Wireframe Structures Research Articles

Does the visual system exploit projective geometry to help solve the motion correspondence problem?

Projective geometry determines how the retinal image of an object deforms as it moves through three-dimensional space. Does the visual system use constraints derived from this information, such as rigidity, to aid the tracking of moving objects? A novel psychophysical technique is introduced for assessing which of two competing motion transformations is ‘preferred’ by the visual system, in a two-frame sequence. In the first experiment, relative preference strengths for translations parallel and perpendicular to the major axis of a wire-frame object were measured by pitting the two against each other. It was found that parallel translations were preferred to perpendicular ones. On the basis of these data a proximity measure for normalising different transformations, independent of any effects of figural similarity, was developed. In the second experiment, two wire-frame planar structures were used to pit one of five transformations (rotation, expansion, vertical expansion, shear and random jitter) against a translation. Preference strength was measured as the translation distance at which the transformation and the translation were perceived with equal frequency. The PSEs were found to collapse on to a single line when plotted against the proximity magnitude, with the exception of a residual preference for pure translation over all other transformations. In general, these results suggest that preference strength for moving wire-frame figures is determined primarily by the proximity of local features on the displacing contour, with little regard for the projective shape transformation.

Accelerating Numerical Electromagnetic Code computation by using the wavelet transform

The Numerical Electromagnetic Code (NEC) is one of the most popular tools for electromagnetic simulation of wireframe structures. The application of NEC is often limited to small to medium sized problems due to its full matrix nature. In this paper, an approach by using the wavelet transform to increase the efficiency and capability of NEC is presented. In the approach, a sparse moment matrix equation can be produced and solved by efficient sparse solver instead of solving full matrix equation in the original NEC. Under close examination, structures with less singularities are found to have much better accuracy and higher compression rates.

Polygons of unequal resistors

Consider an N-sided polygon made of resistors such that the resistances connected between the vertices are 2G times those connected between the center and each vertex. Effective resistance between the center and a vertex of such a polygon is obtained by a recursive procedure. The limiting value of the resistance for large N is found to be a fraction that is not always irrational. The method developed is suitable even for cases where resistances making up the polygon are of arbitrary values so that conventional symmetry arguments would not be applicable. The results are applied to a uniform wire shaped into a circular wheel with evenly spaced spokes, and other wire frame structures.