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Isosurface construction in any dimension using Convex Hulls.
IEEE Trans Vis Comput Graph. 2004 Mar-Apr; 10(2):130-41.IT

Abstract

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.

Authors+Show Affiliations

Bhaniramka P
Silicon Graphics, Mountain View, CA, USA. praveenb@sgi.com
Wenger R
No affiliation info available
Crawfis R
No affiliation info available

MeSH

AlgorithmsComputer GraphicsComputer SimulationImage EnhancementImage Interpretation, Computer-AssistedImaging, Three-DimensionalInformation Storage and RetrievalNumerical Analysis, Computer-AssistedPattern Recognition, AutomatedReproducibility of ResultsSensitivity and SpecificitySignal Processing, Computer-AssistedUser-Computer InterfaceVideo Recording

Pub Type(s)

Comparative Study
Evaluation Study
Journal Article
Research Support, U.S. Gov't, Non-P.H.S.
Validation Study

Language

eng

PubMed ID

15384638

Citation

Bhaniramka, Praveen, et al. "Isosurface Construction in Any Dimension Using Convex Hulls." IEEE Transactions On Visualization and Computer Graphics, vol. 10, no. 2, 2004, pp. 130-41.
Bhaniramka P, Wenger R, Crawfis R. Isosurface construction in any dimension using Convex Hulls. IEEE Trans Vis Comput Graph. 2004;10(2):130-41.
Bhaniramka, P., Wenger, R., & Crawfis, R. (2004). Isosurface construction in any dimension using Convex Hulls. IEEE Transactions On Visualization and Computer Graphics, 10(2), 130-41.
Bhaniramka P, Wenger R, Crawfis R. Isosurface Construction in Any Dimension Using Convex Hulls. IEEE Trans Vis Comput Graph. 2004 Mar-Apr;10(2):130-41. PubMed PMID: 15384638.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Isosurface construction in any dimension using Convex Hulls. AU - Bhaniramka,Praveen, AU - Wenger,Rephael, AU - Crawfis,Roger, PY - 2004/9/24/pubmed PY - 2004/10/20/medline PY - 2004/9/24/entrez SP - 130 EP - 41 JF - IEEE transactions on visualization and computer graphics JO - IEEE Trans Vis Comput Graph VL - 10 IS - 2 N2 - 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. SN - 1077-2626 UR - https://www.unboundmedicine.com/medline/citation/15384638/Isosurface_construction_in_any_dimension_using_Convex_Hulls_ DB - PRIME DP - Unbound Medicine ER -