We discuss using projected manifolds in geometric design and processing. Curves and surfaces are defined in n-space as algebraic sets of the appropriate dimensionality, and their projection into a three-dimensional subspace is considered. In this approach, the additional variables serve to express simply geometric constraints, and so complex surfaces such as offsets, equi-distance surfaces, rou...

The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Indiana Department of Transportation or the Federal Highway Administration at the time of publication. The report does not constitute a standard, specification, or regulation. ...

The writers of this paper see the current highway design standards as a two-dimensional projection which the horizontal and vertical alignments are treated separately. A model developed in this paper considers and study the sight distance as a three-dimensional alignment on the design requirements. The paper examines the required minimum radius of a horizontal curve combined with a crest or sag...

A large metal sculpture, consisting of four orbs, commissioned for the stairway atrium of the Fitzpatrick CIEMAS Engineering Building at Duke University embodies the important idea that Science, Technology, Engineering, Mathematics and Art are closely connected. Made from hundreds of pounds of powder-coated, laser-cut aluminum, with an underlying geometric design, it was assembled at a four-hou...

This paper describes the development and operation of a dual-band time~domain radar system used to measure indoor multipath propagation characteristics in several office buildings and factories. The system operates at 1.3 GHz and 4.0 GHz, and uses 4 ns rms pulses to provide estimates of indoor radio channel impulse responses. The effects of ante.nna diversity, .frequency scaling, and topography...

Piecewise linear maps over triangulations are used extensively in geometric modelling and computer graphics. This short note surveys recent progress on the important question of when such maps are one-to-one, central to which are convex combination maps.

Geometric design of quadratic and cubic developable Be Âzier patches from two boundary curves is studied in this paper. The conditions for developability are derived geometrically from the de Casteljau algorithm and expressed as a set of equations that must be ful®lled by the Be Âzier control points. This set of equations allows us to infer important properties of developable Be Âzier patches t...