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Extra info for ACM Transactions on Graphics (January)
Schaefer and J. Warren Fig. 9. Mask calculated through centroid averaging on each side of the triangle/quad boundary. The mask is exactly half of the regular mask for triangular or quadrilateral surfaces. Applying Sˆ to v yields ˆ = St Ut v + Sq Uq v Sv = St vt + Sq vq 1 v triangle vertices 4 t 1 1 = v + v boundary 8 t1 8 q v quad vertices 4 q The final piecewise definition corresponds to exactly 14 v. Since Ut and Uq do not modify the boundary ˆ = 1 v, Sˆ satisfies the necessary conditions for C 2 continuity for the eigenvectors z i for i = 1 .
G. Baranoski et al. given by γ ξ2 (α, β) = (1 − e− 240 , 2π ξ3 ), where ξ2 and ξ3 are uniformly distributed random numbers ∈ [0, 1], and γ represents the initial thickness of the auroral stream. The accuracy and performance of the simulation is dependent on the number, N , of emission rays. Experiments show, however, asymptotic convergence of the results for larger values of N . The emissions mapped to the screen plane are scaled according to auroral spectral emission and intensity profiles [Baranoski et al.
Fig. 3. Line drawings illustrating an auroral arc break-up. The symbol denotes a vector normal to the plane of the paper. Fig. 4. Sketch showing different stages of an auroral warping process: a) initial arc, b) fold, c) further distorted fold, and d) spiral array. The symbol denotes a vector normal to the plane of the paper. and electric fields. In this section, we outline the most important of these changes according to their spatial scale. 1 Small Scale. When an electron particle stream responsible for producing a small scale structure becomes slightly more dense in a region, it is likely to become contorted and develop a curl [Davis 1992].