical image segmentation and surface reconstruction from object silhouettes.