1,198 research outputs found
Maxwell's Theory of Solid Angle and the Construction of Knotted Fields
We provide a systematic description of the solid angle function as a means of
constructing a knotted field for any curve or link in . This is a
purely geometric construction in which all of the properties of the entire
knotted field derive from the geometry of the curve, and from projective and
spherical geometry. We emphasise a fundamental homotopy formula as unifying
different formulae for computing the solid angle. The solid angle induces a
natural framing of the curve, which we show is related to its writhe and use to
characterise the local structure in a neighborhood of the knot. Finally, we
discuss computational implementation of the formulae derived, with C code
provided, and give illustrations for how the solid angle may be used to give
explicit constructions of knotted scroll waves in excitable media and knotted
director fields around disclination lines in nematic liquid crystals.Comment: 20 pages, 9 figure
Isogeometric analysis applied to frictionless large deformation elastoplastic contact
This paper focuses on the application of isogeometric analysis to model frictionless large deformation contact between deformable bodies and rigid surfaces that may be represented by analytical functions. The contact constraints are satisfied exactly with the augmented Lagrangian method, and treated with a mortar-based approach combined with a simplified integration method to avoid segmentation of the contact surfaces. The spatial discretization of the deformable body is performed with NURBS and C0-continuous Lagrange polynomial elements. The numerical examples demonstrate that isogeometric surface discretization delivers more accurate and robust predictions of the response compared to Lagrange discretizations
Progressive tearing and cutting of soft-bodies in high-performance virtual reality
We present an algorithm that allows a user within a virtual environment to
perform real-time unconstrained cuts or consecutive tears, i.e., progressive,
continuous fractures on a deformable rigged and soft-body mesh model in
high-performance 10ms. In order to recreate realistic results for different
physically-principled materials such as sponges, hard or soft tissues, we
incorporate a novel soft-body deformation, via a particle system layered on-top
of a linear-blend skinning model. Our framework allows the simulation of
realistic, surgical-grade cuts and continuous tears, especially valuable in the
context of medical VR training. In order to achieve high performance in VR, our
algorithms are based on Euclidean geometric predicates on the rigged mesh,
without requiring any specific model pre-processing. The contribution of this
work lies on the fact that current frameworks supporting similar kinds of model
tearing, either do not operate in high-performance real-time or only apply to
predefined tears. The framework presented allows the user to freely cut or tear
a 3D mesh model in a consecutive way, under 10ms, while preserving its
soft-body behaviour and/or allowing further animation.Comment: 9 pages, 11 figures, 3 tables, submitted to "International Conference
on Artificial Reality and Telexistence, Eurographics Symposium on Virtual
Environments 2022
Defining the Pose of any 3D Rigid Object and an Associated Distance
The pose of a rigid object is usually regarded as a rigid transformation,
described by a translation and a rotation. However, equating the pose space
with the space of rigid transformations is in general abusive, as it does not
account for objects with proper symmetries -- which are common among man-made
objects.In this article, we define pose as a distinguishable static state of an
object, and equate a pose with a set of rigid transformations. Based solely on
geometric considerations, we propose a frame-invariant metric on the space of
possible poses, valid for any physical rigid object, and requiring no arbitrary
tuning. This distance can be evaluated efficiently using a representation of
poses within an Euclidean space of at most 12 dimensions depending on the
object's symmetries. This makes it possible to efficiently perform neighborhood
queries such as radius searches or k-nearest neighbor searches within a large
set of poses using off-the-shelf methods. Pose averaging considering this
metric can similarly be performed easily, using a projection function from the
Euclidean space onto the pose space. The practical value of those theoretical
developments is illustrated with an application of pose estimation of instances
of a 3D rigid object given an input depth map, via a Mean Shift procedure
Elasto-mammography: Theory, Algorithm, and Phantom Study
A new imaging modality framework, called
elasto-mammography, is proposed to generate the elastograms of
breast tissues based on conventional X-ray mammography. The
displacement information is extracted from mammography projections
before and after breast compression. Incorporating the
displacement measurement, an elastography reconstruction algorithm
is specifically developed to estimate the elastic moduli of
heterogeneous breast tissues. Case studies with numerical breast
phantoms are conducted to demonstrate the capability of the
proposed elasto-mammography. Effects of noise with measurement,
geometric mismatch, and elastic contrast ratio are evaluated in
the numerical simulations. It is shown that the proposed
methodology is stable and robust for characterization of the
elastic moduli of breast tissues from the projective displacement
measurement
Digital representation of historical globes : methods to make 3D and pseudo-3D models of sixteenth century Mercator globes
In this paper, the construction of digital representations of a terrestrial and celestial globe will be discussed. Virtual digital (3D) models play an important role in recent research and publications on cultural heritage. The globes discussed in this paper were made by Gerardus Mercator (1512-1594) in 1541 and 1551. Four techniques for the digital representation are discussed and analysed, all using high-resolution photographs of the globes. These photographs were taken under studio conditions in order to get equal lighting and to avoid unwanted light spots. These lighting conditions are important, since the globes have a highly reflective varnish covering. Processing these images using structure from motion, georeferencing of separate scenes and the combination of the photographs with terrestrial laser scanning data results in true 3D representations of the globes. Besides, pseudo-3D models of these globes were generated using dynamic imaging, which is an extensively used technique for visualisations over the Internet. The four techniques and the consequent results are compared on geometric and radiometric quality, with a special focus on their usefulness for distribution and visualisation during an exhibition in honour of the five hundredth birthday of Gerardus Mercator
HeadOn: Real-time Reenactment of Human Portrait Videos
We propose HeadOn, the first real-time source-to-target reenactment approach
for complete human portrait videos that enables transfer of torso and head
motion, face expression, and eye gaze. Given a short RGB-D video of the target
actor, we automatically construct a personalized geometry proxy that embeds a
parametric head, eye, and kinematic torso model. A novel real-time reenactment
algorithm employs this proxy to photo-realistically map the captured motion
from the source actor to the target actor. On top of the coarse geometric
proxy, we propose a video-based rendering technique that composites the
modified target portrait video via view- and pose-dependent texturing, and
creates photo-realistic imagery of the target actor under novel torso and head
poses, facial expressions, and gaze directions. To this end, we propose a
robust tracking of the face and torso of the source actor. We extensively
evaluate our approach and show significant improvements in enabling much
greater flexibility in creating realistic reenacted output videos.Comment: Video: https://www.youtube.com/watch?v=7Dg49wv2c_g Presented at
Siggraph'1
Simulation and experimental investigation of high-speed projectile impacting closed-cell aluminum foam
In order to analyze the impact acceleration of the projectile impacting the aluminum foam material, a dynamic non-linear finite element model of the projectile impacting the closed-cell aluminum foam experiment device was established and verified by the experiment. It is found that the numerical simulation results of projectile impact closed-cell aluminum foam are consistent with the change of experimental results. When the projectile impacts the homogeneous closed-cell aluminum foam, the impact acceleration is trapezoidal and the impact peak and pulse width are related to the density of the aluminum foam material. With the increase of the porosity of the aluminum foam, the peak value of the acceleration rises and the pulse width of acceleration decreases
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