Moment-Based Representation for Interoperable Analysis
Methods and system for computing integrals over geometric domains using moment-base representations for interoperability are disclosed. A first computing device may receive data for geometric and field representations of an object, the geometric representation specifying a geometric domain of the ob...
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| creator | Shapiro, Vadim Taber, Andrew Kumar, Goldy Freytag, Michael |
| description | Methods and system for computing integrals over geometric domains using moment-base representations for interoperability are disclosed. A first computing device may receive data for geometric and field representations of an object, the geometric representation specifying a geometric domain of the object, and the field representation specifying a spatially varying physical quantity. The first computing device may integrate a predetermined set of basis functions over the geometric domain multiplied by a field to derive a moment-vector for the object, the moment-vector encapsulating an analytic formulation of the geometric domain that is independent of the geometric and field representations. The first computing device may computationally generate quadrature rules for integrating an arbitrary function by applying moment-fitting to the moment-vector. The quadrature rules may be provided to a second computing device, which may integrate the arbitrary function over the geometric domain by applying the quadrature rules, independently of the geometric and field representations. |
| format | Patent |
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A first computing device may receive data for geometric and field representations of an object, the geometric representation specifying a geometric domain of the object, and the field representation specifying a spatially varying physical quantity. The first computing device may integrate a predetermined set of basis functions over the geometric domain multiplied by a field to derive a moment-vector for the object, the moment-vector encapsulating an analytic formulation of the geometric domain that is independent of the geometric and field representations. The first computing device may computationally generate quadrature rules for integrating an arbitrary function by applying moment-fitting to the moment-vector. The quadrature rules may be provided to a second computing device, which may integrate the arbitrary function over the geometric domain by applying the quadrature rules, independently of the geometric and field representations.</description><language>eng</language><subject>ADDITIVE MANUFACTURING TECHNOLOGY ; ADDITIVE MANUFACTURING, i.e. MANUFACTURING OFTHREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVEAGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING,STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING ; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING ; CALCULATING ; COMPUTING ; CONTROL OR REGULATING SYSTEMS IN GENERAL ; CONTROLLING ; COUNTING ; ELECTRIC DIGITAL DATA PROCESSING ; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS ; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS ORELEMENTS ; PERFORMING OPERATIONS ; PHYSICS ; REGULATING ; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDEDFOR ; SHAPING OR JOINING OF PLASTICS ; TRANSPORTING ; WORKING OF PLASTICS ; WORKING OF SUBSTANCES IN A PLASTIC STATE, IN GENERAL</subject><creationdate>2021</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://worldwide.espacenet.com/publicationDetails/biblio?FT=D&date=20210805&DB=EPODOC&CC=US&NR=2021240159A1$$EHTML$$P50$$Gepo$$Hfree_for_read</linktohtml><link.rule.ids>230,308,780,885,25564,76547</link.rule.ids><linktorsrc>$$Uhttps://worldwide.espacenet.com/publicationDetails/biblio?FT=D&date=20210805&DB=EPODOC&CC=US&NR=2021240159A1$$EView_record_in_European_Patent_Office$$FView_record_in_$$GEuropean_Patent_Office$$Hfree_for_read</linktorsrc></links><search><creatorcontrib>Shapiro, Vadim</creatorcontrib><creatorcontrib>Taber, Andrew</creatorcontrib><creatorcontrib>Kumar, Goldy</creatorcontrib><creatorcontrib>Freytag, Michael</creatorcontrib><title>Moment-Based Representation for Interoperable Analysis</title><description>Methods and system for computing integrals over geometric domains using moment-base representations for interoperability are disclosed. 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A first computing device may receive data for geometric and field representations of an object, the geometric representation specifying a geometric domain of the object, and the field representation specifying a spatially varying physical quantity. The first computing device may integrate a predetermined set of basis functions over the geometric domain multiplied by a field to derive a moment-vector for the object, the moment-vector encapsulating an analytic formulation of the geometric domain that is independent of the geometric and field representations. The first computing device may computationally generate quadrature rules for integrating an arbitrary function by applying moment-fitting to the moment-vector. 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| subjects | ADDITIVE MANUFACTURING TECHNOLOGY ADDITIVE MANUFACTURING, i.e. MANUFACTURING OFTHREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVEAGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING,STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING CALCULATING COMPUTING CONTROL OR REGULATING SYSTEMS IN GENERAL CONTROLLING COUNTING ELECTRIC DIGITAL DATA PROCESSING FUNCTIONAL ELEMENTS OF SUCH SYSTEMS MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS ORELEMENTS PERFORMING OPERATIONS PHYSICS REGULATING SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDEDFOR SHAPING OR JOINING OF PLASTICS TRANSPORTING WORKING OF PLASTICS WORKING OF SUBSTANCES IN A PLASTIC STATE, IN GENERAL |
| title | Moment-Based Representation for Interoperable Analysis |
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