The recent controversy of applicability of quantum formalism to brain dynamics has been critically analyzed. PELLIONISZ and LLINÁS (1982) proposed a functional geometry to understand the internal representation of the events associated to the spacetiming of moving objects in the external world. The joint representation of space and time associated to an event as understood by the brain is shown...

We propose to render geometry using an image based representation. Geometric information is encoded by a texture with depth and rendered by rasterizing the bounding box geometry. For each resulting fragment, a shader computes the intersection of the corresponding ray with the geometry using pre-computed information to accelerate the computation. Our method is almost always artifact free even wh...

A framework for analyzing distortions in non-single viewpoint imaging systems is presented. Such systems possess loci of viewpoints called caustics. In general, perspective (or undistorted) views cannot be computed from images acquired with such systems without knowing scene structure. Views computed without scene structure will exhibit distortions which we call caustic distortions. We first in...

In the literature, perspective space has been introduced as a model of visual space. Perspective space is grounded on the perspective nature of visual space during both binocular and monocular vision. A single parameter, that is, the distance of the vanishing point, transforms the geometry of physical space into that of perspective space. The perspective-space model predicts perceived angles, d...

This Perspective presents a review and survey of the science and philosophy of my research career over the past five decades at Columbia as a physical organic chemist and photochemist. I explore the role of paradigms, structure, and geometric thinking in my own cognitive and intellectual development. The Perspective describes my investigations of high energy content molecules in electronically ...

this paper concerns the design and analysis, of a ball type continuously variable transmission, (b-cvt). this b-cvt has a simple kinematic structure, and same as a toroidal cvt, transmits power by friction on the contact points between input and output discs, that are connected to each other by balls. after, a brief introduction of our b-cvt structure, the performance and traction efficiency of...

Traditionally, students use pencil and ruler to lay out lines and curves over contour maps for roadway geometry design. Numerous calculations of stopping sight distance, minimum turning radius, and curve alignments are required during the roadway design process in order to ensure safety, to minimize economic and environmental impacts, as well as to reduce construction costs. Students usually pe...