Articles Information
                    
                    International Journal of Automation, Control and Intelligent Systems, Vol.1, No.1, May 2015, Pub. Date: Apr. 22, 2015
                    Polygonization Method for Functionally Defined Objects
                    
                     
                    
                    Pages: 1-8 Views: 3345 Downloads: 1245
                    Authors
                    
                    
                    
                        
                            
                                
                                
                                    [01] 
                                
                            
                            
                                Sergey I. Vyatkin, Synthesizing Visualization Systems Laboratory at Institute of Automation and Electrometry, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation. 
                            
                            
                        
                     
                    Abstract
                    
                    
                    
                        Obtaining a triangular mesh from a set of cells intersecting the surface with perturbation functions is considered in this paper. The seamless rendering is discussed. The free forms based on the analytical perturbation functions are presented. A method for polygonization freeform surfaces is proposed.
                    
                    Keywords
                    
                    
                    
                        Seamless Rendering, Polygonization, Perturbation Functions, Octree, Polygonizer
                    
                    References
                    
                    
                    
                        
                            
                                
                                
                                    [01]
                                
                            
                            
                                J. F. Blinn. A generation of algebraic surface drawing. ACM Transactions on Graphics, 1(3): 235-256, July 1982 
                            
                            
                        
                            
                                
                                
                                    [02]
                                
                            
                            
                                Bloomenthal J., Shoemake K., “Convolution surfaces”, SIGGRAPH’91, Computer Graphics, vol.25, No.4, 1991, pp. 251-256. 
                            
                            
                        
                            
                                
                                
                                    [03]
                                
                            
                            
                                Bloomenthal J. Modeling the mighty maple. Computer Graphics, 19(3): 305-311, July 1985. 
                            
                            
                        
                            
                                
                                
                                    [04]
                                
                            
                            
                                Wyvill G., McPheeters C., Wyvill B. Data structure for soft objects. The Visual Computer, Vol. 2, No. 4, 1986, pp. 227-234. 
                            
                            
                        
                            
                                
                                
                                    [05]
                                
                            
                            
                                G. Sealy, G. Wyvill. Smoothing of three dimensional models by convolution. In Computer Graphics International’96, June 1996, pp. 184-190. 
                            
                            
                        
                            
                                
                                
                                    [06]
                                
                            
                            
                                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, J68-D(4): 718-725, 1985. 
                            
                            
                        
                            
                                
                                
                                    [07]
                                
                            
                            
                                A. Sherstuyk. Fast ray tracing of implicit surfaces. In Implicit Surfaces’98, pp. 145-153, June 1998. 
                            
                            
                        
                            
                                
                                
                                    [08]
                                
                            
                            
                                McCormack J., Sherstyuk A. Creating and rendering convolution surfaces, Computing Graphics Forum, vol. 17, No.2, 1998, pp. 113-120. 
                            
                            
                        
                            
                                
                                
                                    [09]
                                
                            
                            
                                Ning P., Bloomental J. An evaluation of implicit surface tilers. IEEE Computer Graphics and Applications, Vol. 13, No. 6, 1993, pp. 33-41. 
                            
                            
                        
                            
                                
                                    [10]
                                
                                
                            
                            
                                Bloomental J. et al. Introduction to implicit surfaces (Eds.), Morgan Kaufmann Publishers, 1997, 332 pp. 
                            
                            
                        
                            
                                
                                    [11]
                                
                                
                            
                            
                                P. Liepa. “Filling Holes in Meshes”// Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing, 2003, pp. 200-205. 
                            
                            
                        
                            
                                
                                    [12]
                                
                                
                            
                            
                                J. Bloomenthal. An Implicit Surface Polygonizer. Graphics gems IV, Academic Press Professional, Inc. San Diego, CA, USA 1994, pp. 324-349. 
                            
                            
                        
                            
                                
                                    [13]
                                
                                
                            
                            
                                Lorensen W., Cline H. Marching Cubes: a high resolution 3D surfaces construction algorithm. SIGGRAPH'87, Computer graphics, Vol. 21, No. 4, 1987, pp. 163-169. 
                            
                            
                        
                            
                                
                                    [14]
                                
                                
                            
                            
                                G.M. Hunter and K. Steiglitz. Operations on Images Using Quad Trees. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1(2):145–153, 1979. 
                            
                            
                        
                            
                                
                                    [15]
                                
                                
                            
                            
                                C.L. Jackins and S.L Tanimoto. Oct-trees and their use in representing three dimensional objects. Computer Graphics and Image Processing, 14(3):249–270, 1980. 
                            
                            
                        
                            
                                
                                    [16]
                                
                                
                            
                            
                                I. Gargantini and H.H. Atkinson. Ray Tracing an Octree: Numerical Evaluation of the First Interaction. Computer Graphics Forum, 12(4):199–210, 1993. 
                            
                            
                        
                            
                                
                                    [17]
                                
                                
                            
                            
                                J. L. Bentley. Multidimensional binary search trees used for associative search. Communications of ACM, 18(9):509-516, 1975. 
                            
                            
                        
                            
                                
                                    [18]
                                
                                
                            
                            
                                A. W. Moore. An introductory tutorial on kd-trees Extract from Andrew Moores PhD Thesis: Efficient Memory-based Learning for Robot Control. PhD Thesis; Technical Report No 209. Computer Laboratory. University of Cambridge. 1991. 
                            
                            
                        
                            
                                
                                    [19]
                                
                                
                            
                            
                                T.Karkanis, A.J.Stewart, Curvature dependent triangulation of implicit surfaces, IEEE Computer Graphics Application 2, 2001, pp. 60-69. 
                            
                            
                        
                            
                                
                                    [20]
                                
                                
                            
                            
                                E. Hartmann, A marching method for the triangulation of surfaces, The Visual Computer, Springer, 14:3, 1998, pp. 95-108. 
                            
                            
                        
                            
                                
                                    [21]
                                
                                
                            
                            
                                E. Galin, S. Akkouche, Incremental polygonization of implicit surfaces, Graphic Models and Image Processing, 62, 2000, pp. 19-39. 
                            
                            
                        
                            
                                
                                    [22]
                                
                                
                            
                            
                                S. Akkouche, E. Galin, Adaptive implicit surface polygonization using Marching Triangles, Computer Graphics Forum. 20:2. 2001. pp. 67-80. 
                            
                            
                        
                            
                                
                                    [23]
                                
                                
                            
                            
                                J. Bloomenthal and K. Ferguson. Polygonization of Non-Manifold implicit surfaces. In Robert Cook, editor, SIGGRAPH '95 Conference Proceedings, Annual Conference Series, pp. 309-316. ACM SIGGRAPH, Addison Wesley, August 1995. 
                            
                            
                        
                            
                                
                                    [24]
                                
                                
                            
                            
                                J. Wilhelms and Allen Van Gelder. Octrees for faster isosurface generation. ACM SIGGRAPH Computer Graphics, Volume 24 Issue 5, Nov. 1990, pp. 57-62. 
                            
                            
                        
                            
                                
                                    [25]
                                
                                
                            
                            
                                Bloomenthal J. Polygonization of implicit surfaces. Computer-Aided Geometric Design, Vol. 5, No. 4, 1988, pp. 341-355. 
                            
                            
                        
                            
                                
                                    [26]
                                
                                
                            
                            
                                A. Witkin, P. S. Heckbert. Using particles to sample and control implicit surfaces, SIGGRAPH 94, 1994, pp. 269-277. 
                            
                            
                        
                            
                                
                                    [27]
                                
                                
                            
                            
                                S.I. Vyatkin. Complex Surface Modeling Using Perturbation Functions// Optoelectronics, Instrumentation and Data Processing. – 2007 –Vol. 43, N3. pp. 226-233.