Space-filling curves in adaptive curvilinear coordinates for computer numerically controlled five-axis machining

Mathematics and Computers in Simulation

Volumn 79, Issue 8, 2009, Pages 2385-2402

  Makhanov, S S ^a  

^a THAMMASAT UNIVERSITY   (Thailand)

Author keywords

[No Author keywords available]

Indexed keywords

MACHINE TOOLS; MACHINING; MESH GENERATION;

CONVENTIONAL METHODS; CURVILINEAR COORDINATES; FIVE-AXIS MACHINING; GRID GENERATIONS; SPACE-FILLING CURVES;

COMPUTER CONTROL SYSTEMS;

EID: 63449089709     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2009.01.019     Document Type: Article

References (40)

1. Anotaipaiboon W., and Makhanov S.S. Tool path generation for five-axis NC machining using space-filling curves. Proceeding of The Third Asian Conference on Industrial Automation and Robotics, vol. 1 (2003) 23-28
2. Anotaipaiboon W., and Makhanov S.S. Tool path generation for five-axis NC machining using adaptive space-filling curves. International Journal of Production Research 43 (2005) 1643-1665
3. Asano T., Ranjan D., Roos T., Welzl E., and Widmayer P. Space-filling curves and their use in the design of geometric data structures. Theoretical Computer Science 181 1 (1997) 3-15
4. Bieterman M.B., and Sandstrom D.R. A curvilinear tool-path method for pocket machining. Journal of Materials Processing Technology 125 4 (2003) 709-715
5. Bohez E., Makhanov S.S., and Sonthipermpoon K. Adaptive nonlinear tool path optimization for five-axis machining. International Journal of Production Research 38 (2000) 4329-4343
6. De Boor C. A Practical Guide to Splines (2001), Springer, New York, USA
7. Brackbill J.U., and Saltzman J.S. Adaptive zoning for singular problems in two dimensions. Journal of Computational Physics 46 (1982) 342-368
8. Charakhchyan A.A., and Ivanenko S.A. A variational form of the Winslow grid generator. Journal of Computational Physics 136 2 (1997) 385-398
9. Cox J.J., Takezaki T., Ferguson H.R.P., Kohkonen K.E., and Mulkay E.L. Space-filling curves in tool-path applications. Computer Aided Design 26 (1994) 215-224
10. Cole A.J. Compaction techniques for raster scan graphics using space-filling curves. The Computer Journal 30 1 (1987) 87-92
11. Dafner R., Cohen-Or D., and Matias Y. Context-based space filling curves. Computer Graphics Forum 19 3 (2000) 209-218
12. Farin G.E. NURBS: From Projective Geometry to Practical Use (1999), A.K. Peters Ltd., Natick, MA, USA
13. Gao J., Chen X., Zheng D., Yilmaz O., and Gindy N. Adaptive restoration of complex geometry parts through reverse engineering application. Advances in Engineering Software 37 9 (2006) 592-600
14. Griffiths J.G. Toolpath based on Hilbert's curve. Advances in Engineering Software 26 (1994) 839-844
15. Hopcroft J.E., and Ullman J.D. Introduction to Automata Theory, Languages and Computation (1979), Addison-Wesley, New York
16. Ivanenko S.A. Generation of non-degenerate meshes. USSR Computational Mathematics and Mathematical Physics 28 (1988) 141-146
17. Ivanenko S.A., Thompson J.F., Soni B.K., and Weatherill N.P. Harmonic Mappings Handbook of Grid Generation, vol. 8 (1999), CRC Press LLC 1-43
18. 1 NURBS Boundary Gregory Patches. Computer Aided Design 33 (2001) 293-306
19. Lam W.M., and Shapiro J.H. A class of fast algorithms for the Peano-Hilbert space-filling curve. Proceedings ICIP-94, IEEE Computer Society, vol. 1 (1994) 638-641
20. Lauwers B., Dejonghe P., and Kruth J.P. Optimal and collision free tool posture in five-axis machining through the tight integration of tool path generation and machining simulation. Computer Aided Desing 35 (2003) 421-432
21. Lawder J.K., and King P.J.H. Querying multi-dimensional data indexed using the Hilbert space-filling curve. ACM SIGMOD Record 30 1 (2001) 19-24
22. Lee Y.-S. Admissible tool orientation control of gouging avoidance for 5-axis complex surface machining. Computer Aided Design 29 (1997) 507-521
23. Lo C.-C. Efficient cutter-path planning for five-axis surface for machining with a flat-end cutter. Computer Aided Desing 31 (1999) 557-566
24. Makhanov S.S. An application of the grid generation techniques to optimize a tool-path of industrial milling robots. Journal of Computational Mathematics and Mathematical Physics 39 (1999) 1589-1600
25. Makhanov S.S., and Ivanenko S.A. Grid generation as applied to optimize cutting operations of a five-axis milling machine. Applied Numerical Mathematics 46 (2003) 353-377
26. Makhanov S.S., Batanov D., Bohez E., Sonthipaumpoon K., Anotaipaiboon W., and Tabucanon M. On the tool-path optimization of a milling robot". Computers & Industrial Engineering 43 (2002) 455-472
27. Pascucci V., and Frank R.J. Global static indexing for real-time exploration of very large regular grids. (CDROM). Supercomputing'01, Proceedings of the 2001 ACM/IEEE Conference on Supercomputing (2001)
28. Piegl L., and Tiller W. The NURBS Book (1995), Springer-Verlag, London, UK
29. Rao A., and Sarma R. On local gouging in five-axis sculptured surface machining using flat end tools. Computer Aided Design (2000) 409-420
30. Robert F.S. Applied Combinatorics (1984), Prentice-Hall, Englewood CLiffs, NJ p. 32
31. Sagan H. Space-Filling Curves (1994), Springer-Verlag, New York
32. Schamberger S., and Wierum J.-M. Partitioning finite element meshes using space-filling curves. Future Generation Computer Systems 21 5 (2005) 759-766
33. Song Z., and Roussopoulos N. Using Hilbert curve in image storing and retrieving. MULTIMEDIA'00, Proceedings of the 2000 ACM Workshops on Multimedia (2000) 167-170
34. Soni B.K., Koomullil R., Thompson D.S., and Thornburg H. Solution adaptive grid strategies based on point redistribution. Computer Methods in Applied Mechanics and Engineering 189 4 (2000) 1183-1204
35. Thomson J.F., Soni B., and Weatherill N. Handbook of Grid Generation (1999), CRC Press
36. Velho L., and Gomes J. Digital halftoning with space filling curves. SIGGRAPH'91, Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques (1991) 81-90
37. Winslow A.M. Numerical solution of the quasilinear Poisson equation in a non-uniform triangle mesh. Journal of Computational Physics 1 2 (1966) 149-172
38. Yang K.-M., Wu L., and Mills M. Fractal based image coding scheme using Peano scanning. Proceedings of 1988 IEEE International Symposium on Circuits and Systems (1988) 2301-2304
39. Yoon J.-H. Tool tip gouging avoidance and optimal tool positioning for 5-axis sculptured surface machining. International Journal of Production Research 41 (2003) 2125-2142
40. Zhang Y., and Webber R.E. Space diffusion: an improved parallel halftoning technique using space-filling curves. SIGGRAPH'93, Proceedings of the 20th Annual Conference on Computer graphics and Interactive Techniques (1993) 305-312