Abstract: In implementation of techniques for progressively generating fine polygon meshes, a computing device implements a mesh progression system to receive a coarse polygon mesh. The mesh progression system generates a fine polygon mesh that has a higher level of resolution than the coarse polygon mesh by decoding the coarse polygon mesh using a machine learning model. The mesh progression system then receives additional data describing a residual feature of a polygon mesh. Based on the additional data, the mesh progression system generates an adjusted fine polygon mesh that has a higher level of resolution than the fine polygon mesh.

Abstract: Methods, systems, and non-transitory computer readable storage media are disclosed for utilizing one or more neural networks to recursively subdivide a three-dimensional mesh according to local geometries of vertices in the three-dimensional mesh. For example, the disclosed system can determine a local geometry (e.g., a one-ring neighborhood of half-flaps) for each vertex in a three-dimensional mesh. For each subdivision iteration, the disclosed system can then utilize a neural network to determine displacement coordinates for existing vertices in the three-dimensional mesh and coordinates for new vertices added to edges between the existing vertices in the three-dimensional mesh in accordance with the local geometries of the existing vertices. Furthermore, the disclosed system can generate a subdivided three-dimensional mesh based on the determined displacement coordinates for the existing vertices and the determined coordinates for the new vertices.

Abstract: A system accesses a virtual scene including a three-dimensional (3D) object and a mesh object that models a cloth object. The system performs a refinement simulation to model a drape of the cloth object over the 3D object. Performing the refinement simulation includes, for each of a sequence of mesh resolutions: determining a configuration of the mesh model that minimizes a proxy energy function of a finest mesh resolution of the sequence of mesh resolutions. The system generates, for display via a user interface during the refinement simulation, an editable preview object comprising the mesh object at a coarsest level mesh resolution. The system receives a modification to the editable preview object and displays the modified editable preview object. A configuration of a finest level mesh resolution of the mesh object in the refinement simulation is geometrically consistent with a configuration of the modified editable preview object.

Abstract: Techniques for determining a swept volume of an object moving along a trajectory in a 3D space are disclosed. In some examples, a computer graphics application accesses a representation of the object, such as the signed distance field (SDF), and the trajectory information describing the movement path in the 3D space over a time period. The 3D space is represented using a grid of voxels each having multiple vertices. The computer graphics application determines the swept volume of the object in the 3D space by evaluating a subset of the grid of voxels (e.g., the voxels surrounding the surface of the swept volume). The number of voxels in the subset of voxels is less than the number of voxels in the grid of voxels. The computer graphics application further generates a representation of the swept volume surface for output.

Abstract: Methods, systems, and non-transitory computer readable storage media are disclosed for utilizing one or more neural networks to recursively subdivide a three-dimensional mesh according to local geometries of vertices in the three-dimensional mesh. For example, the disclosed system can determine a local geometry (e.g., a one-ring neighborhood of half-flaps) for each vertex in a three-dimensional mesh. For each subdivision iteration, the disclosed system can then utilize a neural network to determine displacement coordinates for existing vertices in the three-dimensional mesh and coordinates for new vertices added to edges between the existing vertices in the three-dimensional mesh in accordance with the local geometries of the existing vertices. Furthermore, the disclosed system can generate a subdivided three-dimensional mesh based on the determined displacement coordinates for the existing vertices and the determined coordinates for the new vertices.

Abstract: Techniques for determining a swept volume of an object moving along a trajectory in a 3D space are disclosed. In some examples, a computer graphics application accesses a representation of the object, such as the signed distance field (SDF), and the trajectory information describing the movement path in the 3D space over a time period. The 3D space is represented using a grid of voxels each having multiple vertices. The computer graphics application determines the swept volume of the object in the 3D space by evaluating a subset of the grid of voxels (e.g., the voxels surrounding the surface of the swept volume). The number of voxels in the subset of voxels is less than the number of voxels in the grid of voxels. The computer graphics application further generates a representation of the swept volume surface for output.

Abstract: Methods, systems, and non-transitory computer readable storage media are disclosed for utilizing one or more neural networks to recursively subdivide a three-dimensional mesh according to local geometries of vertices in the three-dimensional mesh. For example, the disclosed system can determine a local geometry (e.g., a one-ring neighborhood of half-flaps) for each vertex in a three-dimensional mesh. For each subdivision iteration, the disclosed system can then utilize a neural network to determine displacement coordinates for existing vertices in the three-dimensional mesh and coordinates for new vertices added to edges between the existing vertices in the three-dimensional mesh in accordance with the local geometries of the existing vertices. Furthermore, the disclosed system can generate a subdivided three-dimensional mesh based on the determined displacement coordinates for the existing vertices and the determined coordinates for the new vertices.

Abstract: Methods, systems, and non-transitory computer readable storage media are disclosed for iteratively decimating a three-dimensional mesh utilizing successive self-parameterization. For example, the disclosed system can self-parameterize local geometries of a three-dimensional mesh using surface mappings within a two-dimensional surface mapping space. The disclosed system can collapse edges in the three-dimensional mesh to create new vertices from the collapsed edges. The disclosed system can parameterize the collapsed edges based on the surface mappings to collapse corresponding edges within the surface mapping space. The disclosed system can thus generate a decimated three-dimensional mesh by collapsing edges in the three-dimensional mesh while providing a bijective map between points in the decimated three-dimensional mesh and corresponding points in the three-dimensional mesh.

Abstract: Methods, systems, and non-transitory computer readable storage media are disclosed for utilizing one or more neural networks to recursively subdivide a three-dimensional mesh according to local geometries of vertices in the three-dimensional mesh. For example, the disclosed system can determine a local geometry (e.g., a one-ring neighborhood of half-flaps) for each vertex in a three-dimensional mesh. For each subdivision iteration, the disclosed system can then utilize a neural network to determine displacement coordinates for existing vertices in the three-dimensional mesh and coordinates for new vertices added to edges between the existing vertices in the three-dimensional mesh in accordance with the local geometries of the existing vertices. Furthermore, the disclosed system can generate a subdivided three-dimensional mesh based on the determined displacement coordinates for the existing vertices and the determined coordinates for the new vertices.

Abstract: Methods, systems, and non-transitory computer readable storage media are disclosed for iteratively decimating a three-dimensional mesh utilizing successive self-parameterization. For example, the disclosed system can self-parameterize local geometries of a three-dimensional mesh using surface mappings within a two-dimensional surface mapping space. The disclosed system can collapse edges in the three-dimensional mesh to create new vertices from the collapsed edges. The disclosed system can parameterize the collapsed edges based on the surface mappings to collapse corresponding edges within the surface mapping space. The disclosed system can thus generate a decimated three-dimensional mesh by collapsing edges in the three-dimensional mesh while providing a bijective map between points in the decimated three-dimensional mesh and corresponding points in the three-dimensional mesh.

Abstract: An image processing system receives an input depth image with a surface that is not developable and generates an output depth image with a piecewise developable surface that approximates the input depth image. Height values for the output depth image are determined using an optimization problem that balances data fidelity and developability. Data fidelity is based on minimizing differences in height values of pixels in the output depth image and height values of pixels in the input depth image. Developability is based on rank minimization of Hessians computed for pixels in the output depth image. In some configurations, the optimization problem is formulated as a semi-definite programming problem and solved using a tailor-made alternating direction method of multipliers algorithm.