July 2004

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Problem:

• Given a set of points S = {x_i} on a surface M (piecewise 2D manifold*), find a surface M* that closely approximates M.

* The manifold requirement (i.e., having a local coordinate system (chart) for each surface patch which is assumed locally flat (with a tangent space at each point)) might be too restrictive.

Common Assumptions:

1. "Sufficiently well sampled" sets: refers to the density properties of the point cloud.
    
2. Additional geometric information is available, e.g.: a normal field
    

Harder problems:

1. Make no particular assumptions on the density, without access to additional geometric information.
    
2. The point set S is noisy along the normal field: i.e., we may have a dense volumetric sampling (a sausage) along the surface M, rather than being precisely sampling a piecewise 2D manifold M.
    

NB: Our goal (work on 3D scaffolds) is to tackle point 1 above. The vast majority of papers/published methods do not address either of these harder problems.

Next: Principal methods

Last Updated: June 30, 2004