I'm happy to announce the 1.0b release of Alvis, a 3D alpha-shape visualizer. This version is a slightly improved version of what we showed at SIGGRAPH'92. It is ready for anonymous ftp from ftp.ncsa.uiuc.edu (141.142.20.50), file: SGI/Alpha-shape/Alvis-1.0b.tar.Z Ftp it using binary mode and do a uncompress Alvis-1.0b.tar.Z tar xvfp Alvis-1.0b.tar which will create a directory Alvis-1.0 with the SGI executables of the 1.0 release, including README files and some sample data. System requirements: o SGI workstation running Irix 4.0 or later. o 32 MB memory advisable. o Alvis-1.0 release needs less than 2 MB disk space. Contact address: alpha@ncsa.uiuc.edu Find attached excerpts from the Alvis-1.0/README file shortly discribing the concept of three-dimensional alpha shapes. For more rigorous definitions consult our paper [1], which is also available in PostScript format, incl (some of the B&W) figures: SGI/Alpha-shape/Paper.ps.Z SGI/Alpha-shape/Fig[1-6].ps.Z Enjoy, and remember... ________________________________________________________________________ | | | This code is a new kind of SHAREWARE: YOU share with us your | | experience in applying Alvis to engineering and science problems, | | and WE do our best to develop the software so it can meet your needs. | |________________________________________________________________________| --Ernst. ------- snip ----- snip ----- snip ----- snip ----- snip ----- snip -------- Copyright (c) 1991, 1992 The Board of Trustees of the University of Illinois ... Three-dimensional Alpha Shapes Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the "shape" of the set. For that purpose, we introduced the formal notion of the family of alpha shapes of a finite point set in 3D space, R^3; see [1]. Each shape is a polytope, derived from the Delaunay triangulation of the point set, with a parameter alpha controlling the desired level of detail. The employed algorithms construct the entire family of shapes for a given set of size n in worst-case time O(n^2). Conceptually, alpha shapes are a generalization of the convex hull of a point set. Let S be a finite set in R^3 and alpha a non-negative real number. The alpha shape of S is a polytope that is neither necessarily convex nor connected. For alpha = infinity, the alpha shape is identical to the convex hull of S. However, as alpha decreases, the shape shrinks by gradually developing cavities. These cavities may join to form tunnels, and even holes may appear Intuitively, a piece of the polytope disappears when alpha becomes small enough so that a sphere with radius alpha, or several such spheres, can occupy its space without enclosing any of the points of S. Think of R^3 filled with Styrofoam and the points of S made of more solid material, such as rock. Now imagine a spherical eraser with radius alpha. It is omnipresent in the sense that it carves out Styrofoam at all positions where it does not enclose any of the sprinkled rocks, that is, points of S. The resulting object is called the alpha hull. To make things more feasible, we straighten the object's surface by substituting straight edges for the circular ones and triangles for the spherical caps. The thus obtained object is the alpha shape of S. It is a polytope in a fairly general sense: it can be concave and even disconnected, it can contain two-dimensional patches of triangles and one-dimensional strings of edges, and its components can be as small as single points. The parameter alpha controls the maximum ``curvature'' of any cavity of the polytope. Refer to [1] for the formal definitons. ... REFERENCES The alpha shape programs are based on the theory of alpha shapes, Delaunay triangulations, and simulated perturbation. There are three main papers that had a significant influence on the program development. [1] Herbert Edelsbrunner and Ernst Mucke. Three-dimensional alpha shapes. To appear in Computer Graphics. Proceedings to the Boston Volume Visualization Workshop, 1992. [2] Barry Joe. Construction of three-dimensional Delaunay triangulations using local transformations. Computer Aided Geometric Design, volume 8, number 2, pages 123-142, 1991. [3] Herbert Edelsbrunner and Ernst Mucke. Simulation of Simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics, volume 9, number 1, pages 66-104, 1990.