Abstract: Methods and apparatus for 3D sketching may provide an interface for creating 3D drawings from 2D and 3D input, and for creating 3D curve networks. The technique may provide tools for 2D sketching that enable 2D sketching in 3D space, and for creating a network of intersecting 3D curves. The technique may provide user interface elements and techniques that facilitate the curve drawing tasks. For 2D sketching, the technique may provide methods for interpreting imprecise user 2D strokes as continuous, high-quality 3D curves. The technique may provide the ability to edit existing 3D curves using sketched 2D strokes. The technique may enable sketching of 3D curves by rotating a drawing plane and/or by creating drawing surfaces on which curves may be added. The technique may provide user interface elements for converting curves in 3D space into a curve network.

Abstract: Methods and apparatus for generating curved extrusions. A user interface may be provided via which the value of one or more extrusion parameters and/or a reference point may be changed. An extrusion may be generated from an initial 2D object according to the set of extrusion parameters and/or the reference point.

Abstract: Methods and apparatus for generating curved extrusions. A user interface may be provided via which the value of one or more extrusion parameters and/or a reference point may be changed. An extrusion may be generated from an initial 2D object according to the set of extrusion parameters and/or the reference point.

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 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: Methods and apparatus for providing Sobolev pre-conditioning for optimizing ill-conditioned functionals. A power n is initialized to a maximum power (e.g., 8). For k (e.g., 10) iterations of an optimization pipeline, a matrix M is built by considering all powers of the Laplacian matrix up to the power indicated by n, the Sobolev gradient is computed from the standard gradient, and the computed Sobolev gradient is passed to a numerical optimizer. After the k iterations are complete, if n is at a minimum power (e.g., 1), then the algorithm resets n to the maximum power. Otherwise, n is decremented. For the next k iterations, the matrix M is again built by considering all powers of the Laplacian matrix up to the power indicated by the current value of n. This method is continued until all iterations have completed or until some other terminating condition is reached.

Abstract: Methods and apparatus for generating an n-sided patch by sketching on a three-dimensional reference surface. A user draws a closed curve on a 3D surface; the drawn outline is taken as a boundary for an N-sided patch. If the user does not close the curve, the system may automatically close the curve, as a closed outer boundary curve may be required to produce an N-sided patch. The boundary conditions, the positions, and the surface normals at the boundary are inferred automatically from the 3D surface that the user has drawn the curve on. In addition, boundary curves for the same patch may be drawn on different 3D shapes; multiple 3D shapes may be used as the template or canvas on which the user draws curves from which a patch is to be generated.

Abstract: Methods and apparatus for generating curved extrusions. A user interface may be provided via which the value of one or more extrusion parameters and/or a reference point may be changed. The extrusion parameters may include a depth parameter that controls the amount of extrusion, an X angle parameter that controls the angle of bend in the X direction, a Y angle parameter that controls the angle of bend in the Y direction, a scale parameter that controls the scale factor, and a twist parameter that controls the angle of extrusion twist. A weight function for changing one or more of the extrusion parameters non-uniformly along the sweep path may also be provided. An extrusion may be generated from an initial 2D object according to the set of extrusion parameters and the reference point.

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 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: Various embodiments of a system and methods for generating 3D surface patches from unconstrained 3D curves are described. The system may receive a set of unconstrained 3D wireframe curves that represent a 3D wireframe model. The 3D wireframe curves may be unorganized, may have inconsistent orientations, and may have an arbitrary number and type of curve intersections. The system may automatically generate the 3D surface patches, dependent on the 3D wireframe curves. The 3D surface patches may form a 3D surface that connects the 3D wireframe curves. The 3D surface patches may be generated from faces of the 3D wireframe model. The faces may be elementary cycles extracted from the 3D wireframe model. The system may receive user input which indicates changes to the 3D surface patches. A user may change, create, and/or delete 3D surface patches to achieve a desired 3D surface that represents the 3D wireframe model.

Abstract: Methods and apparatus for decomposing an N-sided patch into multiple patches. A single patch may be decomposed into multiple, disjoint, and possibly abutting patches. An internal constraint curve may be selected, and a new patch with the constraint curve as the boundary may be generated. If the constraint curve is closed, it is turned into a hole in the original patch. If the constraint curve is not closed, the system closes the curve. The 3D position, surface normal, and possibly other information such as an up direction required for every point along the boundary of the new patch may be taken from the original patch surface. The new patch(es) may be edited independent of the original patch and may be further decomposed into more patches.

Abstract: Methods and apparatus for interactively rotating three-dimensional (3D) objects using multitouch gestures. To perform a roll gesture, multiple touch points are detected on a multitouch-enabled device. The touch points are associated with, or select, a 3D object displayed on the device. The centroid of the touch points is computed, and motion of the centroid, resulting from motion of the touch points, is tracked. When motion of the centroid is detected, a displacement is obtained, and the displacement is mapped to a rotation transformation. The 3D object may then be rotated according to the rotation transformation, and a 2D projection of the rotated 3D object is displayed. If the number of touch points changes, rotation may be reset without rotating the object. Alternatively, displacement from the previous centroid to the new centroid is determined and the object is rotated accordingly.

Abstract: Methods and apparatus for 3D sketching may provide an interface for creating 3D drawings from 2D and 3D input, and for creating 3D curve networks. The technique may provide tools for 2D sketching that enable 2D sketching in 3D space, and for creating a network of intersecting 3D curves. The technique may provide user interface elements and techniques that facilitate the curve drawing tasks. For 2D sketching, the technique may provide methods for interpreting imprecise user 2D strokes as continuous, high-quality 3D curves. The technique may provide the ability to edit existing 3D curves using sketched 2D strokes. The technique may enable sketching of 3D curves by rotating a drawing plane and/or by creating drawing surfaces on which curves may be added. The technique may provide user interface elements for converting curves in 3D space into a curve network.

Abstract: Various embodiments of a system and methods for generating 3D surface patches from unconstrained 3D curves are described. The system may receive a set of unconstrained 3D wireframe curves that represent a 3D wireframe model. The 3D wireframe curves may be unorganized, may have inconsistent orientations, and may have an arbitrary number and type of curve intersections. The system may automatically generate the 3D surface patches, dependent on the 3D wireframe curves. The 3D surface patches may form a 3D surface that connects the 3D wireframe curves. The 3D surface patches may be generated from faces of the 3D wireframe model. The faces may be elementary cycles extracted from the 3D wireframe model. The system may receive user input which indicates changes to the 3D surface patches. A user may change, create, and/or delete 3D surface patches to achieve a desired 3D surface that represents the 3D wireframe model.

Abstract: Methods and apparatus for interactively rotating three-dimensional (3D) objects using multitouch gestures. To perform a roll gesture, multiple touch points are detected on a multitouch-enabled device. The touch points are associated with, or select, a 3D object displayed on the device. The centroid of the touch points is computed, and motion of the centroid, resulting from motion of the touch points, is tracked. When motion of the centroid is detected, a displacement is obtained, and the displacement is mapped to a rotation transformation. The 3D object may then be rotated according to the rotation transformation, and a 2D projection of the rotated 3D object is displayed. If the number of touch points changes, rotation may be reset without rotating the object. Alternatively, displacement from the previous centroid to the new centroid is determined and the object is rotated accordingly.

Abstract: Methods and apparatus for generating curved extrusions. A user interface may be provided via which the value of one or more extrusion parameters and/or a reference point may be changed. The extrusion parameters may include a depth parameter that controls the amount of extrusion, an X angle parameter that controls the angle of bend in the X direction, a Y angle parameter that controls the angle of bend in the Y direction, a scale parameter that controls the scale factor, and a twist parameter that controls the angle of extrusion twist. A weight function for changing one or more of the extrusion parameters non-uniformly along the sweep path may also be provided. An extrusion may be generated from an initial 2D object according to the set of extrusion parameters and the reference point.

Abstract: Methods and apparatus for decomposing an N-sided patch into multiple patches. A single patch may be decomposed into multiple, disjoint, and possibly abutting patches. An internal constraint curve may be selected, and a new patch with the constraint curve as the boundary may be generated. If the constraint curve is closed, it is turned into a hole in the original patch. If the constraint curve is not closed, the system closes the curve. The 3D position, surface normal, and possibly other information such as an up direction required for every point along the boundary of the new patch may be taken from the original patch surface. The new patch(es) may be edited independent of the original patch and may be further decomposed into more patches.

Abstract: Methods and apparatus for providing Sobolev pre-conditioning for optimizing ill-conditioned functionals. A power n is initialized to a maximum power (e.g., 8). For k (e.g., 10) iterations of an optimization pipeline, a matrix M is built by considering all powers of the Laplacian matrix up to the power indicated by n, the Sobolev gradient is computed from the standard gradient, and the computed Sobolev gradient is passed to a numerical optimizer. After the k iterations are complete, if n is at a minimum power (e.g., 1), then the algorithm resets n to the maximum power. Otherwise, n is decremented. For the next k iterations, the matrix M is again built by considering all powers of the Laplacian matrix up to the power indicated by the current value of n. This method is continued until all iterations have completed or until some other terminating condition is reached.

Abstract: Methods and apparatus for generating an n-sided patch by sketching on a three-dimensional reference surface. A user draws a closed curve on a 3D surface; the drawn outline is taken as a boundary for an N-sided patch. If the user does not close the curve, the system may automatically close the curve, as a closed outer boundary curve may be required to produce an N-sided patch. The boundary conditions, the positions, and the surface normals at the boundary are inferred automatically from the 3D surface that the user has drawn the curve on. In addition, boundary curves for the same patch may be drawn on different 3D shapes; multiple 3D shapes may be used as the template or canvas on which the user draws curves from which a patch is to be generated.