Creating suitable dense point samples of manifolds embedded in some metric space or simply subsets of such a metric space is essential for point-based modelling of well-characterised manifolds. This is some work on producing such sampling sequences and various applications predominantly related to point-based rendering. The software for this is begin developed at the Hekate development site.
Low-Discrepancy Sampling
This is the PhD work of Jonathan Quinn about creating low-discrepancy sampling seqeunces of surfaces utilising space-filling curves. This has been applied to point-based rendering, remeshing and robotic painting (in collaboration with Jonathan Corney and Finlay McPherson). Jonathan's supervisors are Frank Langbein and Ralph Martin.
Density-Controlled Low-Discrepancy Sampling and Meshing of 3D Geometric Models
High quality point samples are crucial for measuring and representing continuous data for computational applications. To cover a data set well, the samples must be uniformly distributed, but must not exhibit high regularity, such as present in a regular grid, to avoid sampling artefacts. For this project a sampling algorithm for 3D domains to represent CAD models has been devised by generalising an approach to sampling surfaces in 3D. Experiments show that the resulting samples are of high quality, close to the theoretical limit, as indicated by a discrepancy measure. Furthermore, 3D meshes were generated from the point samples using Delaunay triangulation. Measuring the tetrahedron quality of these meshes to evaluate their suitability for finite element simluations indicates that the mesh quality is better than expected, but requires improvement. Especially at the 3D domain's boundary the tetrahedrons are of low quality, which we intend to address in future work.
This work has been carried out by Kevin Sullivan under the supervision of Frank Langbein and Jonathan Quinn.
This project was supported by The Nuffield Foundation, Undergraduate Research Bursary 35473.
Java Point-Based Renderer
A point-based rendering application implemented by Kevin Sullivan under the supervision of Jonathan Quinn and some general guidance of Frank Langbein.
Sampling,http://www.langbein.org/research/points/sampling by Frank C Langbein [ 2/December/2008, 17:24].
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