{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T20:43:55Z","timestamp":1779309835668,"version":"3.51.4"},"reference-count":23,"publisher":"ASME International","issue":"3","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2001,9,1]]},"abstract":"<jats:p>This paper proposes a constructive representation scheme for heterogeneous objects (or FGMs). In particular, this scheme focuses on the construction of complicated heterogeneous objects, guaranteeing desired material continuities at all the interfaces. In order to create various types of heterogeneous primitives, we first describe methods for specifying material composition functions such as geometry-independent, geometry-dependent functions, and multiple sets of these functions. Constructive Material Composition (CMC) and corresponding heterogeneous Boolean Operators (e.g., material union, difference, intersection, and partition) are then proposed to illustrate how material continuities are dealt with. Finally, we will describe the model hierarchy and data structure for computer representation. Even though the constructive representation alone is sufficient for modeling heterogeneous objects, the proposed scheme pursues a hybrid representation between decomposition and construction. That is because hybrid representation can avoid unnecessary growth of binary trees.<\/jats:p>","DOI":"10.1115\/1.1403448","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T09:03:10Z","timestamp":1027760590000},"page":"205-217","update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":63,"title":["Constructive Representation of Heterogeneous Objects"],"prefix":"10.1115","volume":"1","author":[{"given":"Ki-Hoon","family":"Shin","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI\u200948109-2125"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Debasish","family":"Dutta","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI\u200948109-2125"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2001,6,1]]},"reference":[{"key":"2019100521365497900_r1","doi-asserted-by":"crossref","unstructured":"Bendsoe, M., and Kikuchi, N., 1988, \u201cGenerating Optimal Topologies in Structural Design Using a Homogenization Method,\u201d Comput. Methods Appl. Mech. Eng., 71, pp. 197\u2013224.","DOI":"10.1016\/0045-7825(88)90086-2"},{"key":"2019100521365497900_r2","doi-asserted-by":"crossref","unstructured":"Cherkaev, A. , 1994, \u201cRelaxation of Problems of Optimal Structural Design,\u201d Int. J. Solids Struct., 31, No. 16, pp. 2251\u20132280.","DOI":"10.1016\/0020-7683(94)90209-7"},{"key":"2019100521365497900_r3","unstructured":"Ashley, S. , 1991, \u201cRapid Prototyping Systems,\u201d Mech. Eng. (Am. Soc. Mech. Eng.), pp. 34\u201343."},{"key":"2019100521365497900_r4","doi-asserted-by":"crossref","unstructured":"Rajagopalan, S., Goldman, R., Shin, K. H., Kumar, V., Cutkosky, M., and Dutta, D., 2001, \u201cRepresentation of Heterogeneous Objects During Design, Processing and Freeform-Fabrication,\u201d Mater. Des., 22, No. 3, pp. 185\u2013197.","DOI":"10.1016\/S0261-3069(00)00065-0"},{"key":"2019100521365497900_r5","doi-asserted-by":"crossref","unstructured":"Jackson, T. R., Liu, H., Patrikalakis, N. M., Sachs, E. M., and Cima, M. J., 1999, \u201cModeling and Designing Functionally Graded Material Components for Fabrication With Local Composition Control,\u201d Mater. Des., 20, No. 2\/3, pp. 63\u201375.","DOI":"10.1016\/S0261-3069(99)00011-4"},{"key":"2019100521365497900_r6","unstructured":"Jackson, T., 2000, \u201cAnalysis of Functionally Graded Material Representation Methods,\u201d Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA."},{"key":"2019100521365497900_r7","unstructured":"Kumar, V. Ashok, and Wood, Aaron, 1999, \u201cRepresentation and Design of Heterogeneous Components,\u201d Proc. SFF Conference, Austin, TX."},{"key":"2019100521365497900_r8","unstructured":"Wu, Zhongke, Seah, Hock Soon, and Lin, Feng, 1999, \u201cNURBS-Based Volume Modeling,\u201d Proc. Int. Workshop on Volume Graphics, Swansea, pp. 321\u2013330."},{"key":"2019100521365497900_r9","unstructured":"Park, S. M., Crawford R. H., and Beaman, J. J., 2000, \u201cFunctionally Gradient Material Representation by Volumetric Multi-Texturing for Solid Freeform Fabrication,\u201d presented at the 11th Annual Solid Freeform Fabrication Symposium, Austin, TX."},{"key":"2019100521365497900_r10","doi-asserted-by":"crossref","unstructured":"Kumar, V., and Dutta, D., 1998, \u201cAn Approach to Modeling and Representation of Heterogeneous Objects,\u201d ASME J. Mech. Des., 120, No. 4, pp. 659\u2013667.","DOI":"10.1115\/1.2829329"},{"key":"2019100521365497900_r11","unstructured":"Kumar, V., 1998, \u201cSolid Modeling and Algorithms for Heterogeneous Objects,\u201d Ph.D. Thesis, Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI."},{"key":"2019100521365497900_r12","doi-asserted-by":"crossref","unstructured":"Requicha, A. , 1980, \u201cRepresentation for Rigid Solids: Theory, Methods and Systems,\u201d Computing Surveys, 12, No. 4No. 4.","DOI":"10.1145\/356827.356833"},{"key":"2019100521365497900_r13","unstructured":"Hoffman, C., 1989, Geometric & Solid Modeling, Morgan Kaufmann Publishers."},{"key":"2019100521365497900_r14","doi-asserted-by":"crossref","unstructured":"Liu, H., Cho, W., Jackson, T. R., Patrikalakis, N. M., and Sachs, E. M., 2000, \u201cAlgorithms for Design and Interrogation of Functionally Gradient Material Objects,\u201d Proc. ASME 26th Design Automation Conference, Baltimore, MD, Paper No. DETC2000\/DAC-14278.","DOI":"10.1115\/DETC2000\/DAC-14278"},{"key":"2019100521365497900_r15","doi-asserted-by":"crossref","unstructured":"Suresh, S., and Mortensen, A., 1997, \u201cFunctionally Graded Metals and Metal-Ceramic Composites: Thermomechanical Behavior,\u201d Int. Mater. Rev., 42, No. 3, pp. 85\u2013116.","DOI":"10.1179\/095066097790093217"},{"key":"2019100521365497900_r16","doi-asserted-by":"crossref","unstructured":"Shepard, D., 1968, \u201cA Two-Dimensional Interpolation Function for Irregularly Spaced Data,\u201d Proc. 23 Nat. Conf. ACM, pp. 517\u2013524.","DOI":"10.1145\/800186.810616"},{"key":"2019100521365497900_r17","doi-asserted-by":"crossref","unstructured":"Alfeld, P. , 1985, \u201cMultivariate Perpendicular Interpolation,\u201d SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 22, pp. 96\u2013106.","DOI":"10.1137\/0722006"},{"key":"2019100521365497900_r18","doi-asserted-by":"crossref","unstructured":"Rvachev, V. L., Sheiko, T. I., Shapiro, V., and Tsukanov, I., 2000, \u201cTransfinite Interpolation Over Implicitly Defined Sets,\u201d Technical Report SAL 2000-1, Spatial Automation Lab., Univ. of Wisconsin.","DOI":"10.1016\/S0167-8396(01)00015-2"},{"key":"2019100521365497900_r19","unstructured":"Rvachev, V. L. , 1967, \u201cTheory of R-Functions and Some Applications,\u201d Naukova Dumka, in Russian."},{"key":"2019100521365497900_r20","unstructured":"ACIS Geometric Modeler: Application Guide, 1995, Spatial Technology Inc."},{"key":"2019100521365497900_r21","unstructured":"Weiler, K. J., 1986, \u201cThe Radial Edge Structure: A Topological Representation for Non-Manifold Geometric Modeling,\u201d in: M. J. Wozny, H. McLaughlin, and J. Encarnacao, eds., Geometric Modeling for CAD Applications, Elsevier Science Publishers, Holland, pp. 3\u201336."},{"key":"2019100521365497900_r22","doi-asserted-by":"crossref","unstructured":"Bhashyam, S., Shin, K. H., and Dutta, D., 2000, \u201cAn Integrated CAD System for Design of Heterogeneous Objects,\u201d Rapid Prototyping J., 6, No. 2, pp. 119\u2013135.","DOI":"10.1108\/13552540010323547"},{"key":"2019100521365497900_r23","unstructured":"Donomoto T., Miura N., Funatani K., and Miyake N., 1983, SAE Tech. Paper No. 83052, Detroit, MI."}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/1\/3\/205\/5483945\/205_1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/1\/3\/205\/5483945\/205_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,23]],"date-time":"2023-04-23T10:35:32Z","timestamp":1682246132000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/1\/3\/205\/445283\/Constructive-Representation-of-Heterogeneous"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,6,1]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2001,9,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.1403448","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"value":"1530-9827","type":"print"},{"value":"1944-7078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,6,1]]}}}