Tim Volodine, Michael S. Floater, Dirk Roose


We propose an algorithm which constructs an interpolating triangular mesh from a closed point cloud of arbitrary genus. The algorithm first constructs an intermediate structure called a Delaunay cover, which forms a barrier between the inside and the outside of the object. This structure is used to build a boolean voxel grid, with cells intersecting the cover colored black and all other cells colored white. The outer surface of the voxel grid is snapped to the point cloud by replacing each exterior surface vertex with the closest point in the point cloud. The snapped mesh is processed such that it is manifold and consists of triangles with good aspect ratio. We show that if a fine voxel grid is used, the snapping yields Delaunay-like triangulation of the original points. High grid resolutions are possible because of the Delaunay cover and a new contouring method, which extracts the outer surface of the grid with O(n2 ) worst case space complexity, where n is the number of voxels in one dimension.


  1. Amenta, N., Choi, S., and Kolluri, R. (2001). The power crust, unions of balls, and the medial axis transform. Computational Geometry: Theory and Applications, 19(2-3):127-153.
  2. Bernardini, F., Mittleman, J., Rushmeier, H., Silva, C., and Taubin, G. (1999). The ball-pivoting algorithm for surface reconstruction. IEEE Transactions on Visualization and Computer Graphics, 5(4):349-359.
  3. Boada, I., Coll, N., and Sellarés, J. (2002). Hierarchical planar voronoi diagram approximations. In Proceedings of the 14th Canadian Conference on Computational Geometry, pages 40-45.
  4. Carr, J. C., Beatson, R. K., Cherrie, J., Mitchell, T. J., Fright, W. R., McCallum, B. C., and Evans, T. R. (2001). Reconstruction and representation of 3d objects with radial basis functions. In ACM SIGGRAPH 2001, pages 67-76.
  5. Curless, B. and Levoy, M. (1996). A volumetric method for building complex models from range images. Computer Graphics, 30(Annual Conference Series):303- 312.
  6. Dey, T. K. (2006). Curve and Surface Reconstruction: Algorithms with Mathematical Analysis. Cambridge University Press.
  7. Edelsbrunner, H. and M ücke, E. P. (1994). Threedimensional alpha shapes. ACM Transactions on Graphics, 13(1):43-72.
  8. Floater, M. and Reimers, M. (2001). Meshless parameterization and surface reconstruction. Comp. Aided Geom. Design, 18:77-92.
  9. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., and Stuetzle, W. (1992). Surface reconstruction from unorganized points. In ACM SIGGRAPH 1992, pages 71-78.
  10. Hornung, A. and Kobbelt, L. (2006). Robust reconstruction of watertight 3d models from non-uniformly sampled point clouds without normal information. In Eurographics Symposium on Geometry Processing, pages 41-50.
  11. Jeong, W. and Kim, C. (2002). Direct reconstruction of displaced subdivision surface from unorganized points. In Graphical Models, volume 64(2), pages 78-93.
  12. Ju, T. (2004). Robust repair of polygonal models. ACM Trans. Graph., 23(3):888-895.
  13. Ju, T., Losasso, F., Schaefer, S., and Warren, J. (2002). Dual contouring of hermite data. ACM Trans. Graph., 21(3):339-346.
  14. Kobbelt, L. P., Vorsatz, J., Labsik, U., and Seidel, H.-P. (1999). A shrink wrapping approach to remeshing polygonal surfaces. In Computer Graphics Forum (Eurographics 7899), volume 18(3), pages 119-130.
  15. Lavender, D., Bowyer, A., Davenport, J., Wallis, A., and Woodwark, J. (1992). Voronoi diagrams of settheoretic solid models. IEEE Computer Graphics and Applications, 12(5):69-77.
  16. Lorensen, W. and Cline, H. (1987). Marching cubes: A high resolution 3d surface construction algorithm. ACM Trans. Graph., 21(4):163-170.
  17. Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., and Seidel, H.-P. (2003). Multi-level partition of unity implicits. ACM Trans. Graph., 22(3):463-470.
  18. Pauly, M., Kobbelt, L. P., and Gross, M. (2006). Pointbased multiscale surface representation. ACM Trans. Graph., 25(2):177-193.
  19. Scheidegger, C., Fleishman, S., and Silva, C. (2005). Triangulating point-set surfaces with bounded error. In Proceedings of the third Eurographics Symposium on Geometry Processing, pages 63-72.
  20. Szeliski, R. and Tonnesen, D. (1992). Surface modeling with oriented particle systems. In SIGGRAPH 1992, Computer Graphics Proceedings, pages 185-194.
  21. Wood, Z., Hoppe, H., Desbrun, M., and Schröder, P. (2004). Removing excess topology from isosurfaces. ACM Trans. Graph., 23(2):190-208.
  22. Zwicker, M. and Gotsman, C. (2004). Meshing point clouds using spherical parameterization. In Proceedings of the Eurographics Symposium on Point-Based Graphics.

Paper Citation

in Harvard Style

Volodine T., S. Floater M. and Roose D. (2007). VOLUMETRIC SNAPPING: WATERTIGHT TRIANGULATION OF POINT CLOUDS . In Proceedings of the Second International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, ISBN 978-972-8865-71-9, pages 53-60. DOI: 10.5220/0002079800530060

in Bibtex Style

author={Tim Volodine and Michael S. Floater and Dirk Roose},
booktitle={Proceedings of the Second International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,},

in EndNote Style

JO - Proceedings of the Second International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,
SN - 978-972-8865-71-9
AU - Volodine T.
AU - S. Floater M.
AU - Roose D.
PY - 2007
SP - 53
EP - 60
DO - 10.5220/0002079800530060