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公开(公告)号：US10740968B2
公开(公告)日：2020-08-11
申请号：US16275136
申请日：2019-02-13
申请人： Pixar
IPC分类号： G06T17/20
摘要： 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.
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公开(公告)号：US10818059B1
公开(公告)日：2020-10-27
申请号：US16514852
申请日：2019-07-17
申请人： Pixar
摘要： 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.
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公开(公告)号：US10366184B1
公开(公告)日：2019-07-30
申请号：US15941928
申请日：2018-03-30
申请人： Pixar
摘要： 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.
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公开(公告)号：US10586401B2
公开(公告)日：2020-03-10
申请号：US15969587
申请日：2018-05-02
申请人： Pixar
摘要： 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.” In other cases, compound brushes, each based on a regularized Kelvinlet, may be used for arbitrarily fast decay; a linear combination of brushes based on regularized Kelvinlets may be used to impose pointwise constraints on displacements and gradients; locally affine forms of regularized Kelvinlets may be used for certain sculpting brushes; brush displacement constraints may be imposed by superimposing regularized Kelvinlets of different radial scales; and symmetrized deformations may be generated by copying and reflecting forces produced by regularized Kelvinlets.
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公开(公告)号：US10192346B2
公开(公告)日：2019-01-29
申请号：US15279252
申请日：2016-09-28
申请人： Pixar
摘要： 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.
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公开(公告)号：US10002461B2
公开(公告)日：2018-06-19
申请号：US15409005
申请日：2017-01-18
申请人： Pixar
IPC分类号： G06T17/20
CPC分类号： G06T17/205
摘要： 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.
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公开(公告)号：US10984581B2
公开(公告)日：2021-04-20
申请号：US16514816
申请日：2019-07-17
申请人： Pixar
摘要： 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.
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公开(公告)号：US10861233B1
公开(公告)日：2020-12-08
申请号：US16514779
申请日：2019-07-17
申请人： Pixar
摘要： 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.
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