Point-based Modelling

Representing manifolds and more generally arbitrary continuous subsets by dense point sets instead of algebraic complexes or other discrete representations with explicit topology seems to avoid many of the problems of discrete representations. It has been used mainly for rendering in point-based rendering, but may also be of use for other geometric modelling tasks.

In particular we are working on sampling, differential geometry on point representations, simulations and some related issues. Linking a low level point representation with quite high level geometry descriptions may also be useful for modelling.

  • Sampling. 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 beg...
  • Uniform Surface Point Sampling for Direct Write Applications

    Finlay N. McPherson, Jonathan A. Quinn, Jonathan Corney, Frank C. Langbein, Ralph R. Martin. Uniform Surface Point Sampling for Direct Write Applications.

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  • Point Sampling

    Low-Discrepancy Sampling

    This is the PhD work of Jonathan Quinn about creating low-discrepancy sampling sequwnces 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.

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    Publications

    • J.A. Quinn, F. C. Langbein, Y.-K. Lai, R. R. Martin. Fast Low-discrepancy Sampling of Parametric Surfaces and Meshes. Proc. Maths of Surfaces XIV (CD ROM), Institute of Mathematics and its Applications, 2013.

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    • J.A. Quinn, F. C. Langbein, Y.-K. Lai, R. R. Martin. Generalised Anisotropic Stratified Surface Sampling. IEEE Trans. Visualization and Computer Graphics 19 (7), 1143-1157, 2013.

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    • J.A. Quinn, F. Sun, F. C. Langbein, Y.-K. Lai, W. Wang, R. R. Martin. Improved Initialisation for Centroidal Voronoi Tessellation and Optimal Delaunay Triangulation. Computer Aided Design, 44(11):1062-1071, 2012.

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    • J. A. Quinn, F. C. Langbein, R. R. Martin. Low-Discrepancy Sampling of Meshes for Rendering. In: Proc. Symp. Point-Based Graphics, Eurographics Assocication, pp. 19-28, 2007.

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    • J. A. Quinn, F. C. Langbein, R. R. Martin, G. Elber. Density-Controlled Sampling of Parametric Surfaces Using Adaptive Space-Filling Curves. In: M.-S. Kim, K. Shimada (eds), Proc. Geometric Modeling and Processing, Springer LNCS, 4077:465-484, 2006.

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            Partners

            • Y.-K. Lai
              Cardiff University, UK

            • Finlay N. McPherson
              School of Engineering & Physical Sciences, Heriot Watt University, UK.

            • Jonathan Corney
              University of Strathclyde, Glasgow, UK.

            • K. S. Sullivan
              Cardiff University, UK

            • Jonathan Quinn
              School of Computer Science and Informatics, Cardiff University, UK.

            • Ralph R Martin
              School of Computer Science and Informatics, Cardiff University, Cardiff, UK.

            • Frank C Langbein
              School of Computer Science, Cardiff University, Cardiff, UK.

            Funding