Isosurface construction in any dimension using Convex Hulls.
We present an algorithm for constructing isosurfaces in any dimension. The input to the algorithm is a set of scalar values in a d-dimensional regular grid of (topological) hypercubes. The output is a set of (d-1)-dimensional simplices forming a piecewise linear approximation to the isosurface. The algorithm constructs the isosurface piecewise within each hypercube in the grid using the convex hull of an appropriate set of points. We prove that our algorithm correctly produces a triangulation of a (d-1)-manifold with boundary. In dimensions three and four, lookup tables with 2(8) and 2(16) entries, respectively, can be used to speed the algorithm's running time. In three dimensions, this gives the popular Marching Cubes algorithm. We discuss applications of four-dimensional isosurface construction to time varying isosurfaces, interval volumes, and morphing.
Bhaniramka
Praveen
P
Silicon Graphics, Mountain View, CA, USA. praveenb@sgi.com
Wenger
Rephael
R
Crawfis
Roger
R
D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D014584:User-Computer Interface; D014741:Video Recording / Q000379:methods