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International Conference on Geometric Modeling and Processing

GMP 2006: Geometric Modeling and Processing - GMP 2006 pp 514–527Cite as

Finding All Undercut-Free Parting Directions for Extrusions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4077))

Abstract

For molding and casting processes, geometries that have undercut-free parting directions (UFPDs) are preferred for manufacturing. Identifying all UFPDs for arbitrary geometries at interactive speeds remains an open problem, however; for polyhedral parts with n vertices, existing algorithms take at least O(n 4) time. In this paper, we introduce a new algorithm to calculate all the UFPDs for extrusions, an important class of geometry for manufacturing in its own right and a basic geometric building block in solid modeling systems. The algorithm is based on analyzing the 2D generator profile for the extrusion, building on our previous results for 2D undercut analysis of polygons. The running time is O(n 2logn) to find the exact set of UFPDs or O(n) to find a slightly conservative superset of the UFPDs, where n is the geometric complexity of the 2D generator profile. Using this approach, the set of possible UFPDs for a part containing multiple extruded features can be reduced based upon an analysis of each such feature, efficiently identifying many parts that have no UFPDs and reducing the search time for complete algorithms that find all UFPDs.

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References

  1. Ravi, B., Srinivasan, M.N.: Decision criteria for computer-aided parting surface design. Computer-Aided Design 22(1), 11–18 (1990)

    Article  Google Scholar 

  2. Wong, T., Tan, S.T., Sze, W.S.: Parting line formation by slicing a 3D CAD model. Engineering with Computers 14(4), 330–343 (1998)

    Article  MATH  Google Scholar 

  3. Chen, Y.H.: Determining parting direction based on minimum bounding box and fuzzy logics. Int. J. Mach. Tools Manufact. 37(9), 1189–1199 (1997)

    Article  Google Scholar 

  4. Hui, K.C., Tan, S.T.: Mould design with sweep operations - a heuristic search approach. Computer-Aided Design 24(2), 81–91 (1992)

    Article  MATH  Google Scholar 

  5. Hui, K.C.: Geometric aspects of the mouldability of parts. Computer-Aided Design 29(3), 197–208 (1997)

    Article  Google Scholar 

  6. Chen, L.-L., Chou, S.-Y., Woo, T.C.: Parting directions for mould and die design. Computer-Aided Design 25(12), 762–768 (1993)

    Article  MATH  Google Scholar 

  7. Woo, T.C.: Visibility maps and spherical algorithms. Computer-Aided Design 26(1), 6–16 (1994)

    Article  MATH  Google Scholar 

  8. Chen, L.-L., Chou, S.-Y.: Partial Visibility for Selecting a Parting Direction in Mold and Die Design. Journal of Manufacturing Systems 14(5), 319–330 (1995)

    Article  Google Scholar 

  9. Weinstein, M., Manoochehri, S.: Geometric Influence of a Molded Part on the Draw Direction Range and Parting Line Locations. Journal of Mechanical Design 118(3), 29–39 (1996)

    Article  Google Scholar 

  10. Wuerger, D., Gadh, R.: Virtual prototyping of die design. Part one: Theory and formulation. Concurrent Engineering: Research and Applications 5(4), 307–315 (1997)

    Article  Google Scholar 

  11. Wuerger, D., Gadh, R.: Virtual Prototyping of Die Design. Part Two: Algorithmic, Computational, and Practical Considerations. Concurrent Engineering: Research and Applications 5(4), 317–326 (1997)

    Article  Google Scholar 

  12. Ha, J., Yoo, K., Hahn, J.: Characterization of polyhedron monotonicity. Computer-Aided Design 38(1), 48–54 (2006)

    Article  MATH  Google Scholar 

  13. Requicha, A.A.G.: Representations for Rigid Solids: Theory, Methods, and Systems. ACM Computing Surveys 12(4), 437–464 (1980)

    Article  Google Scholar 

  14. Ganter, M.A., Skoglund, P.A.: Feature extraction for casting core development. In: 17th Design Automation Conference presented at the 1991 ASME Design Technical Conferences, Miami, FL, pp. 93–100. American Society of Mechanical Engineers (1991)

    Google Scholar 

  15. Fu, M.W., Fuh, J.Y.H., Nee, A.Y.C.: Generation of optimal parting direction based on undercut features in injection molded parts. IIE Transactions 31(10), 947–955 (1999)

    Google Scholar 

  16. Fu, M.W., Fuh, J.Y.H., Nee, A.Y.C.: Undercut feature recognition in an injection mould design system. Computer-Aided Design 31(12), 777–790 (1999)

    Article  MATH  Google Scholar 

  17. Ye, X.G., Fuh, J.Y.H., Lee, K.S.: A hybrid method for recognition of undercut features from moulded parts. Computer-Aided Design 33(14), 1023–1034 (2001)

    Article  Google Scholar 

  18. Yin, Z., Ding, H., Xiong, Y.: Virtual prototyping of mold design: geometric mouldability analysis for near-net-shape manufactured parts by feature recognition and geometric reasoning. Computer-Aided Design 33(2), 137–154 (2001)

    Article  Google Scholar 

  19. Rappaport, D., Rosenbloom, A.: Moldable and castable polygons. Computational Geometry: Theory and Applications 4(4), 219–233 (1994)

    MATH  MathSciNet  Google Scholar 

  20. Bose, P., Bremner, D.: Determining the Castability of Simple Polyhedra. Algorithmica 17(1-2), 84–113 (1997)

    Article  MathSciNet  Google Scholar 

  21. McMains, S., Chen, X.: Finding undercut-free parting directions for polygons with curved edges. ASME Journal of Computing and Information Science in Engineering 6(1), 60–68 (2006)

    Article  Google Scholar 

  22. Ahn, H.K., de Berg, M., Bose, P., Cheng, S.W., Halperin, D., Matousek, J., Schwarzkopf, O.: Separating an object from its cast. Computer-Aided Design 34(8), 547–559 (2002)

    Article  Google Scholar 

  23. Elber, G., Chen, X., Cohen, E.: Mold Accessibility via Gauss Map Analysis. Journal of Computing and Information Science in Engineering 5(2), 79–85 (2005)

    Article  Google Scholar 

  24. Khardekar, R., Burton, G., McMains, S.: Finding Feasible Mold Parting Directions Using Graphics Hardware. Computer-Aided Design 38(4), 327–341 (2006)

    Article  Google Scholar 

  25. Kurth, G.R., Gadh, R.: Virtual prototyping of die-design: determination of die-open directions for near-net-shape manufactured parts with extruded or rotational features. Computer Integrated Manufacturing System 10(1), 69–81 (1997)

    Article  Google Scholar 

  26. de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational geometry: algorithms and applications. Springer, New York (2000)

    MATH  Google Scholar 

  27. Boothroyd, G., Dewhurst, P., Knight, W.: Product design for manufacture and assembly. M. Dekker, New York (2002)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of California, Berkeley, CA, 94720, USA

    Xiaorui Chen & Sara McMains

Authors
  1. Xiaorui Chen
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  2. Sara McMains
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Editor information

Editors and Affiliations

  1. Seoul National University, Korea

    Myung-Soo Kim

  2. Carnegie Mellon University, Pittsburgh, PA, USA

    Kenji Shimada

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© 2006 Springer-Verlag Berlin Heidelberg

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Chen, X., McMains, S. (2006). Finding All Undercut-Free Parting Directions for Extrusions. In: Kim, MS., Shimada, K. (eds) Geometric Modeling and Processing - GMP 2006. GMP 2006. Lecture Notes in Computer Science, vol 4077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11802914_36

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  • DOI: https://doi.org/10.1007/11802914_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36711-6

  • Online ISBN: 978-3-540-36865-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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