An arbitrary mesh network scheme using rational splines

A C1 surface scheme is described which interpolates points defined on an arbitrary mesh network. The scheme involves the blending of strip ‘functions’ developed from a rational spline method. The rational spline provides interval and point tension weights which can be used to control the shape of the surface scheme

Smooth parametric surfaces and n-sided patches

The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed

Progressive surface modeling scheme from unorganised curves

This paper presents a novel surface modelling scheme to construct a freeform surface progressively from unorganised curves representing the boundary and interior characteristic curves. The approach can construct a base surface model from four ordinary or composite boundary curves and support incremental surface updating from interior characteristic curves, some of which may not be on the final surface. The base surface is first constructed as a regular Coons surface and upon receiving an interior curve sketch, it is then updated. With this progressive modelling scheme, a final surface with multiple sub-surfaces can be obtained from a set of unorganised curves and transferred to commercial surface modelling software for detailed modification. The approach has been tested with examples based on 3D motion sketches; it is capable of dealing with unorganised design curves for surface modelling in conceptual design. Its limitations have been discussed

Partial Differential Equations for 3D Data Compression and Reconstruction

This paper describes a PDE-based method for 3D reconstruction of surface patches. The PDE method is exploited using data obtained from standard 3D scanners. First the original surface data are intersected by a number of cutting planes whose intersection points on the mesh are represented by Fourier transforms in each plane. Information on the number of vertices and scale of the surface are defined and, together, these efficiently define the compressed data. The PDE method is then applied at the reconstruction stage by defining PDE surface patches between the cutting planes

Electromagnetic Wave Theory and Applications

Contains table of contents for Section 3, reports on six research projects and a list of publications and conference papers.Joint Services Electronics Program Contract DAAL03-89-C-0001National Science Foundation Grant ECS 86-20029Schlumberger- Doll ResearchU.S. Army Research Office Contract DAAL03 88-K-0057U.S. Navy - Office of Naval Research Contract N00014-90-J-1002National Aeronautics and Space Administration Grant NAGW-1617U.S. Navy - Office of Naval Research Grant N00014-89-J-1107National Aeronautics and Space Administration Grant NAGW-1272National Aeronautics and Space Administration Agreement 958461U.S. Army - Corps of Engineers Contract DACA39-87-K-0022U.S. Air Force - Electronic Systems Division Contract F19628-88-K-0013U.S. Navy - Office of Naval Research Grant N00014-89-J-1019Digital Equipment CorporationIBM CorporationU.S. Department of Transportation Contract DTRS-57-88-C-00078Defence Advanced Research Projects Agency Contract MDA972-90-C-002

Computational fluid dynamics of vortex flow controls at low flow rates

PublishedJournal ArticleA vortex flow control with differing outlet shapes is investigated computationally at low flow rates. The volume of fluid method was utilised to track the moving free surface. In order to achieve a smooth free surface, interface compression coupled with the inter-gamma compressive scheme was used. The turbulent evolution of the two-phase flow was modelled by solving the Reynolds-averaged Navier-Stokes equations with the k-ε model for turbulent quantities. Validation of the results was carried out by analysing the total head and discharge coefficient for the three outlet shapes at various flow rates and comparing these results with experimental data. Very good agreement with the experimental data was obtained

On the equivalence between the cell-based smoothed finite element method and the virtual element method

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D