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| Keywords: Partition of unity illustration.svg Illustration of en Partition of unity self-made with MATLAB tweaked in Inkscape 03 38 9 August 2007 UTC Oleg Alexandrov Source code MATLAB <source lang Matlab > illustration of partitition of unity For simplicity we cheat by using scaled sums of gaussians instead of bump functions function main figure 1 ; clf; hold on; axis equal; axis off; lw 2; linewidth h 0 1; grid size endpoints of the interval a -5; b 10; Sample -2 1 -1 3 -0 4 1 3 1 8 3 1 4 5; red 0 867 0 06 0 14; blue 0 129 205/256; green 0 200 70/256; yellow 254 194 0/256; Colors red' blue' green' yellow; L 2 4 6 8; X a h b; Y zeros length L length X ; Yt 0 X; gaussian with mean zero variance zsigma zsigma 0 55; f inline 'exp -x 2/2/zsigma /zsigma/sqrt 2 pi ' ; pos 1; for i 1 length Sample if i > L pos pos pos+1; end Ycur f X-Sample i zsigma ; Y pos Y pos + Ycur; Yt Yt+Ycur; end Xtp Ytp make_periodic a b h X Yt ; Yr 0 Xtp; for pos 1 length L Xp Yp make_periodic a b h X Y pos ; Yp Yp /Ytp; Yr Yr + Yp; plot Xp Yp 'color' Colors pos 'linewidth' lw ; end plot Xtp 0 Yr 'k' 'linewidth' lw ; plot Xtp Yr 'k' 'linewidth' lw/1 4 'linestyle' '--' ; fs 20; shiftx -0 3; shifty -0 0; text Xtp 1 +shiftx 0+shifty '0' 'fontsize' fs ; text Xtp 1 +shiftx 1+shifty '1' 'fontsize' fs ; saveas gcf 'Partition_of_unity_illustration eps' 'psc2' ; plot2svg 'Partition_of_unity_illustration svg' ; function Xp Yp make_periodic a b h X Y Take a function defined on the real line Wrap the real line around Sum the overlapping parts Get a periodic function T 8; as -3; bs as+T; A as-a /h; B bs-a /h; N length Y ; Y B-A+1 B Y B-A+1 B + Y 1 A ; Y A+1 A+N-B Y A+1 A+N-B + Y B+1 N ; Yp Y A+1 B ; Xp X A+1 B ; </source> Differential geometry Images with Matlab source code Files by User Oleg Alexandrov from en wikipedia SVG mathematics | ||||
