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| Keywords: Diffeomorphism of a square.svg Illustration of a diffeomorphism self-made with MATLAB 04 25 18 January 2008 UTC Oleg Alexandrov Source code MATLAB <source lang matlab > Compute a diffeomorphism from a square to a square which leave the boundary fixed function main N 20; num of grid points epsilon 0 1; displacement for each small diffeomorphism num_comp 10; number of times the diffeomorphism is composed with itself S linspace -1 1 N ; X Y meshgrid S ; Z X; W Y; take num_comp compositions of the same small diffeomorphism for iter 1 num_comp for i 1 N for j 1 N Z i j W i j small_diffeo Z i j W i j epsilon ; end end end graphing settings lw 2; mycolor 1 0 0 1; small 0 1; figure 1 ; clf; hold on; for i 1 N plot X i Y i 'linewidth' lw 'color' mycolor ; plot X i Y i 'linewidth' lw 'color' mycolor ; end axis -1-small 1+small -1-small 1+small ; axis equal; axis off; figure 2 ; clf; hold on; for i 1 N plot Z i W i 'linewidth' lw 'color' mycolor ; plot Z i W i 'linewidth' lw 'color' mycolor ; end axis -1-small 1+small -1-small 1+small ; axis equal; axis off; function z w small_diffeo x y epsilon ; A1 epsilon cos pi x +1 cos pi y +1 /4 0; A2 epsilon cos pi x/2 cos pi y/2 ; A A1+A2 /2; z x + -y A; w y + x A; </source> Diffeomorphisms Files by User Oleg Alexandrov from en wikipedia | ||||
