Spelling suggestions: "subject:"martial differential equations (PDEs)"" "subject:"martial differential aquations (PDEs)""
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On the spine of a PDE surfaceUgail, Hassan January 2003 (has links)
yes / The spine of an object is an entity that can characterise the
object¿s topology and describes the object by a lower dimension. It has
an intuitive appeal for supporting geometric modelling operations.
The aim of this paper is to show how a spine for a PDE surface can
be generated. For the purpose of the work presented here an analytic
solution form for the chosen PDE is utilised. It is shown that the spine
of the PDE surface is then computed as a by-product of this analytic
solution.
This paper also discusses how the of a PDE surface can be used to manipulate
the shape. The solution technique adopted here caters for periodic
surfaces with general boundary conditions allowing the possibility of the
spine based shape manipulation for a wide variety of free-form PDE surface
shapes.
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Method of surface reconstruction using partial differential equationsUgail, Hassan, Kirmani, N. January 2006 (has links)
No
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3D facial data fitting using the biharmonic equation.Ugail, Hassan January 2006 (has links)
This paper discusses how a boundary-based surface fitting approach can be utilised to smoothly reconstruct a given human face where the scan data corresponding to the face is provided. In particular, the paper discusses how a solution to the Biharmonic equation can be used to set up the corresponding boundary value problem. We show how a compact explicit solution method can be utilised for efficiently solving the chosen Biharmonic equation.
Thus, given the raw scan data of a 3D face, we extract a series of profile curves from the data which can then be utilised as boundary conditions to solve the Biharmonic equation. The resulting solution provides us a continuous single surface patch describing the original face.
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Method of boundary based smooth shape design.Ugail, Hassan January 2005 (has links)
The discussion in this paper focuses on how boundary
based smooth shape design can be carried out. For this we
treat surface generation as a mathematical boundary-value
problem. In particular, we utilize elliptic Partial Differential
Equations (PDEs) of arbitrary order. Using the methodology
outlined here a designer can therefore generate the
geometry of shapes satisfying an arbitrary set of boundary
conditions. The boundary conditions for the chosen PDE
can be specified as curves in 3-space defining the profile
geometry of the shape.
We show how a compact analytic solution for the chosen
arbitrary order PDE can be formulated enabling complex
shapes to be designed and manipulated in real time.
This solution scheme, although analytic, satisfies exactly,
even in the case of general boundary conditions, where the
resulting surface has a closed form representation allowing
real time shape manipulation. In order to enable users
to appreciate the powerful shape design and manipulation
capability of the method, we present a set of practical examples.
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Partial differential equations for function based geometry modelling within visual cyberworldsUgail, Hassan, Sourin, A. January 2008 (has links)
We propose the use of Partial Differential Equations (PDEs) for shape modelling within visual cyberworlds.
PDEs, especially those that are elliptic in nature, enable surface modelling to be defined as boundary-value problems.
Here we show how the PDE based on the Biharmonic equation subject to suitable boundary conditions can
be used for shape modelling within visual cyberworlds. We discuss an analytic solution formulation for the Biharmonic
equation which allows us to define a function based geometry
whereby the resulting geometry can be visualised efficiently
at arbitrary levels of shape resolutions. In particular, we discuss how function based PDE surfaces can be readily integrated within VRML and X3D environments
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Parametric design of aircraft geometry using partial differential equationsAthanasopoulos, Michael, Ugail, Hassan, Gonzalez Castro, Gabriela January 2009 (has links)
No / This paper presents a surface generation tool designed for the construction of aircraft geometry. The software generates complex geometries which can be crafted or modified by the user in real time. The surface generation is based on partial differential equations (PDEs). The PDE method can produce different configurations of aircraft shapes interactively. Each surface is generated by a number of curves representing the character lines of a given part of the aircraft shape that can be manipulated in real time. Different surfaces then blend to create the full shape of the airplane. An important function of the proposed tool is its ability to change the aircraft shape through the adjustments of parameters associated with the initial curves. The user can apply linear transformations to the curves generating the airplane through simple input from the computer keyboard and the mouse. The updated curves can then be used to generate the surface leading to different configurations of a given airplane shape. The work presents detailed descriptions on the PDE method, parametric design and manipulation of aircrafts along with graphical demonstrations of its abilities and a series of examples to illustrate the capacity of the methodology implemented.
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On interactive design using the PDE method.Ugail, Hassan, Bloor, M.I.G., Wilson, M.J. January 1998 (has links)
No
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Shape reconstruction using partial differential equationsUgail, Hassan, Kirmani, S. January 2006 (has links)
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.
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Spine based shape parameterisation for PDE surfacesUgail, Hassan 15 May 2009 (has links)
Yes / The aim of this paper is to show how the spine of a PDE surface can be generated and how it can be used to efficiently parameterise a PDE surface. For the purpose of the work presented here an approximate analytic solution form for the chosen PDE is utilised. It is shown that the spine of the PDE surface is then computed as a by-product of this analytic solution. Furthermore, it is shown that a parameterisation can be introduced on the spine enabling intuitive manipulation of PDE surfaces.
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Manipulation of PDE surfaces using an interactively defined parameterisationUgail, Hassan, Bloor, M.I.G., Wilson, M.J. January 1999 (has links)
No / Manipulation of PDE surfaces using a set of interactively defined parameters is considered. The PDE method treats surface design as a boundary-value problem and ensures that surfaces can be defined using an appropriately chosen set of boundary conditions and design parameters. Here we show how the data input to the system, from a user interface such as the mouse of a computer terminal, can be efficiently used to define a set of parameters with which to manipulate the surface interactively in real time.
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