Spiraling Edge: fast surface reconstruction from partially organized sample points

Abstract

Many applications produce three-dimensional points that must be further processed to generate a surface. Surface reconstruction algorithms that start with a set of unorganized points are extremely time-consuming. Sometimes, however, points are generated such that there is additional information available to the reconstruction algorithm. We present Spiraling Edge, a specialized algorithm for surface reconstruction that is three orders of magnitude faster than algorithms for the general case. In addition to sample point locations, our algorithm starts with normal information and knowledge of each point's neighbors. Our algorithm produces a localized approximation to the surface by creating a star-shaped triangulation between a point and a subset of its nearest neighbors. This surface patch is extended by locally triangulating each of the points along the edge of the patch. As each edge point is triangulated, it is removed from the edge and new edge points along the patch's edge are inserted in its place. The updated edge spirals out over the surface until the edge encounters a surface boundary and stops growing in that direction, or until the edge reduces to a small hole that is filled by the final triangle.

Survey on 3D Surface Reconstruction

“…From the candidate points and points in the local Delaunay neighborhood, the triangulated surface is generated in the last step. A similar approach with more assumptions for the dataset is presented in [19].…”

“…The Ball Pivoting Algorithm [19] is very simple and efficient in terms of memory requirement and computing resource consumption. Moreover, it is robust to noise and capable of handling real range scan data.…”

Re-Sampled Based Mixed Surface Reconstruction Algorithm

“…近年来，随着三维测量设备的普及，对扫描结果进 行曲面重建已成为快速获取几何模型的一个关键步骤， 在虚拟训练、逆向工程等领域均具有重要的意义。过去 的几十年中，国内外很多研究者针对散乱数据的三角网 格曲面重建问题进行了广泛的研究，Hoppe等人 [1][2][3] 通过 采用抽取等值面的MC(Marching Cube，步进立方体) 算法来重建三角网格模型， 虽然自动化程度较高,但对于 曲面边界以及尖锐棱边部分的重建效果则不够理想。 Edelsbrunner [4] 等提出了α -shape的概念，通过删除四面 体凸包中其包围球或外接圆半径大于α 的四面体、 三角 形和边得到重建表面。该方法虽然能够有效地避免曲面 自交，但重建速度较慢。Crossno [5] …”

Twinned meshes for dynamic triangulation of implicit surfaces

“…A triangular mesh can be obtained from a particle system via Delaunay triangulation at each animation step [11]. A faster method is to take into account neighboring information given by the particle system [9]. More time can be saved by exploiting temporal coherence making the triangulation evolve with the particle system [28].…”