4,996 research outputs found
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
An exact general remeshing scheme applied to physically conservative voxelization
We present an exact general remeshing scheme to compute analytic integrals of
polynomial functions over the intersections between convex polyhedral cells of
old and new meshes. In physics applications this allows one to ensure global
mass, momentum, and energy conservation while applying higher-order polynomial
interpolation. We elaborate on applications of our algorithm arising in the
analysis of cosmological N-body data, computer graphics, and continuum
mechanics problems.
We focus on the particular case of remeshing tetrahedral cells onto a
Cartesian grid such that the volume integral of the polynomial density function
given on the input mesh is guaranteed to equal the corresponding integral over
the output mesh. We refer to this as "physically conservative voxelization".
At the core of our method is an algorithm for intersecting two convex
polyhedra by successively clipping one against the faces of the other. This
algorithm is an implementation of the ideas presented abstractly by Sugihara
(1994), who suggests using the planar graph representations of convex polyhedra
to ensure topological consistency of the output. This makes our implementation
robust to geometric degeneracy in the input. We employ a simplicial
decomposition to calculate moment integrals up to quadratic order over the
resulting intersection domain.
We also address practical issues arising in a software implementation,
including numerical stability in geometric calculations, management of
cancellation errors, and extension to two dimensions. In a comparison to recent
work, we show substantial performance gains. We provide a C implementation
intended to be a fast, accurate, and robust tool for geometric calculations on
polyhedral mesh elements.Comment: Code implementation available at https://github.com/devonmpowell/r3
Placental Flattening via Volumetric Parameterization
We present a volumetric mesh-based algorithm for flattening the placenta to a
canonical template to enable effective visualization of local anatomy and
function. Monitoring placental function in vivo promises to support pregnancy
assessment and to improve care outcomes. We aim to alleviate visualization and
interpretation challenges presented by the shape of the placenta when it is
attached to the curved uterine wall. To do so, we flatten the volumetric mesh
that captures placental shape to resemble the well-studied ex vivo shape. We
formulate our method as a map from the in vivo shape to a flattened template
that minimizes the symmetric Dirichlet energy to control distortion throughout
the volume. Local injectivity is enforced via constrained line search during
gradient descent. We evaluate the proposed method on 28 placenta shapes
extracted from MRI images in a clinical study of placental function. We achieve
sub-voxel accuracy in mapping the boundary of the placenta to the template
while successfully controlling distortion throughout the volume. We illustrate
how the resulting mapping of the placenta enhances visualization of placental
anatomy and function. Our code is freely available at
https://github.com/mabulnaga/placenta-flattening .Comment: MICCAI 201
Efficient moving point handling for incremental 3D manifold reconstruction
As incremental Structure from Motion algorithms become effective, a good
sparse point cloud representing the map of the scene becomes available
frame-by-frame. From the 3D Delaunay triangulation of these points,
state-of-the-art algorithms build a manifold rough model of the scene. These
algorithms integrate incrementally new points to the 3D reconstruction only if
their position estimate does not change. Indeed, whenever a point moves in a 3D
Delaunay triangulation, for instance because its estimation gets refined, a set
of tetrahedra have to be removed and replaced with new ones to maintain the
Delaunay property; the management of the manifold reconstruction becomes thus
complex and it entails a potentially big overhead. In this paper we investigate
different approaches and we propose an efficient policy to deal with moving
points in the manifold estimation process. We tested our approach with four
sequences of the KITTI dataset and we show the effectiveness of our proposal in
comparison with state-of-the-art approaches.Comment: Accepted in International Conference on Image Analysis and Processing
(ICIAP 2015
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