354 research outputs found
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surface remeshing in arbitrary codimensions
We present a method for remeshing surfaces that is both general and efficient. Existing efficient methods are restrictive in the type of remeshings they produce, while methods that are able to produce general types of remeshings are generally based on iteration, which prevents them from producing remeshes at interactive rates. In our method, the input surface is directly mapped to an arbitrary (possibly high-dimensional) range space, and uniformly remeshed in this space. Because the mesh is uniform in the range space, all the quantities encoded in the mapping are bounded, resulting in a mesh that is simultaneously adapted to all criteria encoded in the map, and thus we can obtain remeshings of arbitrary characteristics. Because the core operation is a uniform remeshing of a surface embedded in range space, and this operation is direct and local, this remeshing is efficient and can run at interactive rates.Engineering and Applied Science
Three dimensional loop quantum gravity: physical scalar product and spin foam models
In this paper, we address the problem of the dynamics in three dimensional
loop quantum gravity with zero cosmological constant. We construct a rigorous
definition of Rovelli's generalized projection operator from the kinematical
Hilbert space--corresponding to the quantization of the infinite dimensional
kinematical configuration space of the theory--to the physical Hilbert space.
In particular, we provide the definition of the physical scalar product which
can be represented in terms of a sum over (finite) spin-foam amplitudes.
Therefore, we establish a clear-cut connection between the canonical
quantization of three dimensional gravity and spin-foam models. We emphasize
two main properties of the result: first that no cut-off in the kinematical
degrees of freedom of the theory is introduced (in contrast to standard
`lattice' methods), and second that no ill-defined sum over spins (`bubble'
divergences) are present in the spin foam representation.Comment: Typos corrected, version appearing in Class. Quant. Gra
Homeomorphic Tetrahedralization of Multi-material Images with Quality and Fidelity Guarantees
We present a novel algorithm for generating three-dimensional unstructured tetrahedral meshes of multi-material images. The algorithm produces meshes with high quality since it provides a guaranteed dihedral angle bound of up to 19.47° for the output tetrahedra. In addition, it allows for user-specified guaranteed bounds on the two-sided Hausdorff distance between the boundaries of the mesh and the boundaries of the materials. Moreover, the mesh boundary is proved to be homeomorphic to the object surface. The algorithm is fast and robust, it produces a sufficiently small number of mesh elements that comply with these guarantees, as compared to other software. The theory and effectiveness of our method are illustrated with the experimental evaluation on synthetic and real medical data
Ghost on the Shell: An Expressive Representation of General 3D Shapes
The creation of photorealistic virtual worlds requires the accurate modeling
of 3D surface geometry for a wide range of objects. For this, meshes are
appealing since they 1) enable fast physics-based rendering with realistic
material and lighting, 2) support physical simulation, and 3) are
memory-efficient for modern graphics pipelines. Recent work on reconstructing
and statistically modeling 3D shape, however, has critiqued meshes as being
topologically inflexible. To capture a wide range of object shapes, any 3D
representation must be able to model solid, watertight, shapes as well as thin,
open, surfaces. Recent work has focused on the former, and methods for
reconstructing open surfaces do not support fast reconstruction with material
and lighting or unconditional generative modelling. Inspired by the observation
that open surfaces can be seen as islands floating on watertight surfaces, we
parameterize open surfaces by defining a manifold signed distance field on
watertight templates. With this parameterization, we further develop a
grid-based and differentiable representation that parameterizes both watertight
and non-watertight meshes of arbitrary topology. Our new representation, called
Ghost-on-the-Shell (G-Shell), enables two important applications:
differentiable rasterization-based reconstruction from multiview images and
generative modelling of non-watertight meshes. We empirically demonstrate that
G-Shell achieves state-of-the-art performance on non-watertight mesh
reconstruction and generation tasks, while also performing effectively for
watertight meshes.Comment: Technical Report (26 pages, 16 figures, Project Page:
https://gshell3d.github.io/
Wavelet representation of contour sets
Journal ArticleWe present a new wavelet compression and multiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contours and compactly stores this parametrization rather than function values sampled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of coefficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the corresponding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to volumetric domains, time-varying contours, and level sets of vector fields
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