Implicit Surface Polygonization With Particle Sampling

The first step in reverse engineering is acquiring point data with3D scanners. It isnecessary to remove the inaccurate, remove noises and repair holes. Then, Reconstruct surfaceswith the obtained data. Implicit surface reconstruction is a kind of surface reconstruction. Theimplicit surface is defined implicitly by a function, which makes it efficient to check forwhether point is inside, efficient to find intersections, and efficient to Boolean operate. Thus,the rendering of the implicit surface becomes popular, while it is always difficult to render.The polygonizaiton meshes is approximation of rendering of implicit surface, whichconsists of sampling with particle systems and combination sampling points using somealgorithms. The reliability of the sampling points is related to the efficient of the meshes, therobust and fairing of which assures the rendering.In the process of implicit surfaces rendering, the parameters adjustment is not effective,and the accuracy is beyond our control. We introduce an approach to sampling static implicitsurfaces depended on curvature with particles. A seed particle, which is chosen first,initializes other particles. There are repulsion forces between particles, defined byelectrostatic function. The direction of the forces constrains the particle moving. The particlesgradually move to a balance situation. We present a cube rotation back-projection for theparticles project back to the surface. The projection point is solved by bisection methods. Theparticles update themselves until they reach a uniform state, the pre-sampling. The forcebetween particles changes by curvature. Then with particles diffusion and update we get thefinal sampling. The sampling depended on curvature makes surface rendering effective. Thebisection methods make the error in projection point seeking be controlled. There are fourparameters to adjust, the edge length of cubes, initial value of repulsion radius, the thresholdto evaluate state and the error precision. The methods can be suitable for triangulation meshes,examples are showed to demonstrate the availability of which.We select the crust-based surface reconstruction. After get the Voronoi vertices of thepoints, it is easy to calculate the poles. Divide the space, composed with sampling points andtheir poles, into Delaunay tetrahedrons. After extract the triangles, the vertices on which all arethe sample points, we get the final triangular meshes. Meshes are fairing and robust and it is not necessary to subdivision, which effectively represent surfaces. The triangulation meshes areshowed in the end.