Hole filing and sharp edge extraction for surface completion of point set models

Abstract

A point set, one of the tools to represent geometry in 3D, has been used typically as original data to reconstruct triangular meshes or surfaces such as NURBS. As it became possible to represent surfaces only using point sets due to their high-density acquisition, there are extensive studies about surface completion methods by adding properties of surfaces to points directly since the 21st century. Though such researches give great quality for fitting smooth surfaces, there still remain several problems. If a point set has the defects where there is no data, especially when the sizes of such regions are quite large, it is difficult to repair with previous methods. In addition, since most of them are focusing on how to fit surfaces smoothly by removing noises, they rarely deal with sharp edges or small detailed features automatically. In this research, I accomplish the work to repair geometrical and apparent defects of incomplete point sets with big holes. This work does not only use boundary information of the hole to smoothly fill it, but use context of the whole model, and paste the most similar region among existing parts by deforming the copy as the appropriate shape with hole boundary. Appearance (texture) information as well as shape can be repaired in the same framework. Finding feature lines of point surfaces, especially sharp edges, the measure to calculate sharpness is defined to represent shapes rather than estimate curvatures with near neighbor points like most previous methods. Finally, as an application for manufacturing, I introduce a new computational framework to generate tool paths for machining directly from point sets using algebraic point set surfaces. This method does not suffer from local interferences, the main trouble of traditional offset methods with triangular meshes. The global interference can be also removed easily and the errors of final paths are acceptable.