11,654 research outputs found
Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation
Generative models for 3D geometric data arise in many important applications
in 3D computer vision and graphics. In this paper, we focus on 3D deformable
shapes that share a common topological structure, such as human faces and
bodies. Morphable Models and their variants, despite their linear formulation,
have been widely used for shape representation, while most of the recently
proposed nonlinear approaches resort to intermediate representations, such as
3D voxel grids or 2D views. In this work, we introduce a novel graph
convolutional operator, acting directly on the 3D mesh, that explicitly models
the inductive bias of the fixed underlying graph. This is achieved by enforcing
consistent local orderings of the vertices of the graph, through the spiral
operator, thus breaking the permutation invariance property that is adopted by
all the prior work on Graph Neural Networks. Our operator comes by construction
with desirable properties (anisotropic, topology-aware, lightweight,
easy-to-optimise), and by using it as a building block for traditional deep
generative architectures, we demonstrate state-of-the-art results on a variety
of 3D shape datasets compared to the linear Morphable Model and other graph
convolutional operators.Comment: to appear at ICCV 201
TetSplat: Real-time Rendering and Volume Clipping of Large Unstructured Tetrahedral Meshes
We present a novel approach to interactive visualization and exploration of large unstructured tetrahedral meshes. These massive 3D meshes are used in mission-critical CFD and structural mechanics simulations, and typically sample multiple field values on several millions of unstructured grid points. Our method relies on the pre-processing of the tetrahedral mesh to partition it into non-convex boundaries and internal fragments that are subsequently encoded into compressed multi-resolution data representations. These compact hierarchical data structures are then adaptively rendered and probed in real-time on a commodity PC. Our point-based rendering algorithm, which is inspired by QSplat, employs a simple but highly efficient splatting technique that guarantees interactive frame-rates regardless of the size of the input mesh and the available rendering hardware. It furthermore allows for real-time probing of the volumetric data-set through constructive solid geometry operations as well as interactive editing of color transfer functions for an arbitrary number of field values. Thus, the presented visualization technique allows end-users for the first time to interactively render and explore very large unstructured tetrahedral meshes on relatively inexpensive hardware
Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes
In this article we present a new class of high order accurate
Arbitrary-Eulerian-Lagrangian (ALE) one-step WENO finite volume schemes for
solving nonlinear hyperbolic systems of conservation laws on moving two
dimensional unstructured triangular meshes. A WENO reconstruction algorithm is
used to achieve high order accuracy in space and a high order one-step time
discretization is achieved by using the local space-time Galerkin predictor.
For that purpose, a new element--local weak formulation of the governing PDE is
adopted on moving space--time elements. The space-time basis and test functions
are obtained considering Lagrange interpolation polynomials passing through a
predefined set of nodes. Moreover, a polynomial mapping defined by the same
local space-time basis functions as the weak solution of the PDE is used to map
the moving physical space-time element onto a space-time reference element. To
maintain algorithmic simplicity, the final ALE one-step finite volume scheme
uses moving triangular meshes with straight edges. This is possible in the ALE
framework, which allows a local mesh velocity that is different from the local
fluid velocity. We present numerical convergence rates for the schemes
presented in this paper up to sixth order of accuracy in space and time and
show some classical numerical test problems for the two-dimensional Euler
equations of compressible gas dynamics.Comment: Accepted by "Communications in Computational Physics
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