Abstract: Techniques of refining a model of a complex surface can include refining, upon insertion of a new control point, only those blending functions corresponding to the control points adjacent to the control point being inserted. The resulting curves cannot be considered as B-splines because the relationship between blending functions corresponding to adjacent control points no longer has a fixed relationship. Rather, the resulting blending functions, denoted herein as “S-splines,” sacrifice this fixed relationship in exchange for the ability to specify how many blending functions corresponding to adjacent control points are refined when performing exact local refinement. S-splines do not produce excess control points and have a simple representation. While the resulting functions representing the surface are not B-splines, they allow for exact refinement without affecting the blending functions corresponding to control points not neighboring the new control point.

Abstract: Techniques of refining a model of a complex surface can include refining, upon insertion of a new control point, only those blending functions corresponding to the control points adjacent to the control point being inserted. The resulting curves cannot be considered as B-splines because the relationship between blending functions corresponding to adjacent control points no longer has a fixed relationship. Rather, the resulting blending functions, denoted herein as “S-splines,” sacrifice this fixed relationship in exchange for the ability to specify how many blending functions corresponding to adjacent control points are refined when performing exact local refinement. S-splines do not produce excess control points and have a simple representation. While the resulting functions representing the surface are not B-splines, they allow for exact refinement without affecting the blending functions corresponding to control points not neighboring the new control point.

Abstract: Techniques of refining a model of a complex surface can include deriving a set of refinement rules based on eigen polyhedra in a plane. Such rules reduce the refinement of a mesh in the plane to a scale and translation of the eigen polyhedron. Such refinement rules may then be applied to a non-uniform mesh in three-dimensional space having an extraordinary point in place of conventional refinement rules used in Catmull-Clark surfaces or NURBS surfaces. When these refinement rules are applied to a non-uniform mesh having an extraordinary point, the limiting surface is G1 at the extraordinary point, i.e., the tangent surfaces of the limiting mesh are continuous at the extraordinary point.

Abstract: Techniques of refining a model of a complex surface can include deriving a set of refinement rules based on eigen polyhedra in a plane. Such rules reduce the refinement of a mesh in the plane to a scale and translation of the eigen polyhedron. Such refinement rules may then be applied to a non-uniform mesh in three-dimensional space having an extraordinary point in place of conventional refinement rules used in Catmull-Clark surfaces or NURBS surfaces. When these refinement rules are applied to a non-uniform mesh having an extraordinary point, the limiting surface is G1 at the extraordinary point, i.e., the tangent surfaces of the limiting mesh are continuous at the extraordinary point.

Abstract: Modeling genealogical trees that span multiple pages can include the creation and use of navigable links between related nodes. When it is determined that a display layout of a genealogical tree will span a plurality of viewable pages by a document viewer, a descendent node is identified that genealogical links directly to a related ancestor node on another page. A selectable ancestor page link is then created and displayed proximate the descendent relative node which, when selected, causes the viewer to render the page containing the ancestor relative node. A selectable descendent page link is also created and displayed proximate the ancestor relative node which, when selected, causes the viewer to render the particular page containing the descendent relative node. Intelligent formatting can also be used to identify and remove or refrain from displaying duplicate branches of the genealogical tree.

Abstract: A system and method is provided for defining a bi-cubic spline surface in a computing environment. One operation in the method is creating a control mesh with a substantially rectangular structure. A further operation is inferring from the control mesh the tensor product B-spline basis functions for each control point. The surface can then be computed based on the basis functions and the control mesh.

Abstract: A system and method is provided for defining a bi-cubic spline surface in a computing environment. One operation in the method is creating a control mesh with a substantially rectangular structure. A further operation is inferring from the control mesh the tensor product B-spline basis functions for each control point. The surface can then be computed based on the basis functions and the control mesh.

Abstract: A method of using a computer graphic system for free-form deformation of geometric models. The method is based on the use of a control-point grid which is imposed on the model and which can then be moved by a system designer to specify a deformation to a particular region of the model. Displacement of control points on the grid provides the designer with an intuitive appreciation for the resulting affect in terms of deformation on the specified region of the geometric model. The free-form deformation of the model is accomplished through the use of a trivariate vector rational polynomial in which the displaced control points represent coefficients of the polynomial. The method provides a powerful and highly flexible technique that can be adapted and used in the environment of virtually any presently known solid modeling system, such as CSG or B-rep. The method can be used to deform surface primitives of any type or degree, such as planes, quadrics, parametric surface patches or implicitly defined surfaces.

Abstract: A method is disclosed for the determination of the shape of a flat section of fabric prior to application of the fabric to a curved surface.