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Image-Space Caustics and Curvatures

by Xuan Yu, et al.
"... Caustics are important visual phenomena, as well as challenging global illumination effects in computer graphics. Physically caustics can be interpreted from one of two perspectives: in terms of photons gathered on scene geometry, or in terms of a pair of caustic surfaces. These caustic surfaces are ..."
Abstract - Cited by 7 (2 self) - Add to MetaCart
Caustics are important visual phenomena, as well as challenging global illumination effects in computer graphics. Physically caustics can be interpreted from one of two perspectives: in terms of photons gathered on scene geometry, or in terms of a pair of caustic surfaces. These caustic surfaces

Gravitational Lensing by Dark Matter Caustics

by Vakif K. Onemli , 2004
"... There are compelling reasons to believe that the dark matter of the universe is constituted, in large part, by non-baryonic collisionless particles with very small primordial velocity dispersion. Such particles are called cold dark matter (CDM). The leading candidates are axions and weakly interacti ..."
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is tangent to a smooth caustic surface. The curvature of the surface at the tangent point is positive, negative, or zero. In the fourth case, the line of sight passes near a cusp. For each case we derive the map between the image and source planes. In some cases, a point source has multiple images

Flat surfaces with singularities in Euclidean 3-space, preprint

by Satoko Murata, Masaaki Umehara , 605
"... ABSTRACT. It is classically known that complete flat (that is, zero Gaussian curvature) surfaces in Euclidean 3-space R 3 are cylinders over space curves. This implies that the study of global behaviour of flat surfaces requires the study of singular points as well. If a flat surface f admits singul ..."
Abstract - Cited by 12 (4 self) - Add to MetaCart
ABSTRACT. It is classically known that complete flat (that is, zero Gaussian curvature) surfaces in Euclidean 3-space R 3 are cylinders over space curves. This implies that the study of global behaviour of flat surfaces requires the study of singular points as well. If a flat surface f admits
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