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Ugail, Hassan (103)

Gonzalez Castro, Gabriela (25)Bukar, Ali M. (9)Sheng, Y. (9)Wilson, M.J. (9)Sweeney, John (7)Whiteside, Benjamin R. (7)Willis, P. (7)Connah, David (6)Athanasopoulos, Michael (5)View MoreSubjectPDE surfaces (19)Partial differential equations (PDEs) (14)Partial differential equations (6)Biharmonic equation (5)PDE method (5)Surface profiling (5)Machine learning (4)Design optimisation (3)Face (3)Face recognition (3)View MoreDate Issued2010 - 2019 (57)2000 - 2009 (44)1998 - 1999 (2)
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Now showing items 1-10 of 103

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Efficient Shape Parametrisation for Automatic Design Optimisation using a Partial Differential Equation Formulation

Ugail, Hassan; Wilson, M.J. (2003)

This paper presents a methodology for efficient shape parametrisation for automatic design optimisation using a partial differential equation (PDE) formulation. It is shown how the choice of an elliptic PDE enables one to define and parametrise geometries corresponding to complex shapes. By using the PDE formulation it is shown how the shape definition and parametrisation can be based on a boundary value approach by which complex shapes can be created and parametrised based on the shape information at the boundaries or the character lines defining the shape. Furthermore, this approach to shape definition allows complex shapes to be parametrised intuitively using a very small set of design parameters.

The Optimal Design and Manufacture of Thin-Walled Polystyrene Structures

Unwin, A.P.; Ugail, Hassan; Bloor, M.I.G.; Wilson, M.J. (2005)

The divider set of explicit parametric geometry

Ugail, Hassan; Aggarwal, A.; Bakopoulos, Y.; Kotsios, S. (IEEE Computer Society., 2008)

In this paper we describe a novel concept for classification
of complex parametric geometry based on the concept
of the Divider Set. The Divider Set is an alternative concept
to maximal disks, Voronoi sets and cut loci. The Divider
Set is based on a formal definition relating to topology
and differential geometry. In this paper firstly we discuss
the formal definition of the Divider Set for complex
3-dimensional geometry. This is then followed by the introduction
of a computationally feasible algorithm for computing
the Divider Set for geometry which can be defined
in explicit parametric form. Thus, an explicit solution form
taking advantage of the special form of the parametric geometry
is presented. We also show how the Divider Set can
be computed for various complex parametric geometry by
means of illustrating our concept through a number of examples

Shape morphing of complex geometries using partial differential equations.

Gonzalez Castro, Gabriela; Ugail, Hassan (Academy Publisher, 2007)

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.

Reconstruction of 3D human facial images using partial differential equations.

Elyan, Eyad; Ugail, Hassan (Academy Publisher, 2007)

One of the challenging problems in geometric
modeling and computer graphics is the construction of
realistic human facial geometry. Such geometry are
essential for a wide range of applications, such as 3D face
recognition, virtual reality applications, facial expression
simulation and computer based plastic surgery application.
This paper addresses a method for the construction of 3D
geometry of human faces based on the use of Elliptic Partial
Differential Equations (PDE). Here the geometry
corresponding to a human face is treated as a set of surface
patches, whereby each surface patch is represented using
four boundary curves in the 3-space that formulate the
appropriate boundary conditions for the chosen PDE. These
boundary curves are extracted automatically using 3D data
of human faces obtained using a 3D scanner. The solution of
the PDE generates a continuous single surface patch
describing the geometry of the original scanned data. In this
study, through a number of experimental verifications we
have shown the efficiency of the PDE based method for 3D
facial surface reconstruction using scan data. In addition to
this, we also show that our approach provides an efficient
way of facial representation using a small set of parameters
that could be utilized for efficient facial data storage and
verification purposes.

Method of trimming PDE surfaces

Ugail, Hassan (Elsevier, 2006)

A method for trimming surfaces generated as solutions to Partial Differential Equations
(PDEs) is presented. The work we present here utilises the 2D parameter
space on which the trim curves are defined whose projection on the parametrically
represented PDE surface is then trimmed out. To do this we define the trim curves
to be a set of boundary conditions which enable us to solve a low order elliptic
PDE on the parameter space. The chosen elliptic PDE is solved analytically, even
in the case of a very general complex trim, allowing the design process to be carried
out interactively in real time. To demonstrate the capability for this technique we
discuss a series of examples where trimmed PDE surfaces may be applicable.

Method of numerical simulation of stable structures of fluid membranes and vesicles.

Ugail, Hassan; Jamil, N.; Satinoianu, R. (World Scientific and Engineering Academy and Society (WSEAS), 2006)

In this paper we study a methodology for the numerical simulation of stable structures of fluid membranes and vesicles in biological organisms. In particular, we discuss the effects of spontaneous curvature on vesicle cell membranes under the bending energy for given volume and surface area. The geometric modeling of the vesicle shapes are undertaken by means of surfaces generated as Partial Differential Equations (PDEs). We combine PDE based geometric modeling with numerical optimization in order to study the stable shapes adopted by the vesicle membranes. Thus, through the PDE method we generate a generic template of a vesicle membrane which is then efficiently parameterized. The parameterization is taken as a basis to set up a numerical optimization procedure which enables us to predict a series of vesicle shapes subject to given surface area and volume.

Shape reconstruction using partial differential equations

Ugail, Hassan; Kirmani, S. (World Scientific and Engineering Academy and Society (WSEAS), 2006)

We present an efficient method for reconstructing complex geometry using an elliptic Partial Differential Equation (PDE) formulation. The integral part of this work is the use of three-dimensional curves within the physical space which act as boundary conditions to solve the PDE. The chosen PDE is solved explicitly for a given general set of curves representing the original shape and thus making the method very efficient. In order to improve the quality of results for shape representation we utilize an automatic parameterization scheme on the chosen curves. With this formulation we discuss our methodology for shape representation using a series of practical examples.

Time-dependent shape parameterisation of complex geometry using PDE surfaces

Ugail, Hassan (Nashboro Press, 2004)

Efficient 3D data representation for biometric applications

Ugail, Hassan; Elyan, Eyad (IOS Press, 2007)

An important issue in many of today's biometric applications is the development of efficient and accurate techniques for representing related 3D data. Such data is often available through the process of digitization of complex geometric objects which are of importance to biometric applications. For example, in the area of 3D face recognition a digital point cloud of data corresponding to a given face is usually provided by a 3D digital scanner. For efficient data storage and for identification/authentication in a timely fashion such data requires to be represented using a few parameters or variables which are meaningful. Here we show how mathematical techniques based on Partial Differential Equations (PDEs) can be utilized to represent complex 3D data where the data can be parameterized in an efficient way. For example, in the case of a 3D face we show how it can be represented using PDEs whereby a handful of key facial parameters can be identified for efficient storage and verification.

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