A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time simulation of smoke. Here we introduce a time-discrete evolution equation for arbitrary closed polygons in 3-space that is a discretisation of the localised induction approximation of filament motion. This discretisation shares with its continuum limit the property that it is a completely integrable system. We apply this polygon evolution to a significant improvement of the numerical algorithms used in Computer Graphics.Comment: 15 pages, 3 figure

Feature preserving smoothing of 3D surface scans

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2004.Includes bibliographical references (p. 63-70).With the increasing use of geometry scanners to create 3D models, there is a rising need for effective denoising of data captured with these devices. This thesis presents new methods for smoothing scanned data, based on extensions of the bilateral filter to 3D. The bilateral filter is a non-linear, edge-preserving image filter; its extension to 3D leads to an efficient, feature preserving filter for a wide class of surface representations, including points and "polygon soups."by Thouis Raymond Jones.S.M

The Douglas-Peucker algorithm for line simplification: Re-evaluation through visualization

The primary aim of this paper is to illustrate the value of visualization in cartography and to indicate that tools for the generation and manipulation of realistic images are of limited value within this application. This paper demonstrates the value of visualization within one problem in cartography, namely the generalisation of lines. It reports on the evaluation of the Douglas-Peucker algorithm for line simplification. Visualization of the simplification process and of the results suggest that the mathematical measures of performance proposed by some other researchers are inappropriate, misleading and questionable