We present a new point set surfacing method based on a data-driven mapping between the parametric and geometric spaces. Our approach takes as input an unstructured and possibly noisy point set representing a two-manifold in R3. To facilitate parameterization, the set is first embedded in R2 using neighborhood-preserving locally linear embedding. A learning algorithm is then trained to learn a mapping between the embedded two-dimensional (2D) coordinates and the corresponding three-dimensional (3D) space coordinates. The trained learner is then used to generate a tessellation spanning the parametric space, thereby producing a surface in the geometric space. This approach enables the surfacing of noisy and non-uniformly distributed point sets. We discuss the advantages of the proposed method in relation to existing methods, and show its utility on a number of test models, as well as its applications to modeling in virtual reality environments.
M. Ersin Yumer, Levent Burak Kara. (2012). Surface Creation on Unstructured Point Sets Using Neural Networks. Computer Aided Design, Volume 44, Issue 7, pp. 644-656.