This paper presents a new point set surfacing method that employs neural networks for regression. Our technique takes as input unstructured and possibly noisy point sets representing two-manifolds in R3. To facilitate parametrization, the set is first embedded in R2 using neighborhood preserving locally linear embedding. A neural network is then constructed and trained that learns a mapping between the embedded 2D parametric coordinates and the corresponding 3D space coordinates. The trained network is then used to generate a tessellation that spans the parametric space, thereby producing a surface in the original space. This approach enables the surfacing of noisy and non-uniformly distributed point sets, and can be applied to open or closed surfaces. We show the utility of the proposed method on a number of test models, as well as its application to freeform surface creation in virtual reality environments.
M. Ersin Yumer, Levent Burak Kara. (2011). Conceptual Design of Freeform Surfaces from Unstructured Point Sets Using Neural Network Regression. ASME International Design Engineering Technical Conferences/DAC. Washington D.C.