Abstract: 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.

Abstract: Methods and systems for evaluation of a physical object directly from a manufacturing process plan are disclosed. A procedural representation of the object may be retrieved from a database. A non-conforming grid of basis functions representing physics to be applied may be determined. Boundary conditions for numerical integration over the object geometry may be determined. The boundary conditions may specify a physical boundary of a portion of the object geometry, and a physical condition applied over the portion. From the procedural representation, geometry and material rules for numerical integration over the portion of the object geometry may be determined. The basis functions may be numerically integrated over the object geometry, and a system of linear equations determined describing the physics subject to the boundary conditions. The system of equations may be solved to evaluate a physical quantity, and a graphical representation of the physical quantity may be displayed.

Abstract: 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 a geometric representation of an object, the geometric representation specifying a geometric domain corresponding to a shape and a contained spatial region of the object. The first computing device may computationally integrate a predetermined set of basis functions over the geometric domain 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 representation. The first computing device may then 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.

Abstract: A method is described for modeling heterogeneous material properties within a geometric model of an object (e.g., within a CAD model). Material functions are defined about material features (i.e., points, surfaces, or areas on or in the model) at which material properties are known, with the material functions each defining the behavior of that feature's material property at locations away from that feature. Combination of the material functions results in a single material function which defines the material properties throughout the geometric model. The resulting material function may then be used in subsequent analyses, such as in computerized behavior analysis of the geometric model. The material function may be constructed such that it meets desired constraints, and has desired smoothness and analytical properties, for ease of use in such subsequent analyses.