TY - GEN

T1 - Contouring 1- and 2-manifolds in arbitrary dimensions

AU - Seong, Joon Kyung

AU - Elber, Gershon

AU - Kim, Myung Soo

PY - 2005

Y1 - 2005

N2 - We propose an algorithm for contouring k-manifolds (k = 1,2) embedded in an arbitrary n-dimensional space. We assume (n-k) geometric constraints are represented as polynomial equations in n variables. The common zero-set of these (n-k) equations is computed as a 1- or 2-manifold, respectively, for k = 1 or k = 2. In the case of 1-manifolds, this framework is a generalization of techniques for contouring regular intersection curves between two implicitlydefined surfaces of the form F(x,y,z) = G(x,y,z) = 0. Moreover, in the case of 2-manifolds, the algorithm is similar to techniques for contouring iso-surfaces of the form F(x, y, z) = 0, where n = 3 and only one (= 3 -2) constraint is provided. By extending the Dual Contouring technique to higher dimensions, we approximate the simultaneous zero-set as a piecewise linear 1- or 2-manifold. There are numerous applications for this technique in data visualization and modeling, including the processing of various geometric constraints for freeform objects, and the computation of convex hulls, bisectors, blendings and sweeps.

AB - We propose an algorithm for contouring k-manifolds (k = 1,2) embedded in an arbitrary n-dimensional space. We assume (n-k) geometric constraints are represented as polynomial equations in n variables. The common zero-set of these (n-k) equations is computed as a 1- or 2-manifold, respectively, for k = 1 or k = 2. In the case of 1-manifolds, this framework is a generalization of techniques for contouring regular intersection curves between two implicitlydefined surfaces of the form F(x,y,z) = G(x,y,z) = 0. Moreover, in the case of 2-manifolds, the algorithm is similar to techniques for contouring iso-surfaces of the form F(x, y, z) = 0, where n = 3 and only one (= 3 -2) constraint is provided. By extending the Dual Contouring technique to higher dimensions, we approximate the simultaneous zero-set as a piecewise linear 1- or 2-manifold. There are numerous applications for this technique in data visualization and modeling, including the processing of various geometric constraints for freeform objects, and the computation of convex hulls, bisectors, blendings and sweeps.

UR - http://www.scopus.com/inward/record.url?scp=33846075622&partnerID=8YFLogxK

U2 - 10.1109/SMI.2005.10

DO - 10.1109/SMI.2005.10

M3 - Conference contribution

AN - SCOPUS:33846075622

SN - 076952379X

SN - 9780769523798

T3 - Proceedings - International Conference on Shape Modeling and Applications, SMI'05

SP - 216

EP - 225

BT - Proceedings - International Conference on Shape Modeling and Applications, SMI'05

PB - IEEE Computer Society

T2 - International Conference on Shape Modeling and Applications, SMI'05

Y2 - 13 June 2005 through 17 June 2005

ER -