Concentric Spherical Representation for Omnidirectional Soft Shadow

2013 ◽  
Vol 32 (6) ◽  
pp. 201-213 ◽  
Author(s):  
Yi Xiao ◽  
Chi Sing Leung ◽  
Tze Yui Ho ◽  
Liang Wan ◽  
Tien Tsing Wong
Keyword(s):  
Spherical Representation ◽  
Soft Shadow

Images, Imagination, and Movement: Pictorial Representations and Their Development in the Work of James Gibson

Perception ◽  
10.1068/p2976 ◽  
2000 ◽  
Vol 29 (6) ◽  
pp. 635-648 ◽  
Author(s):  
James E Cutting
Keyword(s):  
Vector Field ◽  
Optical Flow ◽  
Spherical Representation ◽  
Pictorial Representations ◽  
The Relationship

For more than 30 years James Gibson studied pictures and he studied motion, particularly the relationship between movement through an environment and its visual consequences. For the latter, he also struggled with how best to present his ideas to students and fellow researchers, and employed various representations and formats. This article explores the relationships between the concepts of the fidelity of pictures (an idea he first promoted and later eschewed) and evocativeness as applied to his images. Gibson ended his struggle with an image of a bird flying over a plane surrounded by a spherical representation of a vector field, an image high in evocativeness but less than completely faithful to optical flow.

scholarly journals Casselman’s Basis of Iwahori Vectors and the Bruhat Order

2011 ◽  
Vol 63 (6) ◽  
pp. 1238-1253 ◽  
Author(s):  
Daniel Bump ◽  
Maki Nakasuji
Keyword(s):  
Weyl Group ◽  
Bruhat Order ◽  
Group Element ◽  
The Other ◽  
Intertwining Operators ◽  
Transition Matrices ◽  
Natural Basis ◽  
Spherical Representation ◽  
Langlands Parameters ◽  
Combinatorial Condition

AbstractW. Casselman defined a basis fu of Iwahori fixed vectors of a spherical representation of a split semisimple p-adic group G over a nonarchimedean local field F by the condition that it be dual to the intertwining operators, indexed by elements u of the Weyl group W. On the other hand, there is a natural basis , and one seeks to find the transition matrices between the two bases. Thus, let and . Using the Iwahori–Hecke algebra we prove that if a combinatorial condition is satisfied, then , where z are the Langlands parameters for the representation and α runs through the set S(u, v) of positive coroots (the dual root systemof G) such that with rα the reflection corresponding to α. The condition is conjecturally always satisfied if G is simply-laced and the Kazhdan–Lusztig polynomial Pw0v,w0u = 1 with w0 the long Weyl group element. There is a similar formula for conjecturally satisfied if Pu,v = 1. This leads to various combinatorial conjectures.

scholarly journals Erratum: Spherical representation of omnipotent Smith chart

2009 ◽  
Vol 51 (9) ◽  
pp. 2255-2255
Author(s):  
Yongle Wu ◽  
Haiyu Huang ◽  
Yuanan Liu ◽  
Zehua Gao
Keyword(s):  
Spherical Representation ◽  
Smith Chart

Revectorization‐Based Soft Shadow Mapping

2019 ◽  
Vol 39 (1) ◽  
pp. 389-404
Author(s):  
M. C. F. Macedo ◽  
A. L. Apolinário ◽  
K. A. Agüero
Keyword(s):  
Shadow Mapping ◽  
Soft Shadow

High-Quality Adaptive Soft Shadow Mapping

2007 ◽  
Vol 26 (3) ◽  
pp. 525-533 ◽  
Author(s):  
Gaël Guennebaud ◽  
Loïc Barthe ◽  
Mathias Paulin
Keyword(s):  
High Quality ◽  
Shadow Mapping ◽  
Soft Shadow

Neural Networks Multiobjective Learning With Spherical Representation of Weights

2020 ◽  
Vol 31 (11) ◽  
pp. 4761-4775
Author(s):  
Honovan P. Rocha ◽  
Marcelo A. Costa ◽  
Antonio P. Braga
Keyword(s):  
Neural Networks ◽  
Spherical Representation

On the director surface of a rectilinear congruence

1963 ◽  
Vol 59 (2) ◽  
pp. 503-504 ◽  
Author(s):  
P. Jha ◽  
C. J. Eliezer
Keyword(s):  
Parametric Curves ◽  
Spherical Representation

In this paper, it is shown that certain quantities defined with reference to the rays of a rectilinear congruence, remain unchanged for a change in the director surface, provided that the spherical representation of the congruence is kept unchanged. These quantities may be called semi-invariants. Some known invariants have been expressed in terms of these semi-invariants. An attempt has been made to find how these semi-invariants alter when the parametric curves are changed in any manner.

scholarly journals Soft shadow volumes for ray tracing

2005 ◽  
Author(s):  
Samuli Laine ◽  
Timo Aila ◽  
Ulf Assarsson ◽  
Jaakko Lehtinen ◽  
Tomas Akenine-Möller
Keyword(s):  
Ray Tracing ◽  
Soft Shadow
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