Perturbation Functions in Computer Graphics

Affiliation(s)

Synthesizing Visualization Systems Laboratory, Siberian Branch of the Russian Academy of Sciences, Russian Federation.

Synthesizing Visualization Systems Laboratory, Siberian Branch of the Russian Academy of Sciences, Russian Federation.

ABSTRACT

The problem of real-time photorealistic imaging is discussed. New
techniques for specifying free forms without their approximation by polygons
are considered. Free
forms based on the perturbation functions have an advantage
of spline representation of surfaces, that is, a high degree of smoothness, and
an advantage of arbitrary form for a small number of perturbation functions.
Transformations of geometric objects are described for set-theoretic
operations, projections, offsetting, and metamorphosis. We propose a GPU solution to render freeform objects at high frame rates.

Cite this paper

S. Vyatkin, B. Dolgovesov and M. Gorodilov, "Perturbation Functions in Computer Graphics,"*Modern Instrumentation*, Vol. 2 No. 2, 2013, pp. 26-32. doi: 10.4236/mi.2013.22005.

S. Vyatkin, B. Dolgovesov and M. Gorodilov, "Perturbation Functions in Computer Graphics,"

References

[1] A. Pasko, V. Adzhiev, A. Sourin, et al., “Function Representation in Geometric Modeling: Concepts, Implementation and Applications,” The Visual Computer, Vol. 11, No. 6, 1995, pp. 429-446.

[2] S. I. Vyatkin, M. Gorodilov and B. S. Dolgovesov, “GPU-Based Binary Adaptive Ray Casting for Freeform Objects with Perturbation Functions,” Proceedings of the IASTED International Conferences on Automation, Control, and Information Technology, Novosibirsk, 15-18 June 2010, pp. 223-228.

[3] J. McCormack and A. Sherstyuk, “Creating and Rendering Convolution Surfaces,” Computing Graphics Forum, Vol. 17, No. 2, 1998, pp. 113-120. doi:10.1111/1467-8659.00232

[4] J. Bloomenthal and K. Shoemake, “Convolution Surfaces,” ACM SIGGRAPH Computer Graphics, Vol. 25, No. 4, 1991, pp. 251-256. doi:10.1145/127719.122757

[5] G. Sealy and G. Wyvill, “Smoothing of Three-Dimensional Models by Convolution,” Proceedings of Computer Graphics International, Pohang, 24-28 June 1996, pp. 184-190.

[6] J. F. Blinn, “A Generation of Algebraic Surface Drawing,” ACM Transactions on Graphics, Vol. 1, No. 3, 1982, pp. 235-256. doi:10.1145/357306.357310

[7] H. Nishimura, M. Hirai, T. Kawai, T. Kawata, I. Shirakawa and K. Omura, “Object Modeling by Distribution Function and a Method of Image Generation,” The Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol. J68-D, No. 4, 1985, pp. 718-725.

[8] G. Wyvill, C. McPheeters and B. Wyvill, “Data Structure for Soft Objects,” The Visual Computer, Vol. 2, No. 4, 1986, pp. 227-234. doi:10.1007/BF01900346

[9] J. Bloomenthal, “Modeling the Mighty Maple,” Computer Graphics, Vol. 19, No. 3, 1985, pp. 305-311. doi:10.1145/325165.325249

[10] A. Sherstuyk, “Fast Ray Tracing of Implicit Surfaces,” Computer Graphics Forum, Vol. 18, No. 2, 1999, pp. 139-147.

[11] A. G. Bors and I. Pitas, “Object Classification in 3-D Images Using Alpha-Trimmed Mean Radial Basis Function Network,” IEEE Transactions on Image Processing, Vol. 8, No. 12, 1999, pp. 1744-1756. doi:10.1109/83.806620

[12] J. C Carr, et al., “Reconstruction and Representation of 3D Objects with Radial Basis Functions,” Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, Los Angeles, 12-17 August 2001, pp. 67-76.

[13] S. Matej and R. M. Lewitt, “Practical Considerations for 3-D Image Reconstruction Using Spherically Symmetric Volume Elements,” IEEE Transactions on Medical Imaging, Vol. 15, No. 1, 1996, pp. 68-78. doi:10.1109/42.481442

[14] Y. Kanamori, Z. Szego and T. Nishita, “GPU-Based Fast Ray Casting for a Large Number of Metaballs,” Eurographics, Vol. 27, No. 2, 2008, pp. 351-360.

[15] M. Reimers and J. Seland, “Ray Casting Algebraic Surfaces Using the Frustum Form,” Eurographics, Vol. 27, No. 2, 2008, pp. 361-370.

[16] J. Kruger and R. Westermann, “Acceleration Techniques for GPU-Based Volume Rendering,” 14th IEEE Visualization, Seattle, 24-24 October 2003, pp. 38-42.

[17] C. Loop and J. Blinn, “Real-Time GPU Rendering of Piecewise Algebraic Surfaces,” Proceedings of ACM SIGGRAPH, Vol. 25, No. 3, 2006, pp. 664-670.

[18] A. Corrigan and H. Quynh Dinh, “Computing and Rendering Implicit Surfaces Composed of Radial Basis Functions on the GPU,” International Workshop on Volume Graphics, 2005, pp. 187-195.

[19] M. Hadwiger, C. Sigg, H. Scharsach, K. Buhler and M. Gross, “Real-Time Ray-Casting and Advanced Shading of Discrete Isosurfaces,” Computer Graphics Forum, Vol. 24, No. 3, 2005, pp. 303-312. doi:10.1111/j.1467-8659.2005.00855.x

[20] G. Liktor, “Ray Tracing Implicit Surfaces on the GPU,” Computer Graphics and Geometry, Vol. 10, No. 3, 2008, pp. 36-53.

[21] O. Fryazinov and A. Pasko, “Using GPU for Interactive Ray Casting Functionally Represented Models,” Computer Graphics and Geometry, Vol. 9, No. 1, 2007, pp. 1-17.

[22] S. I. Vyatkin, “Complex Surface Modeling Using Perturbation Functions,” Optoelectronics, Instrumentation and Data Processing, Vol. 43, No. 3, 2007. pp. 40-47. doi:10.3103/S875669900703003X

[23] S. I. Vyatkin, B. S. Dolgovesov and A. T. Valetov, “Geometric Operations for Functionally Defined Objects Using Perturbation Functions,” Optoelectronics, Vol. 40, No. 1, 2004, pp. 65-73.

[24] V. V. Savchenko and A. A. Pasko, “Collision Detection for Functionally Defined Deformable Objects,” In: B. Wyvill and M. P. Gascuel, Eds., The First International Workshop on Implicit Surfaces, Grenoble, 18-19 April 1995, pp. 217-221.

[25] S. I. Vyatkin, B. S. Dolgovesov and A. S. Korsun, “Collision Detection of Functionally Defined Objects in Computer Graphics Tasks,” Optoelectronics, Instrumentation and Data Processing, Vol. 39, No. 6. 2003, pp. 119-126.

[26] S. I. Vyatkin and B. S. Dolgovesov, “A 3D Texture-Based Recursive Multi-Level Ray Casting Algorithm,” Proceedings of the Second IASTED International Multi-Conference on Automation, Control, and Information Technology, Novosibirsk, 20-24 June 2005, pp. 92-97.

[27] S. I. Vyatkin, “A 3D Texture-Based Rendering Algorithm,” Computer Graphics and Geometry, Vol. 8, No. 3, 2006, pp. 65-78. http://www.cgg-journal.com/2006-3/05.htm

[1] A. Pasko, V. Adzhiev, A. Sourin, et al., “Function Representation in Geometric Modeling: Concepts, Implementation and Applications,” The Visual Computer, Vol. 11, No. 6, 1995, pp. 429-446.

[2] S. I. Vyatkin, M. Gorodilov and B. S. Dolgovesov, “GPU-Based Binary Adaptive Ray Casting for Freeform Objects with Perturbation Functions,” Proceedings of the IASTED International Conferences on Automation, Control, and Information Technology, Novosibirsk, 15-18 June 2010, pp. 223-228.

[3] J. McCormack and A. Sherstyuk, “Creating and Rendering Convolution Surfaces,” Computing Graphics Forum, Vol. 17, No. 2, 1998, pp. 113-120. doi:10.1111/1467-8659.00232

[4] J. Bloomenthal and K. Shoemake, “Convolution Surfaces,” ACM SIGGRAPH Computer Graphics, Vol. 25, No. 4, 1991, pp. 251-256. doi:10.1145/127719.122757

[5] G. Sealy and G. Wyvill, “Smoothing of Three-Dimensional Models by Convolution,” Proceedings of Computer Graphics International, Pohang, 24-28 June 1996, pp. 184-190.

[6] J. F. Blinn, “A Generation of Algebraic Surface Drawing,” ACM Transactions on Graphics, Vol. 1, No. 3, 1982, pp. 235-256. doi:10.1145/357306.357310

[7] H. Nishimura, M. Hirai, T. Kawai, T. Kawata, I. Shirakawa and K. Omura, “Object Modeling by Distribution Function and a Method of Image Generation,” The Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol. J68-D, No. 4, 1985, pp. 718-725.

[8] G. Wyvill, C. McPheeters and B. Wyvill, “Data Structure for Soft Objects,” The Visual Computer, Vol. 2, No. 4, 1986, pp. 227-234. doi:10.1007/BF01900346

[9] J. Bloomenthal, “Modeling the Mighty Maple,” Computer Graphics, Vol. 19, No. 3, 1985, pp. 305-311. doi:10.1145/325165.325249

[10] A. Sherstuyk, “Fast Ray Tracing of Implicit Surfaces,” Computer Graphics Forum, Vol. 18, No. 2, 1999, pp. 139-147.

[11] A. G. Bors and I. Pitas, “Object Classification in 3-D Images Using Alpha-Trimmed Mean Radial Basis Function Network,” IEEE Transactions on Image Processing, Vol. 8, No. 12, 1999, pp. 1744-1756. doi:10.1109/83.806620

[12] J. C Carr, et al., “Reconstruction and Representation of 3D Objects with Radial Basis Functions,” Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, Los Angeles, 12-17 August 2001, pp. 67-76.

[13] S. Matej and R. M. Lewitt, “Practical Considerations for 3-D Image Reconstruction Using Spherically Symmetric Volume Elements,” IEEE Transactions on Medical Imaging, Vol. 15, No. 1, 1996, pp. 68-78. doi:10.1109/42.481442

[14] Y. Kanamori, Z. Szego and T. Nishita, “GPU-Based Fast Ray Casting for a Large Number of Metaballs,” Eurographics, Vol. 27, No. 2, 2008, pp. 351-360.

[15] M. Reimers and J. Seland, “Ray Casting Algebraic Surfaces Using the Frustum Form,” Eurographics, Vol. 27, No. 2, 2008, pp. 361-370.

[16] J. Kruger and R. Westermann, “Acceleration Techniques for GPU-Based Volume Rendering,” 14th IEEE Visualization, Seattle, 24-24 October 2003, pp. 38-42.

[17] C. Loop and J. Blinn, “Real-Time GPU Rendering of Piecewise Algebraic Surfaces,” Proceedings of ACM SIGGRAPH, Vol. 25, No. 3, 2006, pp. 664-670.

[18] A. Corrigan and H. Quynh Dinh, “Computing and Rendering Implicit Surfaces Composed of Radial Basis Functions on the GPU,” International Workshop on Volume Graphics, 2005, pp. 187-195.

[19] M. Hadwiger, C. Sigg, H. Scharsach, K. Buhler and M. Gross, “Real-Time Ray-Casting and Advanced Shading of Discrete Isosurfaces,” Computer Graphics Forum, Vol. 24, No. 3, 2005, pp. 303-312. doi:10.1111/j.1467-8659.2005.00855.x

[20] G. Liktor, “Ray Tracing Implicit Surfaces on the GPU,” Computer Graphics and Geometry, Vol. 10, No. 3, 2008, pp. 36-53.

[21] O. Fryazinov and A. Pasko, “Using GPU for Interactive Ray Casting Functionally Represented Models,” Computer Graphics and Geometry, Vol. 9, No. 1, 2007, pp. 1-17.

[22] S. I. Vyatkin, “Complex Surface Modeling Using Perturbation Functions,” Optoelectronics, Instrumentation and Data Processing, Vol. 43, No. 3, 2007. pp. 40-47. doi:10.3103/S875669900703003X

[23] S. I. Vyatkin, B. S. Dolgovesov and A. T. Valetov, “Geometric Operations for Functionally Defined Objects Using Perturbation Functions,” Optoelectronics, Vol. 40, No. 1, 2004, pp. 65-73.

[24] V. V. Savchenko and A. A. Pasko, “Collision Detection for Functionally Defined Deformable Objects,” In: B. Wyvill and M. P. Gascuel, Eds., The First International Workshop on Implicit Surfaces, Grenoble, 18-19 April 1995, pp. 217-221.

[25] S. I. Vyatkin, B. S. Dolgovesov and A. S. Korsun, “Collision Detection of Functionally Defined Objects in Computer Graphics Tasks,” Optoelectronics, Instrumentation and Data Processing, Vol. 39, No. 6. 2003, pp. 119-126.

[26] S. I. Vyatkin and B. S. Dolgovesov, “A 3D Texture-Based Recursive Multi-Level Ray Casting Algorithm,” Proceedings of the Second IASTED International Multi-Conference on Automation, Control, and Information Technology, Novosibirsk, 20-24 June 2005, pp. 92-97.

[27] S. I. Vyatkin, “A 3D Texture-Based Rendering Algorithm,” Computer Graphics and Geometry, Vol. 8, No. 3, 2006, pp. 65-78. http://www.cgg-journal.com/2006-3/05.htm