Abstract: A method is provided for detecting regions of high curvature on a curve. The method comprises receiving a curve function and automatically arc length parameterizing the curve function. The local average curvature over the arc length parameterized curve function is automatically computed. One or more regions where the local average curvature turns at least a predetermined angle over a given interval are automatically indicated. The indicated regions are then output.

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: 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 method is provided for detecting regions of high curvature on a curve. The method comprises receiving a curve function and automatically arc length parameterizing the curve function. The local average curvature over the arc length parameterized curve function is automatically computed. One or more regions where the local average curvature turns at least a predetermined angle over a given interval are automatically indicated. The indicated regions are then output.

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.