Abstract: Systems and methods generate a modified three-dimensional mesh representation of an object using a trained neural network. A computer system receives a set of input values for posing an initial mesh defining a surface of a three-dimensional object. The computer system provides the input values to a neural network trained on posed meshes generated using a rigging model to generate mesh offset values based upon the set of input values and the initial mesh. The neural network includes an input layer, an output layer, and a plurality of intermediate layers. The computer system generates, by the output layer of the neural network, a set of offset values corresponding to a set of three-dimensional target points based on the set of input values. The offset values are applied to the initial mesh to generate a posed mesh. The computer system outputs the posed mesh for generating an animation frame.

Abstract: Embodiments provide for three-dimensional cloth modeling are provided. A first mesh comprising a plurality of faces defined by a plurality of edges is accessed, and a render mesh is generated using quadrangulated tessellation of the first mesh, where the render mesh comprises quad faces. One or more attributes of the plurality of faces of the first mesh are transferred to one or more of the quad faces of the render mesh using a stochastic transfer operation. The render mesh is displayed via a graphical user interface (GUI).

Abstract: Systems and methods automatically generate contours on an illustrated object for performing an animation. Contour lines are generated on the surface of the object according to criteria related to the shape of the surface of the object. Points of the contour lines that are occluded from a virtual camera are identified. The occluded points are removed to generate visible lines. The visible lines are extruded to define a three-dimensional volume defining contours of the object. The object itself, along with the three-dimensional volume, are illuminated and rendered. The parameters defining the opacity and color of the contour may differ from corresponding parameters of the rest of the object, so that the contours stand out and define portions of the object. The contours are useful in contexts such as defining areas of an object that is fuzzy or cloudy in appearance, as well as creating certain artistic effects.

Abstract: Systems and methods automatically generate contours on an illustrated object for performing an animation. Contour lines are generated on the surface of the object according to criteria related to the shape of the surface of the object. Points of the contour lines that are occluded from a virtual camera are identified. The occluded points are removed to generate visible lines. The visible lines are extruded to define a three-dimensional volume defining contours of the object. The object itself, along with the three-dimensional volume, are illuminated and rendered. The parameters defining the opacity and color of the contour may differ from corresponding parameters of the rest of the object, so that the contours stand out and define portions of the object. The contours are useful in contexts such as defining areas of an object that is fuzzy or cloudy in appearance, as well as creating certain artistic effects.

Abstract: Embodiments provide for cut-aware UV transfer. Embodiments include receiving a surface correspondence map that maps points of a source mesh to points of a target mesh. Embodiments include generating a set of functions encoding locations of seam curves and wrap curves from a source UV map of the source mesh. Embodiments include using the set of functions and the surface correspondence map to determine a target UV map that maps a plurality of target seam curves and a plurality of target wrap curves to the target mesh. Embodiments include transferring a two-dimensional parametrization of the source UV map to the target UV map.

Abstract: Embodiments provide for cut-aware UV transfer. Embodiments include receiving a surface correspondence map that maps points of a source mesh to points of a target mesh. Embodiments include generating a set of functions encoding locations of seam curves and wrap curves from a source UV map of the source mesh. Embodiments include using the set of functions and the surface correspondence map to determine a target UV map that maps a plurality of target seam curves and a plurality of target wrap curves to the target mesh. Embodiments include transferring a two-dimensional parametrization of the source UV map to the target UV map.

Abstract: Embodiments provide for transferring mesh connectivity. Embodiments include receiving a definition of a correspondence between a first curve for a source mesh and a second curve for a target shape. Embodiments include initializing an output mesh by setting a third plurality of vertices in the output mesh equal to a first plurality of vertices in the source mesh. Embodiments include transforming the output mesh by modifying the third plurality of vertices based on the first curve, the second curve, and a second plurality of vertices of the target mesh. Vertices of the third plurality of vertices that relate to the first curve are conformed to a shape defined by the second curve, and vertex modifications that result in affine transformations of faces in the output mesh are favored. Embodiments include using the output mesh to transfer an attribute from the source mesh to the target shape.

Abstract: Embodiments provide for sculpt transfer. Embodiments include identifying a source polygon of a source mesh that corresponds to a target polygon of a target mesh. Embodiments include determining a first matrix defining a first rotation that aligns a target rest state of the target polygon to a source rest state of the source polygon, determining a second matrix defining a linear transformation that aligns the source rest state to a source pose of the source polygon, wherein the linear transformation comprises rotating and stretching, determining a third matrix defining a second rotation that aligns the source pose to the target rest state, and determining a fourth matrix defining a third rotation that aligns the source rest state to the source pose. Embodiments include determining a target pose of the target polygon based on the target rest state, the first matrix, the second matrix, the third matrix, and the fourth matrix.

Abstract: Surface relaxation techniques are disclosed for smoothing the shapes of three-dimensional (3D) virtual geometry. In one embodiment, a surface relaxation application determines, for each of a number of vertices of a 3D virtual geometry, span-aware weights for each edge incident to the vertex based on the alignment of other edges incident to the vertex with an orthonormal frame of the edge constructed using a decal map. The surface relaxation application uses such span-aware weights to compute weighted averages that provide surface relaxation offsets. Further, the surface relaxation application may restore relaxation offsets from an original to a deformed geometry by determining relaxation offsets for both geometries and transferring the relaxation offsets from the original to the deformed 3D geometry using a blending of the determined relaxation offsets and a rotation. In another embodiment, volume is preserved by computing relaxation offsets in the plane and lifting relaxed vertices back to 3D.

Abstract: Systems, methods, and articles of manufacture for physically-based sculpting of virtual elastic materials are provided. The physically-based sculpting in one embodiment simulates elastic responses to localized distributions of force produced by sculpting with a brush-like force (e.g., grab, twist, pinch, scale) using one or more regularized solutions to equations of linear elasticity applied to a virtual infinite elastic space, referred to herein as “regularized Kelvinlets.

Abstract: Surface relaxation techniques are disclosed for smoothing the shapes of three-dimensional (3D) virtual geometry. In one embodiment, a surface relaxation application determines, for each of a number of vertices of a 3D virtual geometry, span-aware weights for each edge incident to the vertex based on the alignment of other edges incident to the vertex with an orthonormal frame of the edge constructed using a decal map. The surface relaxation application uses such span-aware weights to compute weighted averages that provide surface relaxation offsets. Further, the surface relaxation application may restore relaxation offsets from an original to a deformed geometry by determining relaxation offsets for both geometries and transferring the relaxation offsets from the original to the deformed 3D geometry using a blending of the determined relaxation offsets and a rotation. In another embodiment, volume is preserved by computing relaxation offsets in the plane and lifting relaxed vertices back to 3D.

Abstract: Systems, methods and articles of manufacture for rendering images depicting materials are disclosed. A stable Neo-Hookean energy model is disclosed which does not include terms that can produce singularities, or require the use of arbitrarily selected clamping parameters. The stable Neo-Hookean energy may include a length-preserving term and volume-preserving term(s), and the volume-preserving terms themselves may include term(s) from a Taylor expansion of a logarithm of a measurement of volume. The stable Neo-Hookean energy may further include an origin barrier term that increases the difficulty of reaching the origin and expands a mesh in response to a perturbation when the mesh is at the origin. Closed-form expressions of eigenvalues and eigenvectors of a Hessian of the stable Neo-Hookean energy are disclosed, which may be used in a simulation of a material to, e.g., project the Hessian to semi-positive-definiteness in Newton iterations used to determine a substantially minimal energy configuration.

Abstract: This disclosure provides an approach for automatically generating UV maps for modified three-dimensional (3D) virtual geometry. In one embodiment, a UV generating application may receive original 3D geometry and associated UV panels, as well as modified 3D geometry created by deforming the original 3D geometry. The UV generating application then extracts principal stretches of a mapping between the original 3D geometry and the associated UV panels and transfers the principal stretches, or a function thereof, to a new UV mapping for the modified 3D geometry. Transferring the principal stretches or the function thereof may include iteratively performing the following steps: determining new UV points assuming a fixed affine transformation, determining principal stretches of a transformation between the modified 3D geometry and the determined UV points, and determining a correction of a transformation matrix for each triangle to make the matrix a root of a scoring function.

Abstract: Systems, methods, and articles of manufacture for physically-based sculpting of virtual elastic materials are provided. The physically-based sculpting in one embodiment simulates elastic responses to localized distributions of force produced by sculpting with a brush-like force (e.g., grab, twist, pinch, scale) using one or more regularized solutions to equations of linear elasticity applied to a virtual infinite elastic space, referred to herein as “regularized Kelvinlets.

Abstract: Techniques are disclosed for solving geometry processing tasks on a subdivision surface of an input geometry using a subdivision exterior calculus (SEC) framework. A control polygonal mesh is received for generating a subdivision surface model. The polygonal mesh is associated with subdivision levels. To generate the subdivision surface model, one or more subdivision matrices of the polygonal mesh is determined at each subdivision level. One or more SEC matrices is computed from the subdivision matrices. The differential equation required by the geometry processing application is then solved numerically on the input control mesh using the SEC matrices.

Abstract: This disclosure provides an approach for automatically generating UV maps for modified three-dimensional (3D) virtual geometry. In one embodiment, a UV generating application may receive original 3D geometry and associated UV panels, as well as modified 3D geometry created by deforming the original 3D geometry. The UV generating application then extracts principle stretches of a mapping between the original 3D geometry and the associated UV panels and transfers the principle stretches, or a function thereof, to a new UV mapping for the modified 3D geometry. Transferring the principle stretches or the function thereof may include iteratively performing the following steps: determining new UV points assuming a fixed affine transformation, determining principle stretches of a transformation between the modified 3D geometry and the determined UV points, and determining a correction of a transformation matrix for each triangle to make the matrix a root of a scoring function.

Abstract: Techniques are disclosed for solving geometry processing tasks on a subdivision surface of an input geometry using a subdivision exterior calculus (SEC) framework. A control polygonal mesh is received for generating a subdivision surface model. The polygonal mesh is associated with subdivision levels. To generate the subdivision surface model, one or more subdivision matrices of the polygonal mesh is determined at each subdivision level. One or more SEC matrices is computed from the subdivision matrices. The differential equation required by the geometry processing application is then solved numerically on the input control mesh using the SEC matrices.