F. Cazals, J. Giesen, M. Pauly, A. Zomorodian, Conformal Alpha Shapes, Symposium on Point-Based Graphics (2005), pp. 55-61.


We define a new filtration of the Delaunay triangulation of a finite set of points in Rd, similar to the alpha shape filtration. The new filtration is parameterized by a local scale parameter instead of the global scale parameter in alpha shapes. Since our approach shares many properties with the alpha shape filtration and the local scale parameter conforms to the local geometry we call it conformal alpha shape filtration. The local scale parameter is motivated from applications and previous algorithms in surface reconstruction. We show how conformal alpha shapes can be used for surface reconstruction of non-uniformly sampled surfaces, which is not possible with alpha shapes.


  title = "Conformal Alpha Shapes",
  author = "Cazals, F. and Giesen, J. and Pauly, M. and Zomorodian, A.",
  booktitle = "Proc. Symp. Point-Based Graph.", 
  year = 2005,
  pages = "55---61",