The shape and erosion of pebbles

The shapes of flat pebbles may be characterized in terms of the statistical distribution of curvatures measured along their contours. We illustrate this new method for clay pebbles eroded in a controlled laboratory apparatus, and also for naturally-occurring rip-up clasts formed and eroded in the Mont St.-Michel bay. We find that the curvature distribution allows finer discrimination than traditional measures of aspect ratios. Furthermore, it connects to the microscopic action of erosion processes that are typically faster at protruding regions of high curvature. We discuss in detail how the curvature may be reliable deduced from digital photographs.Comment: 10 pages, 11 figure

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

A profile-driven sketching interface for pen-and-paper sketches

This research is funded by the University of Malta under the research grant R30 31330 and is part of the project Innovative ‘Early Design’ Product Prototyping (InPro).Sketching interface tools are developed to allow designers to benefit from the powerful computational tools avail- able in computer aided design systems. However, despite the number of sketching tools such as PDAs and Tablet PCs available on market, designers typically create a number of initial conceptual ideas using paper-based sketches and scribbles such that these tools remain inaccessible to designers in the early design stages. In this paper we describe a profile-driven, paper-based sketching interface which infers the 3D geometry of objects drawn by designers using the traditional pen and paper sketching. We show that by making full use of the shape information present in the scribbled drawing, it is possible to obtain a paper-based sketching interface that retains the simplicity of the early- stage design drawings while allowing for the modeling of a variety of object shapes.peer-reviewe