Finding All Undercut-Free Parting Directions for Extrusions

  • Xiaorui Chen
  • Sara McMains
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4077)


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.


Extrusion Direction Virtual Prototype Parting Direction Complete Algorithm Vertical Line Segment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ravi, B., Srinivasan, M.N.: Decision criteria for computer-aided parting surface design. Computer-Aided Design 22(1), 11–18 (1990)CrossRefGoogle Scholar
  2. 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)zbMATHCrossRefGoogle Scholar
  3. 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)CrossRefGoogle Scholar
  4. 4.
    Hui, K.C., Tan, S.T.: Mould design with sweep operations - a heuristic search approach. Computer-Aided Design 24(2), 81–91 (1992)zbMATHCrossRefGoogle Scholar
  5. 5.
    Hui, K.C.: Geometric aspects of the mouldability of parts. Computer-Aided Design 29(3), 197–208 (1997)CrossRefGoogle Scholar
  6. 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)zbMATHCrossRefGoogle Scholar
  7. 7.
    Woo, T.C.: Visibility maps and spherical algorithms. Computer-Aided Design 26(1), 6–16 (1994)zbMATHCrossRefGoogle Scholar
  8. 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)CrossRefGoogle Scholar
  9. 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)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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)CrossRefGoogle Scholar
  12. 12.
    Ha, J., Yoo, K., Hahn, J.: Characterization of polyhedron monotonicity. Computer-Aided Design 38(1), 48–54 (2006)CrossRefzbMATHGoogle Scholar
  13. 13.
    Requicha, A.A.G.: Representations for Rigid Solids: Theory, Methods, and Systems. ACM Computing Surveys 12(4), 437–464 (1980)CrossRefGoogle Scholar
  14. 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. 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. 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)zbMATHCrossRefGoogle Scholar
  17. 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)CrossRefGoogle Scholar
  18. 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)CrossRefGoogle Scholar
  19. 19.
    Rappaport, D., Rosenbloom, A.: Moldable and castable polygons. Computational Geometry: Theory and Applications 4(4), 219–233 (1994)zbMATHMathSciNetGoogle Scholar
  20. 20.
    Bose, P., Bremner, D.: Determining the Castability of Simple Polyhedra. Algorithmica 17(1-2), 84–113 (1997)CrossRefMathSciNetGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 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)CrossRefGoogle Scholar
  23. 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)CrossRefGoogle Scholar
  24. 24.
    Khardekar, R., Burton, G., McMains, S.: Finding Feasible Mold Parting Directions Using Graphics Hardware. Computer-Aided Design 38(4), 327–341 (2006)CrossRefGoogle Scholar
  25. 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)CrossRefGoogle Scholar
  26. 26.
    de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational geometry: algorithms and applications. Springer, New York (2000)zbMATHGoogle Scholar
  27. 27.
    Boothroyd, G., Dewhurst, P., Knight, W.: Product design for manufacture and assembly. M. Dekker, New York (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiaorui Chen
    • 1
  • Sara McMains
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA

Personalised recommendations