A Twisted Trapezoidal Shape for Geant4
A Twisted Trapezoidal Shape for Geant4
A Twisted Trapezoidal Shape for Geant4
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⎛⎜⎜( w(u,ϕ)+ Δx⎜(w(u,ϕ)+ Δx⎜⎜⎜⎝G4<strong>Twisted</strong>TrapAlphaSideSurface EquationϕΔϕϕΔϕ)cosϕ− ( u + Δy)sinϕ+ ( u + ΔyThe resulting solutioncontains terms in Sin(ϕ)and Cos(ϕ) which areapproximated with Padéexpansions.Polynom: 7 th order.ϕΔϕϕΔϕ)sinϕ=)cosϕ=u ∈[−Lϕ=Δϕϕ ∈[−1212w(u)=ppxypzΔφ,++ tv+ tv+ tv12b(ϕ),+xyz⎞⎟⎟⎟⎟⎟⎟⎠Δφ]12b(ϕ)b(ϕ)]αa(ϕ)d(ϕ)2 Free parameters (ϕ,u)a(ϕ)d(ϕ)− a(ϕ)⎡d(ϕ)− a(ϕ)⎤+− u⎢− tanα2 4⎥⎣ 2b(ϕ)⎦Nov 2003 Oliver Link, EP-SFT 3
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