So far, we’ve pretty much focused exclusively on meshes as the representation of surfaces. We’ve also talked briefly about implicit and parametric representations. All of these represent the surface as a continuous closed surface. Another interesting approach to defining surfaces is by a collection of points in space. We can do a surprising amount with this, and it has the advantage that we aren’t required to maintain valid mesh connectivity when editing the surface.
We’ll be discussing point-set surfaces by looking at a papers that define them using a moving least squares (MLS) process. Not only is this a useful construction for point-set surfaces, but MLS is a generally useful technique to know about.
M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, and C. Silva. Computing and rendering point set surfaces. IEEE Transactions on Visualization and Computer Graphics. [PDF]
M. Pauly, R. Keiser, L. Kobbelt, M. Gross. Shape modeling with point-sampled geometry. In Proceedings of SIGGRAPH 2003. [PDF]
Here are just a few of the many interesting papers that use point-based representations of surfaces.
J. Wu and L. Kobbelt. Optimized sub-sampling of point sets for surface splatting. Computer Graphics Forum (Eurographics 2004 Proceedings), 23(3), 643-652, 2004. [PDF]
S. Fleishman, D. Cohen-Or, M. Alexa, C. Silva. Progressive point set surfaces. ACM Transactions on Graphics, 22(4):997–1011, October 2003. [PDF]
S. Rusinkiewicz and M. Levoy. QSplat: A multiresolution point rendering system for large meshes. Proceedings of SIGGRAPH 2000, pp. 343–352. [PDF]
N. Amenta and Y. Kil. Defining point-set surfaces, Proceedings of SIGGRAPH 2004, pages 264-270. [PDF]
You might also like to check out the Pointshop3D software.