Abstract: A modeling system is provided which retrieves from memory the 3D virtual model of an object; extract an outer surface of the 3D virtual model, the outer surface including a plurality of faces; identify feature curves in each of the plurality of faces of the outer surface; generate a parameterized surface from the identified feature curves; and output the feature curves and the parameterized surface. The system may generate a list of feature curve pairs that are adjacent to one another; obtain face pairs corresponding to the feature curve pairs; obtain and add a list of faces in the outer surface to a connectivity graph mapping points in 3D space to the feature curves; for each pair of connected faces, evaluate whether an angle difference between normals of the connected faces is greater than a threshold; and then extract a feature curve based on the pair of connected faces.

Abstract: A modeling system is provided which is configured to retrieve from the non-volatile memory the 3D virtual model of an object; define a domain of a parametric surface; project feature curves in the 3D virtual model into the domain of the parametric surface to generate a mapping based on the 3D virtual model and including a plurality of parametric curves; divide the plurality of parametric curves into horizontal and vertical feature curves; extend each of the horizontal feature and vertical feature curves; construct a horizontal interpolant connecting the extended horizontal feature curves; construct a vertical interpolant connecting the extended vertical feature curves; fit the horizontal and vertical interpolants as coordinates of a map to a new parametric domain; and compose the inverse of the map to the new parametric domain with the parametric surface to create a new parametric surface containing the feature curves as isoparametric curves.

Abstract: This description provides tools for lazy evaluation of geometric definitions of objects within procedural programming environments. Computer-based methods provided by these tools may parse input program code that includes statements that are syntactically consistent with a procedural programming language. These statements may also include defined functions that are not syntactically consistent with the procedural programming language. The defined functions may be associated with a given function that is defined according to the procedural programming language. The given function may relate to a geometric design of an object. The methods may identify inputs and outputs to this given function, and may build a dependency graph that relates this given function to other functions, based on the inputs and/or outputs of the given function. The methods may delay evaluating the given function until a triggering event occurs, at which time the methods may evaluate the given function to produce the output.

Abstract: A method for determining a path of travel of an intruder traversing an area of regard (AOR) to a predefined point, where the path of travel has a minimum probability of detection relative to other potential paths of travel of the intruder. The method may comprise: providing three dimensional terrain data concerning the AOR; providing the locations of a plurality of detection sensors implemented in the AOR, with each detection sensor having a known field of view; providing a predetermined single scan detection probability for each of the detection sensors; generating a grid of points that is laid over the AOR; and using the foregoing information to determine a particular path of travel, defined by selected arcs connecting specific ones of the grid of points, of the intruder to the predefined point that represents a minimum probability of detection of the intruder.

Abstract: A method for determining a path of travel of an intruder traversing an area of regard (AOR) to a predefined point, where the path of travel has a minimum probability of detection relative to other potential paths of travel of the intruder. The method may comprise: providing three dimensional terrain data concerning the AOR; providing the locations of a plurality of detection sensors implemented in the AOR, with each detection sensor having a known field of view; providing a predetermined single scan detection probability for each of the detection sensors; generating a grid of points that is laid over the AOR; and using the foregoing information to determine a particular path of travel, defined by selected arcs connecting specific ones of the grid of points, of the intruder to the predefined point that represents a minimum probability of detection of the intruder.

Abstract: This description provides tools for lazy evaluation of geometric definitions of objects within procedural programming environments. Computer-based methods provided by these tools may parse input program code that includes statements that are syntactically consistent with a procedural programming language. These statements may also include defined functions that are not syntactically consistent with the procedural programming language. The defined functions may be associated with a given function that is defined according to the procedural programming language. The given function may relate to a geometric design of an object. The methods may identify inputs and outputs to this given function, and may build a dependency graph that relates this given function to other functions, based on the inputs and/or outputs of the given function. The methods may delay evaluating the given function until a triggering event occurs, at which time the methods may evaluate the given function to produce the output.