The problem of constructing a surface from the information provided by the Marr-Poggio theory of human stereo vision is investigated. It is argued that not only does this theory provide explicit boundary conditions at certain points in the image, but that the imaging process also provides implicit conditions on all other points in the image. This argument is used to derive conditions on possible algorithms for computing the surface. Additional constraining principles are applied to the problem; specifically that the process be performable by a local-support parallel network. Some mathematical tools, differential geometry, Coons surface patches and iterative methods of convergence, relevant to the problem of constructing the surface are outlined. Specific methods for actually computing the surface are examined.

This thesis deals with the principle of capturing images of the retina of fundus camera, their features and then preprocessing. The aim of preprocessing is the correction of nonillumination in images of the retina. The model of non-illumination is obtained by using parametric surfaces. Coons surface was selected from a set of surfaces based on the knowledge of retinal images. This has been approximated by a non-uniform illumination. Then the thesis concentrates on describing the methods involving shading corrections. Compensation of non-uniform illumination is based on the use of parametric surface and selected methods for shading correction. The methods presented in the last chapter were tested on simulated and real data. The results were evaluated subjectively.

This document has two objectives: decomposition of a given trimmed surface into several four-sided subregions and creation of a diffeomorphism from the unit square onto each subregion. We aim at having a diffeomorphism which is easy and fast to evaluate. Throughout this paper one of our objectives is to keep the shape of the curves delineating the boundaries of the trimmed surfaces unchanged. The approach that is used invokes the use of transfinite interpolations. We will describe an automatic manner to specify internal cubic Bezier-spline curves that are to be subsequently interpolated by a Gordon patch. Some theoretical criterion pertaining to the control points of the internal curves is proposed and proved so as to ensure that the resulting Gordon patch is a diffeomorphism. Numerical results are reported to illustrate the approaches. Our benchmarks include CAD objects which come directly from IGES files.

This document serves as a reference for the beta version of our evaluation library ITL. First, it describes a library which gives an easy way for programmers to evaluate the 3D image and the normal vector corresponding to a parameter value which belongs to the unit square. The API functions which are described in this document let programmers make those evaluations without the need to understand the underlying CAD complica- tions. As a consequence, programmers can concentrate on their own scien- tific interests. Our second objective is to describe the input which is a set of parametric four-sided surfaces that have the structure required by some integral equation solvers.

We focus on the programming aspect of the treatment of digitized geometries for subsequent use in mesh-free and mesh-based numerical solvers. That perspective includes the description of our C/C++ implementations which use OpenGL for the visualization and MFC classes for the user interface. We report on our experience about implementing with the IGES interface which serves as input for storage of geometric information. For mesh-free numerical solvers, it is helpful to decompose the boundary of a given solid into a set of four-sided surfaces. Additionally, we will describe the treatment of diffeomorphisms on four-sided domains by using transfinite interpolations. In particular, Coons and Gordon patches are appropriate for dealing with such mappings when the equations of the delineating curves are explicitly known. On the other hand, we show the implementation of the mesh generation algorithms which invoke the Laplace-Beltrami operator. We start from coarse meshes which one refine according to generalized Delaunay techniques. Our software is also featured by its ability of treating assembly of solids in B-Rep scheme.

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We focus on the programming aspect of the treatment of digitized geometries for subsequent use in mesh-free and mesh-based numerical solvers. That perspective includes the description of our C/C++ implementations which use OpenGL for the visualization and MFC classes for the user interface. We report on our experience about implementing with the IGES interface which serves as input for storage of geometric information. For mesh-free numerical solvers, it is helpful to decompose the boundary of a given solid into a set of four-sided surfaces. Additionally, we will describe the treatment of diffeomorphisms on four-sided domains by using transfinite interpolations. In particular, Coons and Gordon patches are appropriate for dealing with such mappings when the equations of the delineating curves are explicitly known. On the other hand, we show the implementation of the mesh generation algorithms which invoke the Laplace-Beltrami operator. We start from coarse meshes which one refine according to generalized Delaunay techniques. Our software is also featured by its ability of treating assembly of solids in B-Rep scheme.

Many computer graphic API’s, including OpenGL, emphasize modeling with rectangular patches, which are especially useful in Computer Aided Geomeric Design (CAGD). However, not all shapes are rectangular; some are triangular or more complex. This paper extends the OpenGL library to support the modeling of triangular patches, Coons patches, and Box-splines patches. Compared with the triangular patch created from degenerate rectangular Bezier patch with the existing functions provided by OpenGL, the triangular Bezier patches can be used in certain design situations and allow designers to achieve high-quality results that are less CPU intense and require less storage space. The addition of Coons patches and Box splines to the OpenGL library also give it more functionality. Both patch types give CAGD users more flexibility in designing surfaces. A library for all three patch types was developed as an addition to OpenGL.

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No / In this paper we present a method for generating Bézier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bézier surfaces whereby we studied the Bézier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bézier solutions of the Euler¿Lagrange equation associated with the most general quadratic functional. We show that there is a large class of fourth-order operators for which Bézier solutions exist and hence we show that such operators can be utilised to generate Bézier surfaces from the boundary information. As part of this work we present a general method for generating these Bézier surfaces. Furthermore, we show that some of the existing techniques for boundary based surface design, such as Coons patches and Bloor¿Wilson PDE method, are indeed particular cases of the generalised framework we present here.