A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe

A PDE patch-based spectral method for progressive mesh compression and mesh denoising

The development of the patchwise partial differential equation (PDE) framework a few years ago has paved the way for the PDE method to be used in mesh signal processing. In this paper, we, for the first time, extend the use of the PDE method to progressive mesh compression and mesh denoising. We, meanwhile, upgrade the existing patchwise PDE method in patch merging, mesh partitioning, and boundary extraction to accommodate mesh signal processing. In our new method, an arbitrary mesh model is partitioned into patches, each of which can be represented by a small set of coefficients of its PDE spectral solution. Since low-frequency components contribute more to the reconstructed mesh than high-frequency ones, we can achieve progressive mesh compression and mesh denoising by manipulating the frequency terms of the PDE solution. Experimental results demonstrate the feasibility of our method in both progressive mesh compression and mesh denoising