{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T13:58:40Z","timestamp":1761487120714,"version":"3.30.2"},"reference-count":29,"publisher":"ASME International","issue":"1","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2004,3,1]]},"abstract":"<jats:p>A typical computer representation of a design includes geometric and physical information organized in a suitable combinatorial data structure. Queries and transformations of these design representations are used to formulate most algorithms in computational design, including analysis, optimization, evolution, generation, and synthesis. Formal properties, and in particular existence and validity of the computed solutions, must be assured and preserved by all such algorithms. Using tools from algebraic topology, we show that a small set of the usual combinatorial operators: boundary (\u2202), coboundary (\u03b4), and dualization *\u2013are sufficient to represent a variety of physical laws and invariants. Specific examples include geometric integrity, balance and equilibrium, and surface smoothing. Our findings point a way toward systematic development of data structures and algorithms for design in a common formal computational framework.<\/jats:p>","DOI":"10.1115\/1.1645863","type":"journal-article","created":{"date-parts":[[2004,3,23]],"date-time":"2004-03-23T23:06:01Z","timestamp":1080083161000},"page":"3-10","update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":6,"title":["Combinatorial Laws for Physically Meaningful Design"],"prefix":"10.1115","volume":"4","author":[{"given":"Vasu","family":"Ramaswamy","sequence":"first","affiliation":[{"name":"Spatial Automation Laboratory, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI\u200953706"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vadim","family":"Shapiro","sequence":"additional","affiliation":[{"name":"Spatial Automation Laboratory, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI\u200953706"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2004,3,23]]},"reference":[{"key":"2019100522033442800_r1","doi-asserted-by":"crossref","unstructured":"Palmer, R., and Shapiro, V., 1993, \u201cChain Models of Physical Behavior for Engineering Analysis and Design,\u201d Res. 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