We consider the problem of whether a given geometry can be molded in a two-part, rigid, reusable mold with opposite removal directions. We describe an efficient algorithm for solving the opposite direction moldability problem for a 2D “polygon” bounded by edges that may be either straight or curved. We introduce a structure, the normal graph of the polygon, that represents the range of normals of the polygon’s edges, along with their connectivity. We prove that the normal graph captures the directions of all lines corresponding to feasible parting directions. Rather than building the full normal graph, which could take time for a polygon bounded by possibly curved edges, we build a summary structure in time and space, from which we can determine all feasible parting directions in time .
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e-mail: mcmains@me.berkeley.edu
e-mail: xrchen@me.berkeley.edu
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March 2006
Technical Papers
Finding Undercut-Free Parting Directions for Polygons with Curved Edges
Sara McMains,
Sara McMains
Department of Mechanical Engineering,
e-mail: mcmains@me.berkeley.edu
University of California
, Berkeley, CA, Berkeley
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Xiaorui Chen
Xiaorui Chen
Department of Mechanical Engineering,
e-mail: xrchen@me.berkeley.edu
University of California
, Berkeley, CA, Berkeley
Search for other works by this author on:
Sara McMains
Department of Mechanical Engineering,
University of California
, Berkeley, CA, Berkeleye-mail: mcmains@me.berkeley.edu
Xiaorui Chen
Department of Mechanical Engineering,
University of California
, Berkeley, CA, Berkeleye-mail: xrchen@me.berkeley.edu
J. Comput. Inf. Sci. Eng. Mar 2006, 6(1): 60-68 (9 pages)
Published Online: October 12, 2005
Article history
Received:
December 1, 2004
Revised:
October 12, 2005
Citation
McMains, S., and Chen, X. (October 12, 2005). "Finding Undercut-Free Parting Directions for Polygons with Curved Edges." ASME. J. Comput. Inf. Sci. Eng. March 2006; 6(1): 60–68. https://doi.org/10.1115/1.2164450
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