Keywords: Level grad.png en wikipedia Maksim page en wikipedia Done with Matlab Level grad svg Source code <pre> Lx1 -1 7; Lx2 2 3; Ly1 -2; Ly2 2; box dimensions N 60; split the box into N x N grid X Y meshgrid Lx1 1/N Lx2 Ly1 1/N Ly2 ; the grid f inline '- y+1 4/25+ x-1 4/10+x 2+y 2-1 ' ; draw the level sets of f fx inline '-2/5 x-1 3-2 x' ; fy inline '-4/25 y+1 3-2 y' ; partial deriv Z f X Y ; the function value figure 1 ; clf; hold on; axis equal; axis off; pop up a figure h 0 5; spacing between heights v -20 h 0 8 0 85; the heights c h contour X Y Z v 'b' ; the level sets at those heights x0 0 1333; y0 -0 0666; coordinates of the top of the hill delta 0 01; descend from the top of the hill with this step size Angles linspace 0 2 pi 20 ; will draw 19 descent curves with Angles i for i 1 length Angles x x0+0 1 cos Angles i ; y y0+0 1 sin Angles i ; starting point Curve_x x; Curve_y y; will hold a descent curve following the gradient descend from the hill for j 1 500 x x-delta fx x ; y y-delta fy y ; Curve_x Curve_x x; Curve_y Curve_y y; append the updated values if max abs x abs y > 5 stop when going beyond the picture frame break; end end plot Curve_x Curve_y 'r' plot the curve of steepest descent end axis Lx1 Lx2 Ly1 Ly2 ; the picture frame saveas gcf 'level_grad eps' 'psc2' save as color postscript Use gimp to convert to png Does anybody know how to reduce aliasing gimp helps but only a bit </pre> 1 date/time username edit summary ---- 19 47 30 January 2006 en User Varuna <nowiki> get rid of ugly tag warning </nowiki> ---- 18 54 23 December 2004 en User Oleg Alexandrov <nowiki> added source code </nowiki> ---- 18 41 23 December 2004 en User Oleg Alexandrov <nowiki> I made this PD </nowiki> Original upload log Legend cur this is the current file del delete this old version rev revert to this old version Click on date to download the file or see the image uploaded on that date del cur 18 41 23 December 2004 en User Oleg_Alexandrov Oleg Alexandrov en User_talk Oleg_Alexandrov Talk 358x336 71326 bytes I made this PD Contour lines Grids Images with Matlab source code Files by User Oleg Alexandrov from en wikipedia |