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Real-time isosurface rendering of smooth fields

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Abstract

This paper presents a new technique for real-time isosurface visualization of three-dimensional smooth fields. This technique enables direct isosurface rendering of smoothly defined fields without generating intermediate polygon models as used in the marching-cube algorithm, a standard technique for isosurface extraction. We developed a parallel algorithm that is suitable for effective computation on graphics hardware by converting any field to a set of polynomials, enabling the detection of intersections between rays and isosurfaces at arbitrary isovalue with small computational cost. In addition, the isovalue to be rendered can be changed in real time, because the algorithm is not restricted to a specific isovalue. The technique can also be applied to the problem of the direct rendering of implicit surfaces that are defined as isosurfaces of smoothly defined fields.

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References

  • Amidror I (2002) Scattered data interpolation methods for electronic imaging systems: a survey. J Electron Imaging 11(2):157–176

    Article  Google Scholar 

  • Atluri SN, Zhu T (1998) A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics. Comput Mech 22(2):117–127

    Article  MathSciNet  MATH  Google Scholar 

  • Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods in Eng 37(2):229–256

    Article  MathSciNet  MATH  Google Scholar 

  • Carr JC, Beatson RK, Cherrie JB, Mitchell TJ, Fright WR, McCallum BC, Evans TR (2001) Reconstruction and representation of 3D objects with radial basis functions. In: Proceedings of SIGGRAPH 2001, pp 67–76

  • Engel K, Hadwiger M, Kniss J, Rezk-Salama C, Weiskopf D (2006) Real-time volume graphics. A K Peters, Natick

    Google Scholar 

  • Gelas A, Valette S, Prost R, Nowinski W (2009) Variational implicit surface meshing. Comput Graph 33(3):312–320

    Article  Google Scholar 

  • Hadwiger M, Sigg C, Scharsach H, Buhler K, Gross M (2005) Real-time ray-casting and advanced shading of discrete isosurfaces. Comp Graph Forum 24(3):303–312

    Article  Google Scholar 

  • Hart J (1996) Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces. Vis Comp 12(10):527–545

    Article  Google Scholar 

  • Jang Y, Weiler M, Hopf M, Huang J, Ebert DS, Gaither KP, Ertl T (2004) Interactively visualizing procedurally encoded scalar fields. In: Joint Eurographics—IEEE TCVG Symposium on Visualization, pp 35–44

  • Kalra D, Barr A (1989) Guaranteed ray intersection with implicit surfaces. In: Proceedings of SIGGRAPH’89, pp 297–306

  • Knoll A, Wald I, Hansen C (2009) Coherent multiresolution isosurface ray tracing. Vis Comp 25(3):209–225

    Article  Google Scholar 

  • Ledergerber C, Guennebaud G, Meyer M, Bacher M, Pfister H (2008) Volume MLS ray casting. IEEE Trans Vis Comp Graph 14(6):1539–1546

    Article  Google Scholar 

  • Levoy M (1990) Efficient ray tracing of volume data. ACM Trans Graph 9(3):99–106

    Article  Google Scholar 

  • Linsen L, Van Long T, Rosenthal P, Rosswog S (2008) Surface extraction from multi-field particle volume data using multi-dimensional cluster visualization. IEEE Trans Vis Comp Graph 14(6):1483–1490

    Article  Google Scholar 

  • Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, Singapore

    Book  MATH  Google Scholar 

  • Liu B, Clapworthy GJ, Dong F (2009) Fast isosurface rendering on a GPU by cell rasterization. Comp Graph Forum 28(8):2151–2164

    Article  Google Scholar 

  • McNamee JM (2007) Numerical methods for roots of polynomials—part I. Elsevier, Amsterdam

    MATH  Google Scholar 

  • Navratil PA, Johnson JL, Bromm V (2007) Visualization of cosmological particle-based datasets. IEEE Trans Vis Comp Graph 13(6):1712–1718

    Article  Google Scholar 

  • Neophytou N, Mueller K (2005) GPU accelerated image aligned splatting. In: Gröller E (ed) Volume Graphics 2005. Eurographics, New York, pp 197–205

  • Ohtake Y, Belyaev A, Alexa M, Turk G, Seidel H-P (2003) Multi-level partition of unity implicits. In: Proceedings of SIGGRAPH 2003, pp 463–470

  • Oka M, Nakata S, Tanaka S (2007) Preprocessing for accelerating convergence of repulsive-particle systems for sampling implicit surfaces. In: Proceedings of IEEE International Conference on Shape Modeling and Applications, pp 232–240

  • Perlin K, Hoffert EM (1989) Hypertexture. In: Proceedings of SIGGRAPH’89, pp 253–262

  • Reiner T, Mückl G, Dachsbacher C (2011) Interactive modeling of implicit surfaces using a direct visualization approach with signed distance functions. Comp Graph 35(3):596–603

    Article  Google Scholar 

  • Rosenthal P, Linsen L (2006) Direct isosurface extraction from scattered volume data. In: Joint Eurographics—IEEE TCVG Symposium on Visualization, pp 99–106

  • Shen C, O’Brien JF, Shewchuk JR (2004) Interpolating and approximating implicit surfaces from polygon soup. In: Proceedings of SIGGRAPH 2004, pp 896–904

  • Stander BT, Hart JC (1997) Guaranteeing the topology of an implicit surface polygonization for interactive modeling. In: Proceedings of SIGGRAPH’97, pp 60–69

  • Tsukamoto Y, Kawashima S, Inoue S, Ito I, Kataoka S, Kojima K, Hasegawa K, Nakata S, Tanaka S (2011) Data fitting independent of grid structure using a volumic version of MPU. J Vis 14(2):161–170

    Article  Google Scholar 

  • Wang JG, Liu GR (2002) A point interpolation meshless method based on radial basis function. Int J Numer Methods Eng 54(11):1623–1648

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. College of Information Science and Engineering, Ritsumeikan University, Kyoto, Japan

    Susumu Nakata & Satoshi Tanaka

  2. Graduate School of Science and Engineering, Ritsumeikan University, Kyoto, Japan

    Shohei Aoyama & Ryosuke Makino

  3. Kinugasa Research Organization, Ritsumeikan University, Kyoto, Japan

    Kyoko Hasegawa

Authors
  1. Susumu Nakata
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  2. Shohei Aoyama
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  3. Ryosuke Makino
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  4. Kyoko Hasegawa
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  5. Satoshi Tanaka
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Correspondence to Susumu Nakata.

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Nakata, S., Aoyama, S., Makino, R. et al. Real-time isosurface rendering of smooth fields. J Vis 15, 179–187 (2012). https://doi.org/10.1007/s12650-011-0119-5

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  • DOI: https://doi.org/10.1007/s12650-011-0119-5

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