Advantages of Topological Tools in Localization Methods
Abstract
Let C = ?X epsilon IR(sup n) / f(X) = 0!, n epsilon ?2,3!, where f is a polynomial function. We want to approximate C by subdividing the parameter space. Most of the usual algorithms raise two problems: data structure management, and the choice of subdivision level which respects the geometry of C. This paper gives a method based on a topological approach. In this work, we specify the local criteria that preserve the topological coherence between the model (the set C) and its volumetric approximation (the set of voxels that contains C). In addition, we determine the local criteria that give the digital analog of (n - 1) dimensional manifolds in IR(sup n). In this way, we determine locally how the set of voxels in digital space may be spread out to describe analogous properties of Euclidean manifolds. This gives efficient criteria for controlling the distribution of voxels and the depth of subdivision. We then obtain an approximation that conserves the topological properties of C. The process of localization based on these criteria is generated by an iterative mesh subdivision and skeleton.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2000
- Accession Number
- ADP012028
Entities
People
- Mohammed Khachan
- Patrick Chenin
Organizations
- Joseph Fourier University