Analysis of the Weight Function for Implicit Moving Least Squares Techniques

Implicit Surface;Surface Reconstruction;Weight Function;Moving Least Squares;Computer Science

Yao, Zhujun

University of Waterloo

关键词: Implicit Surface;    Surface Reconstruction;    Weight Function;    Moving Least Squares;    Computer Science;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/8498/1/Yao_Zhujun.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In this thesis, I analyze the weight functions used in moving least squares (MLS) methods to construct implicit surfaces that interpolate or approximate polygon soup. I found that one previous method that presented an analytic solution to the integrated moving least squares method has issues with degeneracies because they changed the weight functions to decrease too slowly. Inspired by their method, I derived a bound for the choice of weight function for implicit moving least squares (IMLS) methods to avoid these degeneracies in two-dimensions and in three-dimensions. Based on this bound, I give a theoretical proof of the correctness of the moving least squares interpolation and approximation scheme with weight function used in Shen et al. when used on closed polyhedrons. Further, previous IMLS implicit surface reconstruction algorithms thatll holes and gaps create surfaces with obvious bulges due to an intrinsic property of MLS. I propose a generalized IMLS method using a Gaussian distribution function to re-weight each polygon, making nearer polygons dominate and reducing the bulges on holes and gaps.