Abstract: Various embodiments of a method and apparatus for creating editable feature curves for a multi-dimensional model represented by a tessellated mesh are described. A mesh representation of a multi-dimensional model may not support intuitive modification of the model. The mesh representing the multi-dimensional model may be analyzed to extract feature curves that define the characteristics of the multi-dimensional model. Such feature curves may provide an intuitive mechanism for modifying the multi-dimensional model. The model may be modified by changing the constraints of the feature curves defining the model's characteristics. For example, a constraint may be modified to change the angle of the surface on either side of a location on a feature curve. A compressed representation of a multi-dimensional model may include the feature curves that define the shape of multi-dimensional model and a set of boundary curves that represent disjoint regions of the multi-dimensional model.

Abstract: Methods and apparatus for sweep-based freeform deformation of 3-D models may employ a set of intuitive parameters to bend, twist and scale a 3-D model along any direction. The parameters may include a first bend angle, a second bend angle, a twist angle, a scale factor, and a length. Sweep paths may be fitted to an input 3-D model. Each sweep path may be deformed by manipulating one or more parameters for the sweep path. The shape of the 3-D space surrounding each sweep path is deformed according to the sweep path deformations. Deformations in the 3-D space are applied to the 3-D model to deform the model. This allows freeform deformation of the 3-D model by manipulating only a few intuitive parameters. In addition, the sweep path origin and weight functions for each of the parameters may be adjusted by the user.

Abstract: Methods and apparatus for deactivating internal constraint curves when inflating an N-Sided patch. Given a patch representation, the methods simplify the construction of 3D models from 2D sketches. At least some interior constraint curves may be deactivated when inflating an N-sided patch generated from a 2D sketch, or when performing other surface deformation tasks. An inactive constraint is a passive curve that stays on the surface and that gets modified along with the surface when the surface is inflated, but that does not affect the surface itself. By changing parameters stored at the active constraints, embodiments may modify the surface and turn the inactive constraints from flat 2D curves into 3D space curves. The inactive constraints can be activated at any time when their 3D shape meets the user's expectations.

Abstract: Methods and apparatus for interactive curve-based freeform deformation of three-dimensional (3-D) models may provide a user interface that allows a user to interactively deform 3-D models based on simple and intuitive manipulations of a curve drawn on the model (i.e., freeform deformation). The user may apply freeform deformations using touch and/or multitouch gestures to specify and manipulate a deformation curve. The deformations may be applied by deforming the space around a curve/sweep path and deforming the 3-D model accordingly. The freeform deformation methods are not dependent on manipulation of a fixed set of parameters to perform deformations, and may provide for both local and global deformation. One or more weights and user interface elements for controlling those weights may be provided that allow the user to control the extent (region of influence) of the freeform deformations along the curve and/or perpendicular to the curve.

Abstract: Method and apparatus for the interactive enhancement of 2D art with 3D geometry. A surface inflation tool may be used to create a 3D shape by inflating the surface that interpolates the input boundaries. The surface inflation tool may, for example, obtain a closed 2D boundary as input, triangulate the area within the boundary to generate an initial surface, and inflate the surface while maintaining a fixed boundary. Using surface normal values and/or mean curvature values specified at boundary vertices as constraints, the tool may control the inflated surface efficiently using a single linear system. Embodiments handle both smooth and sharp position constraints. Position constraint vertices may also have constraints specified for controlling the inflation of a local surface.

Abstract: Method and apparatus for the interactive enhancement of 2D art with 3D geometry. A surface inflation tool may be used to create a 3D shape by inflating the surface that interpolates the input boundaries. The surface inflation tool may, for example, obtain a closed 2D boundary as input, triangulate the area within the boundary to generate an initial surface, and inflate the surface while maintaining a fixed boundary. Using the mean curvature specified at boundary vertices as a degree of freedom, the tool may control the inflated surface efficiently using a single linear system. Embodiments handle both smooth and sharp position constraints. Position constraint vertices may also have curvature constraints specified for controlling the inflation of a local surface.

Abstract: Method and apparatus for the interactive enhancement of 2D art with 3D geometry. A surface inflation tool may be used to create a 3D shape by inflating the surface that interpolates the input boundaries. The surface inflation tool may, for example, obtain a closed 2D boundary as input, triangulate the area within the boundary to generate an initial surface, and inflate the surface while maintaining a fixed boundary. Using surface normal values and/or mean curvature values specified at boundary vertices as constraints, the tool may control the inflated surface efficiently using a single linear system. Embodiments handle both smooth and sharp position constraints. Position constraint vertices may also have constraints specified for controlling the inflation of a local surface.

Abstract: Method and apparatus for the interactive enhancement of 2D art with 3D geometry. A surface inflation tool may be used to create a 3D shape by inflating the surface that interpolates the input boundaries. The surface inflation tool may, for example, obtain a closed 2D boundary as input, triangulate the area within the boundary to generate an initial surface, and inflate the surface while maintaining a fixed boundary. Using the mean curvature specified at boundary vertices as a degree of freedom, the tool may control the inflated surface efficiently using a single linear system. Embodiments handle both smooth and sharp position constraints. Position constraint vertices may also have curvature constraints specified for controlling the inflation of a local surface.