
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
T. Martin, E. Cohen, M. M. Kirby, "Direct Isosurface Visualization of HexBased HighOrder Geometry and Attribute Representations," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 5, pp. 753766, May, 2012.  
BibTex  x  
@article{ 10.1109/TVCG.2011.103, author = {T. Martin and E. Cohen and M. M. Kirby}, title = {Direct Isosurface Visualization of HexBased HighOrder Geometry and Attribute Representations}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {18}, number = {5}, issn = {10772626}, year = {2012}, pages = {753766}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2011.103}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Direct Isosurface Visualization of HexBased HighOrder Geometry and Attribute Representations IS  5 SN  10772626 SP753 EP766 EPD  753766 A1  T. Martin, A1  E. Cohen, A1  M. M. Kirby, PY  2012 KW  splines (mathematics) KW  computational geometry KW  data visualisation KW  finite element analysis KW  rendering (computer graphics) KW  algebraic function KW  direct isosurface visualization technique KW  hexbased highorder geometry KW  attribute representation KW  unstructured curvilinear hexahedral grids KW  highorder hexahedralbased finite element solution KW  isogeometric analysis KW  trivariate highorder NURBS geometry KW  nonuniform rational Bsplines geometry KW  viewindependent transparency KW  rendering process KW  complexstructured geometry KW  complexunstructured geometry KW  highorder simulation solution KW  medical data set KW  Isosurfaces KW  Splines (mathematics) KW  Surface reconstruction KW  Surface topography KW  Pixel KW  spline and piecewise polynomial interpolation. KW  Isosurface visualization of hexbased highorder geometry and attribute representations KW  numerical analysis KW  roots of nonlinear equations VL  18 JA  IEEE Transactions on Visualization and Computer Graphics ER   
[1] O. Abert, M. Geimer, and S. Müller, "Direct and Fast Ray Tracing of NURBS Surfaces," Proc. IEEE Symp. Interactive Ray Tracing, pp. 161168, 2006.
[2] J. Amanatides, "Ray Tracing with Cones," SIGGRAPH Computer Graphics, vol. 18, no. 3, pp. 129135, 1984.
[3] C.L. Bajaj, R.L. Holt, and A.N. Netravali, "Rational Parametrizations of Nonsingular Real Cubic Surfaces," ACM Trans. Graphics, vol. 17, no. 1, pp. 131, 1998.
[4] J.F. Blinn, "A Generalization of Algebraic Surface Drawing," ACM Trans. Graphics, vol. 1, no. 3, pp. 235256, 1982.
[5] X. Chen, R.F. Riesenfeld, and E. Cohen, "Sliding Windows Algorithm for BSpline Multiplication," SPM '07: Proc. ACM Symp. Solid and Physical Modeling, pp. 265276, 2007.
[6] P. Cignoni, L.D. Floriani, C. Montani, E. Puppo, and R. Scopigno, "Multiresolution Modeling and Visualization of Volume Data Based on Simplicial Complexes," VVS '94: Proc. Symp. Volume Visualization, pp. 1926, 1994.
[7] E. Cohen, R.F. Riesenfeld, and G. Elber, Geometric Modeling with Splines: An Introduction. A.K. Peters, Ltd., 2001.
[8] J.A. Cottrell, A. Reali, Y. Bazilevs, and T.R. Hughes, "Isogeometric Analysis of Structural Vibrations," Computer Methods in Applied Mechanics and Eng., vol. 195, nos. 4143, pp. 52575296, 2006.
[9] R. de Toledo, B. Levy, and J.C. Paul, "Iterative Methods for Visualization of Implicit Surfaces on GPU," ISVC '07: Proc. Int'l Symp. Visual Computing, pp. 598609, Nov. 2007.
[10] J.E.F. Díaz, "Improvements in the Ray Tracing of Implicit Surfaces Based on Interval Arithmetic," PhD thesis, Universitat de Girona, 2008.
[11] A. Efremov, V. Havran, and H.P. Seidel, "Robust and Numerically Stable Bézier Clipping Method for Ray Tracing NURBS Surfaces," SCCG '05: Proc. 21st Spring Conf. Computer Graphics, pp. 127135, 2005.
[12] G. Elber, "Free Form Surface Analysis Using a Hybrid of Symbolic and Numeric Computation," PhD thesis, Computer Science Departmente, Univ. of Utah, 1992.
[13] G. Elber and M.S. Kim, "Geometric Constraint Solver Using Multivariate Rational Spline Functions," SMA '01: Proc. Sixth ACM Symp. Solid Modeling and Applications, pp. 110, 2001.
[14] A. Entezari, R. Dyer, and T. Moller, "Linear and Cubic Box Splines for the Body Centered Cubic Lattice," VIS '04: Proc. Conf. Visualization, pp. 1118, 2004.
[15] J.C. Hart, "Ray Tracing Implicit Surfaces," Proc. SIGGRAPH Course Notes: Design, Visualization and Animation of Implicit Surfaces, pp. 116, 1993.
[16] P.S. Heckbert and P. Hanrahan, "Beam Tracing Polygonal Objects," SIGGRAPH '84: Proc. 11th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 119127, 1984.
[17] J. Hua, Y. He, and H. Qin, "Multiresolution Heterogeneous Solid Modeling and Visualization Using Trivariate Simplex Splines," SM '04: Proc. Ninth ACM Symp. Solid Modeling and Applications, pp. 4758, 2004.
[18] T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs, "Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry, and Mesh Refinement," Computer Methods in Applied Mechanics and Eng., vol. 194, pp. 41354195, 2005.
[19] J.T. Kajiya, "Ray Tracing Parametric Patches," SIGGRAPH '82: Proc. Ninth Ann. Conf. Computer Graphics and Interactive Techniques, pp. 245254, 1982.
[20] T. Kalbe and F. Zeilfelder, "HardwareAccelerated, HighQuality Rendering Based on Trivariate Splines Approximating Volume Data," Computer Graphics Forum, vol. 27, no. 2, pp. 331340, 2008.
[21] M. Kim, A. Entezari, and J. Peters, "Box Spline Reconstruction on the FaceCentered Cubic Lattice," IEEE Trans. Visualization and Computer Graphics, vol. 14, no. 6, pp. 15231530, Nov./Dec. 2008.
[22] J. Kloetzli, M. Olano, and P. Rheingans, "Interactive Volume Isosurface Rendering Using BT Volumes," I3D '08: Proc. Symp. Interactive 3D Graphics and Games, pp. 4552, 2008.
[23] A. Knoll, Y. Hijazi, C.D. Hansen, I. Wald, and H. Hagen, "Interactive Ray Tracing of Arbitrary Implicit Functions," Proc. Eurographics/IEEE Symp. Interactive Ray Tracing, 2007.
[24] A. Knoll, I. Wald, S. Parker, and C. Hansen, "Interactive Isosurface Ray Tracing of Large Octree Volumes," Proc. IEEE Symp. Interactive Ray Tracing, pp. 115124, Sept. 2006.
[25] R. Krawczyk, "Newton Algorithmen Zur Bestimmung Von Nullstellen Mit Fehlerschranken," Computing, vol. 4, pp. 187201, 1969.
[26] M. Levoy, "Efficient Ray Tracing of Volume Data," ACM Trans. Graphics, vol. 9, no. 3, pp. 245261, 1990.
[27] C. Loop and J. Blinn, "RealTime GPU Rendering of Piecewise Algebraic Surfaces," ACM Trans. Graphics, vol. 25, no. 3, pp. 664670, 2006.
[28] W.E. Lorensen and H.E. Cline, "Marching Cubes: A High Resolution 3D Surface Construction Algorithm," SIGGRAPH Computer Graphics, vol. 21, no. 4, pp. 163169, 1987.
[29] S.R. Marschner and R.J. Lobb, "An Evaluation of Reconstruction Filters for Volume Rendering," VIS '94: Proc. Conf. Visualization, pp. 100107, 1994.
[30] M.J. Marsden, "An Identity for Spline Functions with Applications to Variation Diminishing Spline Approximation," J. Approximation Theory, vol. 3, pp. 749, 1970.
[31] W. Martin and E. Cohen, "Representation and Extraction of Volumetric Attributes Using Trivariate Splines," Proc. Symp. Solid and Physical Modeling, pp. 234240, 2001.
[32] M. Meyer, B. Nelson, R. Kirby, and R. Whitaker, "Particle Systems for Efficient and Accurate HighOrder Finite Element Visualization," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 5, pp. 10151026, Sept./Oct. 2007.
[33] R.E. Moore, Interval Analysis. PrenticeHall, 1966.
[34] B. Nelson and R.M. Kirby, "RayTracing Polymorphic Multidomain Spectral/hp Elements for Isosurface Rendering," IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 1, pp. 114125, Jan./Feb. 2006.
[35] T. Nishita, T.W. Sederberg, and M. Kakimoto, "Ray Tracing Trimmed Rational Surface Patches," SIGGRAPH Computer Graphics, vol. 24, no. 4, pp. 337345, 1990.
[36] A. Paiva, H. Lopes, T. Lewiner, and L.H. de Figueiredo, "Robust Adaptive Meshes for Implicit Surfaces," Proc. Brazilian Symp. Computer Graphics and Image Processing, pp. 205212, 2006.
[37] S. Parker, P. Shirley, Y. Livnat, C. Hansen, and P.P. Sloan, "Interactive Ray Tracing for Isosurface Rendering," VIS '98: Proc. Conf. Visualization, pp. 233238, 1998.
[38] A. Raviv and G. Elber, "Interactive Direct Rendering of Trivariate BSpline Scalar Functions," IEEE Trans. Visualization and Computer Graphics, vol. 7, no. 2, pp. 109119, Apr.June 2001.
[39] M. Reimers and J. Seland, "Ray Casting Algebraic Surfaces Using the Frustum Form," Computer Graphics Forum, vol. 27, no. 2, pp. 361370, 2008.
[40] J. Schreiner and C. Scheidegger, "HighQuality Extraction of Isosurfaces from Regular and Irregular Grids," IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 5, pp. 12051212, Sept./Oct. 2006.
[41] T. Sederberg and A. Zundel, "Pyramids that Bound Surface Patches," Graphical Models and Image Processing, vol. 58, no. 1, pp. 7581, Jan. 1996.
[42] P. Shirley, Fundamentals of Computer Graphics. A.K. Peters, Ltd., 2002.
[43] K. Sung and P. Shirley, "Ray Tracing with the BSP Tree," Graphics Gems III, pp. 271274, Academic Press Professional, Inc., 1992.
[44] D.L. Toth, "On Ray Tracing Parametric Surfaces," SIGGRAPH '85: Proc. 12th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 171179, 1985.
[45] O. Wilson, A. VanGelder, and J. Wilhelms, "Direct Volume Rendering via 3D Textures," technical report, Univ. of California at Santa Cruz, 1994.
[46] Y. Zhang, Y. Bazilevs, S. Goswami, C.L. Bajaj, and T.J.R. Hughes, "PatientSpecific Vascular NURBS Modeling for Isogeometric Analysis of Blood Flow," Computer Methods in Applied Mechanics and Eng., vol. 196, nos. 29/30, pp. 29432959, 2007.