Simplicial subdivisions and sampling artifacts

We review several schemes for dividing cubical cells into simplices (tetrahedra) in 3-D for interpolating from sampled data to R/sup 3/ or for computing isosurfaces by barycentric interpolation. We present test data that reveal the geometric artifacts that these subdivision schemes generate, and discuss how these artifacts relate to the filter kernels that correspond to the subdivision schemes.

[1]  Jules Bloomenthal,et al.  An Implicit Surface Polygonizer , 1994, Graphics Gems.

[2]  Paolo Cignoni,et al.  Reconstruction of topologically correct and adaptive trilinear isosurfaces , 2000, Comput. Graph..

[3]  Arie E. Kaufman,et al.  Multiresolution tetrahedral framework for visualizing regular volume data , 1997 .

[4]  Stefan Gnutzmann,et al.  Simplicial pivoting for mesh generation of implicity defined surfaces , 1991, Comput. Aided Geom. Des..

[5]  Gregory M. Nielson,et al.  Computing the separating surface for segmented data , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

[6]  P. Hanrahan,et al.  Area and volume coherence for efficient visualization of 3D scalar functions , 1990, SIGGRAPH 1990.

[7]  Bernd Hamann,et al.  The asymptotic decider: resolving the ambiguity in marching cubes , 1991, Proceeding Visualization '91.

[8]  Solomon Lefschetz,et al.  Introduction to Topology , 1950 .

[9]  P. Hanrahan,et al.  Area and volume coherence for efficient visualization of 3D scalar functions , 1990, VVS.

[10]  Jane Wilhelms,et al.  Topological considerations in isosurface generation , 1994, TOGS.

[11]  Arie E. Kaufman,et al.  Multiresolution tetrahedral framework for visualizing regular volume data , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

[12]  Nelson L. Max,et al.  Sorting and hardware assisted rendering for volume visualization , 1994, VVS '94.

[13]  P. Shirley,et al.  A polygonal approximation to direct scalar volume rendering , 1990, VVS.

[14]  H. Freudenthal.  Simplizialzerlegungen von Beschrankter Flachheit , 1942 .

[15]  Ken Brodlie,et al.  Improving the Robustness and Accuracy of the Marching Cubes Algorithm for Isosurfacing , 2003, IEEE Trans. Vis. Comput. Graph..

[16]  William E. Lorensen,et al.  Marching cubes: a high resolution 3D surface construction algorithm , 1996 .

[17]  Gregory M. Nielson,et al.  Interval volume tetrahedrization , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

[18]  Valerio Pascucci,et al.  Contour trees and small seed sets for isosurface traversal , 1997, SCG '97.

[19]  Gabor T. Herman,et al.  The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm , 1980, SIGGRAPH '80.

[20]  Jack Snoeyink,et al.  Computing contour trees in all dimensions , 2000, SODA '00.

[21]  T. Moller,et al.  Design of accurate and smooth filters for function and derivative reconstruction , 1998, IEEE Symposium on Volume Visualization (Cat. No.989EX300).

[22]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[23]  Martin Kraus,et al.  Hardware-accelerated volume and isosurface rendering based on cell-projection , 2000, Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145).

[24]  Jules Bloomenthal,et al.  Polygonization of implicit surfaces , 1988, Comput. Aided Geom. Des..

[25]  Thomas Theußl,et al.  Isosurfaces on Optimal Regular Samples , 2003, VisSym.

[26]  J. Wilhelms,et al.  Topological considerations in isosurface generation extended abstract , 1990, SIGGRAPH 1990.

[27]  Roger Crawfis,et al.  Efficient subdivision of finite-element datasets into consistent tetrahedra , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

[28]  David C. Banks,et al.  Complex-valued contour meshing , 1996, Proceedings of Seventh Annual IEEE Visualization '96.

[29]  Gregory M. Nielson,et al.  On Marching Cubes , 2003, IEEE Trans. Vis. Comput. Graph..

[30]  Roger Crawfis,et al.  Efficient subdivision of finite-element datasets into consistent tetrahedra , 1997 .

[31]  Paul Ning,et al.  An evaluation of implicit surface tilers , 1993, IEEE Computer Graphics and Applications.

[32]  Dan E. Dudgeon,et al.  Multidimensional Digital Signal Processing , 1983 .

[33]  Kenneth Moreland,et al.  Tetrahedral projection using vertex shaders , 2002, Symposium on Volume Visualization and Graphics, 2002. Proceedings. IEEE / ACM SIGGRAPH.

[34]  Michael P. Garrity.  Raytracing irregular volume data , 1990, VVS.