3D Surface Reconstruction

In the field of scientific visualization you are often in need of real objects' 3D models. As in 2D you may manually construct or design the required models. However, in 3D you even more want the construction process be automated by object digitizing. There are several digitizing methods like computer tomography (CT) that provides a set of 2D x-ray images partitioning the object in slices or 3D Scanner which provide a set of unordered sample points from the object's surface. In addition to the surface samples there may be other surface attributes like color, temperature or pressure.
To reconstruct a model from such digitized scattered data you have to connect the sample points to get a surface approximation. So called Alpha-Shapes are often used for piecewise-linear approximation of dense scattered data. They are a generalization of the Convex-Hull and part of the Delaunay-Triangulation . They consist of points, lines, triangles and tetrahedra. To get a continuous differentiable (i.e. smooth) approximation of the object's surface the alpha shapes are split in several surface parts which are then replaced by polynomial patches.

If you are interested in an introduction, you may read my elaboration (1MB ps.gz).
This paper is based on the reconstruction work of Bajaj , Bernardini and Xu from
Purdue University , Indiana, US.


Computer Animation. Sum.Sem.1996, IFI WWU Münster.