456 research outputs found
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PDE Face: A Novel 3D Face Model
YesWe introduce a novel approach to face models, which
exploits the use of Partial Differential Equations (PDE) to
generate the 3D face. This addresses some common
problems of existing face models. The PDE face benefits
from seamless merging of surface patches by using only a
relatively small number of parameters based on boundary
curves. The PDE face also provides users with a great
degree of freedom to individualise the 3D face by
adjusting a set of facial boundary curves. Furthermore, we
introduce a uv-mesh texture mapping method. By
associating the texels of the texture map with the vertices
of the uv mesh in the PDE face, the new texture mapping
method eliminates the 3D-to-2D association routine in
texture mapping. Any specific PDE face can be textured
without the need for the facial expression in the texture
map to match exactly that of the 3D face model
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Parametric Representations of Facial Expressions on PDE-Based Surfaces
NoParameterisation of facial expressions on PDE surface
representations of human faces are presented in this
work. Taking advantage of the boundary-value approach
inherent to Bloor-Wilson PDE method, facial expressions
are achieved by manipulating the original boundary curves.
Such curves are responsible for generating a surface representation
of a human face in its neutral configuration,
so that regions on these curves represent a given facial
expression in a fast and realistic manner. Additionally, the
parameterisation proposed here is carried out by applying
different mathematical transformations to the affected
curves according to the corresponding facial expression.
Full analytic expressions parameterising some of the most
common facial expressions such as smiling and eyebrow
raising are in this work. Some graphical examples of these
facial expressions are used to illustrate the results obtained
using Bloor-Wilson PDE method as the foundations of the
parameterisation scheme proposed here. Thus, it is shown
that an efficient, intuitive and realistic parameterisation of
facial expressions is attainable using Bloor-Wilson PDE
method in along with a suitable mathematical expression
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PDE-based Facial Animation: Making the Complex Simple
YesDirect parameterisation is among the most widely used facial animation techniques but requires complicated ways to animate face models which have complex topology. This paper develops a simple solution by introducing a PDE-based facial animation scheme. Using a PDE face model means we only need to animate a group of boundary curves without using any other conventional surface interpolation algorithms. We describe the basis of the method and show results from a practical implementation.EPSR
Shape morphing of complex geometries using partial differential equations.
An alternative technique for shape morphing
using a surface generating method using partial differential
equations is outlined throughout this work. The boundaryvalue
nature that is inherent to this surface generation
technique together with its mathematical properties are
hereby exploited for creating intermediate shapes between
an initial shape and a final one. Four alternative shape
morphing techniques are proposed here. The first one is
based on the use of a linear combination of the boundary
conditions associated with the initial and final surfaces,
the second one consists of varying the Fourier mode for
which the PDE is solved whilst the third results from a
combination of the first two. The fourth of these alternatives
is based on the manipulation of the spine of the surfaces,
which is computed as a by-product of the solution. Results
of morphing sequences between two topologically nonequivalent
surfaces are presented. Thus, it is shown that the
PDE based approach for morphing is capable of obtaining
smooth intermediate surfaces automatically in most of the
methodologies presented in this work and the spine has been
revealed as a powerful tool for morphing surfaces arising
from the method proposed here
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Shape Morphing Using PDE Surfaces
NoA methodology for shape morphing using partial differential
equation (PDE) surfaces is presented in this work.
The use of the PDE formulation shows how shape morphing
can be based on a boundary-value approach by which
intermediate shapes can be created. Furthermore, the
mathematical properties of the method give rise to several
alternatives in which morphing one shape into another
can be achieved. Three of these alternatives are presented
here. The first one is based on the gradual variation of
the weighted sum of the boundary conditions for each
surface, the second one consists of varying the Fourier
mode for which the PDE is solved whilst the third results
from a combination of the first two. Examples showing the
efficiency of these methodologies are presented. Thus, it is
shown that the PDE based approach for morphing, when
combined with a parametric variation of the boundary
conditions, is capable of obtaining smooth intermediate
surfaces automatically
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On the Validity of the Imbert-Fick Law: Mathematical Modelling of Eye Pressure Measurement
YesOphthalmologists rely on a device known as the Goldmann applanation tonometer to make intraocular
pressure (IOP) measurements. It measures the force required to press a flat disc against
the cornea to produce a flattened circular region of known area. The IOP is deduced from this
force using the Imbert-Fick principle. However, there is scant analytical justification for this
analysis. We present a mathematical model of tonometry to investigate the relationship between
the pressure derived by tonometry and the IOP. An elementary equilibrium analysis suggests that
there is no physical basis for traditional tonometric analysis. Tonometry is modelled using a hollow
spherical shell of solid material enclosing an elastic liquid core, with the shell in tension and
the core under pressure. The shell is pressed against a rigid flat plane. The solution is found using
finite element analysis. The shell material is anisotropic. Values for its elastic constants are obtained
from literature except where data are unavailable, when reasonable limits are explored.
The results show that the force measured by the Goldmann tonometer depends on the elastic constant
values. The relationship between the IOP and the tonometer readings is complex, showing
potentially high levels of inaccuracy that depend on IOP
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Towards the analytic characterization of micro and nano surface features using the Biharmonic equation
YesThe prevalence of micromoulded components has steadily increased over recent years. The production of such components is extremely sensitive to a number of variables that may potentially lead to significant changes in the surface geometry, often regarded as a crucial determinant of the productÂżs functionality and quality. So far, traditional large-scale quality assessment techniques have been used in micromoulding. However, these techniques are not entirely suitable for small scales . Techniques such as Atomic Force Mi- croscopy (AFM) or White Light Interferometry (WLI) have been used for obtaining full three-dimensional profiles of micromoulded components, pro- ducing large data sets that are very difficult to manage. This work presents a method of characterizing surface features of micro and nano scale based on the use of the Biharmonic equation as means of describing surface profiles whilst guaranteeing tangential (C1) continuity. Thus, the problem of rep- resenting surface features of micromoulded components from massive point clouds is transformed into a boundary-value problem, reducing the amount of data required to describe any given surface feature.The boundary conditions needed for finding a particular solution to the Biharmonic equation are extracted from the data set and the coefficients associated with a suitable analytic solution are used to describe key design parameters or geometric properties of a surface feature. Moreover, the expressions found for describ- ing key design parameters in terms of the analytic solution to the Biharmonic equation may lead to a more suitable quality assessment technique for mi- cromoulding than the criteria currently used. In summary this technique provides a means for compressing point clouds representing surface features whilst providing an analytic description of such features. The work is applicable to many other instances where surface topography is in need of efficient representation
The Effect of Silver Nanofibers on the Deformation Properties of Blood Vessels: Towards the Development of New Nanotechnologies to Prevent Rupture of Aneurysms
An aneurysm is the result of a widening or ballooning of a portion of a blood vessel. The rupture of an aneurysm occurs when the mechanical stress acting on the inner wall exceeds the failure strength of the blood vessel. We propose an innovative approach to prevent the rupture of an aneurysm based on the use of nanotechnology to improve the strength of the blood vessel. We present results on the effect of silver nanofibers on the resistance toward deformation of blood vessels. The silver nanofibers are grown on the surface of the blood vessels. The nanofibers are 120±30ânm in diameter and 2.7±0.8âÎŒm in length. The deformation per applied force of blood vessels was found to decrease from 0.15âm/N in control blood vessels to 0.003âm/N in blood vessels treated with the nanofibers. This represents an increase in the resistance towards deformation of a factor of 50. The increase in the resistance towards deformation is clinically significant since blood pressure increases by factors slightly larger than one in the human body. Treatment of blood vessels with silver nanofibers is a potential translational clinical tool for preventing rupture of aneurysms in a clinical setting
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Thermal contact resistance in micromoulding.
yesThis work outlines a novel approach for determining thermal contact resistance (TCR) in micromoulding. The proposed technique aims to produce TCR predictions with known confidence values and combines experimental evidence (temperature fields and contact angle measurements) with various mathematical modelling procedures (parametric representation of surfaces, finite element analysis and stochastic processes). Here, emphasis is made on the mathematical aspects of the project. In particular, we focus on the description of the parametric surface representation technique based on the use of partial differential equations, known as the PDE method, which will be responsible for characterizing and compressing micro features in either moulds or surface tools.EPSR
Occurrence and sorption behaviour of bisphenols and benzophenone UV-filters in e-waste plastic and vehicle fluff
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