Fast implicit surface reconstruction method based on normal constraints

In this paper, a new procedure for implicit surface reconstruction from oriented points is presented. A normal constraints based implicit polynomials fitting method and the partition of unity approach are fused into our framework. Firstly, a large scale input data is subdivided into some overlapping patches by octree. Then the global implicit surface is transferred into local implicit patch fitting and blending of them. To fit the local implicit polynomials, we build an energy by three steps corresponding to enforcement of the interpolatory constraints, satisfying of normal constraints and enhancement of fitting stability. The unkowns in an implicit polynomial are determined by minimizing this quadratic energy function. It is demonstrated in some experiments with several real data sets that this combination provides an intuitive and effective means to approximate the scattered point data associated normals.