Moving Least Squares for point set smoothing and differential properties estimation

Mentor: MELLADO Nicolas, GIRAUDOT Simon

Project description: The goal of this project is to add Moving Least Squares surface reconstruction algorithms to the point set processing component. This family of algorithms reconstruct an implicit surface from a point set by fitting and projecting each point on a primitive (plane, sphere) fitting its neighborhood. The resulting surface is a smooth approximation of the input point cloud (smoothing degree is controlled by the primitive type and neighborhood size). Depending on the used primitive, several differential properties of the surface can be estimated. This work will be split in two parts. First, implement a wrapper to the Ponca library, a lightweight library for point-based primitive fitting. Second, add algorithms exploiting this wrapper: e.g., smoothing, and differential estimators. Related packages:

• point set smoothing: https://doc.cgal.org/latest/Point_set_processing_3/index.html#Point_set_processing_3Smoothing
• differential estimators: https://doc.cgal.org/latest/Jet_fitting_3/index.html

Required Skills: C++14, Point Sets, Surface Fitting

Contact: nicolas.mellado@irit.fr, simon.giraudot@geometryfactory.com

Link to original proposal: https://github.com/CGAL/cgal/wiki/Project-Ideas#moving-least-squares-for-point-set-smoothing-and-differential-properties-estimation