Shadow maps are the current technique for generating high quality real-time dynamic shadows. This article gives a ‘practical’ introduction to shadow mapping (or projection mapping) with numerous simple examples and source listings. We emphasis some of the typical limitations and common pitfalls when implementing shadow mapping for the first time and how the reader can overcome these problems us...

The H-l heliac recently brought into operation is a medium-sized 3-field-period heliac with major radius Ru=l m, plasma mean minor radius (a)<0.2 m and a wide range of rotational transforms 0.6 G+(O) G 2.0. Electron beam mapping of the vacuum magnetic field was performed using new type of a fluorescent target (movable fluorescent rod array having a transparency about 98%). Up to 150-200 toroida...

We consider shape optimization problems governed by the unsteady Navier-Stokes equations by applying the method of mappings, where the problem is transformed to a reference domain Ωref and the physical domain is given by Ω = τ(Ωref) with a domain transformation τ ∈ W (Ωref). We show the Fréchet-differentiability of τ 7→ (v, p)(τ) in a neighborhood of τ = id under as low regularity requirements ...

We construct the graded q-differential algebra on a ZN -graded algebra by means of a graded q-commutator. We apply this construction to a reduced quantum plane and study the first order differential calculus on a reduced quantum plane induced by the N -differential of the graded q-differential algebra. 1 Graded q-differential algebra In this section given a ZN -graded algebra we construct the g...

The classical Schwarz-Christoffel transformation provides a formula for the conformal mapping of the half-plane onto a plane polygon. A generalization enlarging the class of image domains to include many-sheeted plane polygons with interior winding points was known already to at least Schwarz and Schlifli.' This note is concerned with a further simple extension of the formula which delivers a u...

Due to recent advances in high dynamic range (HDR) technologies, the ability to display HDR images or videos on conventional LCD devices has become more and more important. Many tonemapping algorithms have been proposed to meet this end, the choice of which depends on display characteristics such as luminance range, contrast ratio and gamma correction. An ideal HDR tone-mapping processor should...

Proof. (1) These are the well known classical Plücker relations. For completeness’ sake we include a proof. Let P ∈ ΛV and consider the induced linear mapping ♯P : Λ V ∗ → V . Its image, W , is contained in each linear subspace U of V with P ∈ ΛU . Thus W is the minimal subspace with this property. P is decomposable if and only if dimW = s, and this is the case if and only if w ∧ P = 0 for each...

We exhibit a two-dimensional, acyclic, Eilenberg–Mac Lane space W such that, for every space X, the plus-construction X+ with respect to the largest perfect subgroup of π1(X) coincides, up to homotopy, with the W -nullification of X; that is, the natural map X → X+ is homotopy initial among maps X → Y where the based mapping space map∗(W,Y ) is weakly contractible. Furthermore, we describe the ...

If W is a right-angled Coxeter group, then the group Aut(W ) of automorphisms of W acts on the set of conjugacy classes of involutions in W. Following Tits [16], the kernel of this action is denoted by Aut◦(W ). Since W is a CAT(0) group [12], the index of Aut◦(W ) in Aut(W ) is finite and there is a series 1 Inn(W ) Aut◦(W ) Aut(W ) of normal subgroups of Aut(W ). A presentation for Aut◦(W ) w...

Fix an odd prime p, an algebraic closure Qp, and an isomorphism C ∼ → Qp. Fix an integer N ≥ 1 prime to p, and let T be the polynomial algebra over Z generated by the operators T!, ! ! Np, Up and 〈d〉 , d ∈ (Z/NZ). Set W = Spf(Zp[[Zp ]]), and let W = W rig be the rigid analytic space of characters of Zp together with its universal character χW : Z × p → O(W ) ; we embed Z in W (Qp) by mapping k ...