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: Methods and systems for developing a product using a model that satisfies a region constraint. Data is received. A region constraint is identified. A model that fits the data and satisfies the region constraint is identified using a quadratic objective function and a set of point constraints derived iteratively from the region constraint.

Abstract: A method of planning fiber paths for a composite ply of a composite layup includes determining a first unit vector field. The first unit vector field represents a first approximation of target directions to be followed by tow centerlines of the composite ply. The first unit vector field is determined based on a specified rosette direction, a surface approximation of a nonplanar contoured surface of an object to be formed, and a fiber angle distribution. The method also includes determining, based on specified angle deviation bounds and the first unit vector field, a second unit vector field. The second unit vector field represents a second approximation of the target directions. The second approximation has reduced in-plane curvature relative to the first approximation. The method further includes planning a fiber placement head path for forming the composite ply of the composite layup based on the second unit vector field.

Abstract: A method of planning fiber paths for a composite ply of a composite layup includes determining a first unit vector field. The first unit vector field represents a first approximation of target directions to be followed by tow centerlines of the composite ply. The first unit vector field is determined based on a specified rosette direction, a surface approximation of a nonplanar contoured surface of an object to be formed, and a fiber angle distribution. The method also includes determining, based on specified angle deviation bounds and the first unit vector field, a second unit vector field. The second unit vector field represents a second approximation of the target directions. The second approximation has reduced in-plane curvature relative to the first approximation. The method further includes planning a fiber placement head path for forming the composite ply of the composite layup based on the second unit vector field.