Abstract: A system or tool kit is provided that allows a user to specify a deformation for a model. When the deformation produces anomalies the user can select functions or solutions from the tool kit to be executed that correct the anomalies. When the effect of a warp or deformation extends into a region outside a user specified constraint, a clamp function can be selected from the kit to stop the effect outside of the constraint. When a constraint causes the transition from a warp to a non-warp region to result in a sharp transition a tangent continuous transition function can be applied from the kit. When contradictory modifiers and constraints cause unexpected excursions in the warped model, samples with outlier Laplacians can be culled. When the model includes rigid objects, the motion of the rigid objects can be used as a modifier to allow the rigid objects to move with the deformed model without being deformed.

Abstract: A system or method to distribute curvature in a set of target vertices by computing curvature at boundary vertices of the set of target vertices by use of an umbrella operator. The boundary curvatures may be distributed into the set of target vertices by solving for a system of Umbrella operator equations for curvatures of respective vertices of the set of target vertices, with the computed curvature at the boundary vertices as a boundary condition for the system of equations. The vertices of the set of target vertices may be repositioned relative to the their neighbors according to the solved curvatures of the respective vertices of the set of vertices. The computing, distributing, and repositioning may be repeated, thereby changing the overall shape of the set of target vertices according to the curvature at the boundary vertices.

Abstract: A system or method to distribute curvature in a set of target vertices by computing curvature at boundary vertices of the set of target vertices by use of an umbrella operator. The boundary curvatures may be distributed into the set of target vertices by solving for a system of Umbrella operator equations for curvatures of respective vertices of the set of target vertices, with the computed curvature at the boundary vertices as a boundary condition for the system of equations. The vertices of the set of target vertices may be repositioned relative to the their neighbors according to the solved curvatures of the respective vertices of the set of vertices. The computing, distributing, and repositioning may be repeated, thereby changing the overall shape of the set of target vertices according to the curvature at the boundary vertices.

Abstract: An apparatus, method, and computer readable storage medium for accurately performing Boolean operations on subdivision surfaces. The present invention produces a base mesh which subdivides into a surface which represents the Boolean operation of two subdivision surfaces. The method includes (a) chopping pieces of two Catmull-Clark bases meshes which correspond to pieces of a Boolean surface computed from limit surfaces of the two base meshes; (b) creating new edges on the chopped pieces to create quadrilaterals and triangles; and (c) merging the chopped pieces with the new edges into a Boolean base mesh which approximates the Boolean surface.

Abstract: A system that predistorts a computer generated paint stamp for paint being applied to a 3D computer model of an object. The predistortion is based on a difference in shape and orientation of a texture space polygon, to which the stamp is initially applied, and the corresponding world space target polygon of the model. Because the paint stamps often overlap several polygons of different shapes and orientations, the distortion compensation becomes a weighted average of the distortion compensation for the polygon under the stamp and its nearest neighbors.

Abstract: Planar texture maps which reflect the distances and angles of a 3-D surface are generated. A user is permitted to manually adjust the balance between discontinuity and distortion. The user selectively modifies the 3-D surface, and by doing so adjusts the balance between discontinuity and distortion in the planar map. Each point on the 3-D surface corresponds to a unique point on the planar map. Operations may therefore be performed on the simpler 2-D planar map rather than the more complex 3-D map, and the result of the operations may be uniquely mapped to the 3-D surface. Further, the majority of the vertices on a 3-D surface are mapped automatically, even though the user maintains a high degree of control over the mapping process via altering the 3-D surface boundary. User-selected map vertices may be pinned to a user-selected location, and held fixed while a conventional relaxation technique is applied. This provides the user with a greater degree of control over the relaxation process.

Abstract: A projective body is aligned with a surface to generate texture coordinates for the surface. The present invention includes selecting an appropriate projective body for a given surface, orienting and positioning the surface with respect to the projective body, projecting the surface onto the projective body, and then mapping the projective body onto the texture rectangle. An inertial ellipsoid is used to orient the surface and the projective body. The inertial ellipsoid can also be used as the projective body. Ellipsoidal coordinates are preferably used to project the surface onto the projective body.