Abstract: Deforming a three-dimensional computer-generated model to cause a change of shape of the three-dimensional model includes representing a surface of the model using a surface representation initially comprised of an original surface definition, deriving smooth three-dimensional mapping functions where each mapping function defines a deformation to the surface and at least one mapping function is non-affine, constructing a composition of the mapping functions and the original surface definition where each mapping function is included in the composition in succession in accordance with the order of derivation, and applying the composition after each successive mapping function is included in the composition causing the surface of the three-dimensional model to be deformed while preserving the smoothness to the lowest degree of smoothness of the mapping functions.

Abstract: Deforming a three-dimensional computer-generated model to cause a change of shape of the three-dimensional model includes representing a surface of the model using a surface representation initially comprised of an original surface definition, deriving smooth three-dimensional mapping functions where each mapping function defines a deformation to the surface and at least one mapping function is non-affine, constructing a composition of the mapping functions and the original surface definition where each mapping function is included in the composition in succession in accordance with the order of derivation, and applying the composition after each successive mapping function is included in the composition causing the surface of the three-dimensional model to be deformed while preserving the smoothness to the lowest degree of smoothness of the mapping functions.

Abstract: Computer-implemented method and apparatus for processing data representing a three-dimensional object model includes generating an image of a modeled object. The modeled object is formed from a number of different components that can be arranged in different positions, and the generated image depicts a change in a position of a first one of the components with respect to a second one of the components.

Abstract: Computerized systems for the modeling of real-world objects can include model generation functionality whereby a model is constructed from two-dimensional representations. The functions can include the ability to import two-dimensional representations of a three-dimensional object and arrange the representations on virtual surfaces positioned in a three-dimensional modeling space. The virtual surfaces are positioned to correspond to surfaces on which projections of a three-dimensional model under construction by the user are rendered. A user can interactively construct the three-dimensional model of the object by selecting and manipulating entities of the imported two-dimensional representations and the system can simultaneously display the two-dimensional projections and the three-dimensional model.