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| Keywords: Piecewise linear function2D.svg Illustration of a en piecewise linear function self-made with en MATLAB 02 24 19 June 2007 UTC Oleg Alexandrov Source code MATLAB <source lang Matlab > Draw a piewise-linear function in two dimensions on a given triangulation Due to a bug in plot2svg it can't export 3D pictures well Then I have to take the 3D picture and rotate and project it manually to 2D That makes the code more complicated function main read the triangulation from the data at the end of the code dummy_arg 0; node get_nodes dummy_arg ; np k size node ; ele get_triangles dummy_arg ; nt k size ele ; the function whose piecewise-linear approximation will be graphed f inline '0 07 22-8 x 2-10 y 2 +0 14' ; will keep here the triangles to plot and their colors P zeros 3 nt 3 ; C zeros nt 3 ; iterate through triangles save the coordinates of all the triangles alpha 0 3; for i 1 nt; u ele i 2 ; v ele i 3 ; w ele i 4 ; y1 node u 2 ; x1 node u 3 ; f1 f x1 y1 ; y2 node v 2 ; x2 node v 3 ; f2 f x2 y2 ; y3 node w 2 ; x3 node w 3 ; f3 f x3 y3 ; the color of the given triangle is chosen randomly color alpha rand 1 3 + 1-alpha 1 1 1; store the triangle and its color for the future m 3 i - 2; P m+0 1 x1; P m+0 2 y1; P m+0 3 f1; P m+1 1 x2; P m+1 2 y2; P m+1 3 f2; P m+2 1 x3; P m+2 2 y3; P m+2 3 f3; C i color; end the base the domain of the piecewise linear function P0 P; P0 3 0 P0 3 ; Do a rotation in 3D then plot the projections onto the xy-plane This has to be done by hand since plot2svg has trouble saving 3D graphics a pi/2 5; b 0; c 0; Q do_rotate P a b c ; Q0 do_rotate P0 a b c ; sort the triangles by the third coordinate of the center of gravity after the rotation R zeros nt 2 ; for i 1 nt m 3 i-2; z1 Q m 3 ; z2 Q m+1 3 ; z3 Q m+2 3 ; R i 1 z1+z2+z3 /3; R i 2 i; end R sortrows R 1 ; plot the projection of the rotated figure and the base shape clf; hold on; axis equal; axis off; lw 0 5; black 0 0 0; white 1 1 1; for i 1 nt j R i 2 ; m 3 j-2; fill Q m 1 Q m+1 1 Q m+2 1 Q m 2 Q m+1 2 Q m+2 2 C i ; fill Q0 m 1 Q0 m+1 1 Q0 m+2 1 Q0 m 2 Q0 m+1 2 Q0 m+2 2 white ; plot Q m 1 Q m+1 1 Q m+2 1 Q m 1 Q m 2 Q m+1 2 Q m+2 2 Q m 2 'linewidth' lw 'color' black ; plot Q0 m 1 Q0 m+1 1 Q0 m+2 1 Q0 m 1 Q0 m 2 Q0 m+1 2 Q0 m+2 2 Q0 m 2 'linewidth' lw 'color' black ; end a small fix to avoid a bug with the bounding box when exporting small 0 1; Sx min min Q 1 min Q0 1 -small; Lx max max Q 1 max Q0 1 +small; Sy min min Q 2 min Q0 2 -small; Ly max max Q 2 max Q0 2 +small; plot Lx Ly ' ' 'color' 0 99 white ; plot Sx Sy ' ' 'color' 0 99 white ; axis Sx-small Lx+small Sy-small Ly+small export as eps and svg saveas gcf 'piecewise_linear2D_proj eps' 'psc2' plot2svg 'piecewise_linear2D_proj svg' function node get_nodes dummy_arg node 1 1 0 2 0 913545 0 406737 3 0 669131 0 743145 4 0 309017 0 951057 5 -0 104528 0 994522 6 -0 5 0 866025 7 -0 809017 0 587785 8 -0 978148 0 207912 9 -0 978148 -0 207912 10 -0 809017 -0 587785 11 -0 5 -0 866025 12 -0 104528 -0 994522 13 0 309017 -0 951057 14 0 669131 -0 743145 15 0 913545 -0 406737 16 -0 161265 -0 179103 17 0 313878 0 228046 18 -0 314083 0 348825 19 0 40037 -0 290886 20 0 0609951 -0 58033 21 0 0617879 0 587873 22 -0 587046 1 34875e-16; function ele get_triangles dummy_arg ele 1 10 11 16 2 16 18 22 3 10 22 9 4 10 16 22 5 11 12 20 6 7 22 18 7 21 3 4 8 8 9 22 9 8 22 7 10 1 19 15 11 20 13 14 12 6 18 21 13 6 21 5 14 19 1 17 15 19 16 20 16 11 20 16 17 2 17 1 18 16 17 18 19 6 7 18 20 17 16 19 21 21 4 5 22 3 17 2 23 17 3 21 24 20 12 13 25 19 20 14 26 18 17 21 27 14 15 19; function Q do_rotate P a b c M 1 0 0; 0 cos a sin a ; 0 -sin a cos a cos b 0 -sin b ; 0 1 0; sin b 0 cos b cos c sin c 0; -sin c cos c 0; 0 0 1; m n size P ; Q 0 P; for i 1 m X P i '; X M X; Q i 1 X 1 ; Q i 2 X 2 ; Q i 3 X 3 ; end </source> Piecewise linear functions Images with Matlab source code Files by User Oleg Alexandrov from en wikipedia Finite element modelling | ||||
