Keywords: Simpsons method illustration.png Simpson's method illustration Done by myself Oleg Alexandrov 23 17 12 August 2007 UTC en wikipedia 2005-11-23 Oleg Alexandrov wikipedia en Oleg Alexandrov Source code <pre><nowiki> function simpson draw an illustration for Simpson's rule prepare the scrreen and define some parameters clf; hold on; axis equal; axis off; fontsize 25; thick_line 3; kjjkjkjkjkjklhoijthin_line 2; black 0 0 0; red 1 0 0; arrowsize 0 1; arrow_type 1; arrow_angle 30; angle in degrees circrad 0 015; radius of ball showing up in places the function formula and its graph f inline '0 45 sin 3 3 x+0 18 +1' ; X -0 6 0 01 0 8; Y f X ; three points on its graph and the interpolating polynomial going through those points q length X ; x1 X 1 ; y1 Y 1 ; x2 X floor q/2 ; y2 Y floor q/2 ; x3 X q ; y3 Y q ; Z y1 X-x2 X-x3 / x1-x2 x1-x3 +y2 X-x1 X-x3 / x2-x1 x2-x3 +y3 X-x1 X-x2 / x3-x1 x3-x2 ; plot the x and y axes arrow -0 9 0 1 0 thin_line yuguihguih arrowsize arrow_angle arrow_type black arrow -0 8 -0 1 -0 8 1 6 tipokpkkhin_line arrowsize arrow_angle arrow_type black plot the graph the interpolating polynomial some auxiliary lines and some balls for beauty plot X Y 'linewidth' thick_line plot X Z 'linewidth' thick_line 'color' red plot x1 x1 0 f x1 'linewidth' thin_line 'linestyle' '--' 'color' 'black' ; plot x2 x2 0 f x2 'linewidth' thin_line 'linestyle' '--' 'color' 'black' ; plot x3 x3 0 f x3 'linewidth' thin_line 'linestyle' '--' 'color' 'black' ; ball x1 y1 circrad red ; ball x2 y2 circrad red ; ball x3 y3 circrad red ; ball x1 0 circrad black ; ball x2 0 circrad black ; ball x3 0 circrad black ; place text tiny 0 1; p0 x1+x2 /2; q0 x2+x3 /2; H text x1 -tiny 'x0' ; set H 'fontsize' fontsize 'HorizontalAlignment' 'c' H text x2 -tiny 'x1' ; set H 'fontsize' fontsize 'HorizontalAlignment' 'c' H text x3 -tiny 'x2' ; set H 'fontsize' fontsize 'HorizontalAlignment' 'c' H text p0 0 43+f p0 'P2 x ' ; set H 'fontsize' fontsize 'HorizontalAlignment' 'c' 'color' 'red' H text q0 0 15+f q0 'f x ' ; set H 'fontsize' fontsize 'HorizontalAlignment' 'c' 'color' 'blue' saveas gcf 'Simpsons_method_illustration eps' 'psc2' export to eps function ball x y r color Theta 0 0 1 2 pi; X r cos Theta +x; Y r sin Theta +y; H fill X Y color ; set H 'EdgeColor' 'none' ; function arrow start stop thickness arrow_size sharpness arrow_type color Function arguments start stop start and end coordinates of arrow vectors of size 2 thickness thickness of arrow stick arrow_size the size of the two sides of the angle in this picture -> sharpness angle between the arrow stick and arrow side in degrees arrow_type 1 for filled arrow otherwise the arrow will be just two segments color arrow color a vector of length three with values in 0 1 convert to complex numbers i sqrt -1 ; start start 1 +i start 2 ; stop stop 1 +i stop 2 ; rotate_angle exp i pi sharpness/180 ; points making up the arrow tip besides the stop point point1 stop - arrow_size rotate_angle stop-start /abs stop-start ; point2 stop - arrow_size/rotate_angle stop-start /abs stop-start ; if arrow_type 1 filled arrow plot the stick but not till the end looks bad t 0 5 arrow_size cos pi sharpness/180 /abs stop-start ; stop1 t start+ 1-t stop; plot real start stop1 imag start stop1 'LineWidth' thickness 'Color' color ; fill the arrow H fill real stop point1 point2 imag stop point1 point2 color ; set H 'EdgeColor' 'none' else two-segment arrow plot real start stop imag start stop 'LineWidth' thickness 'Color' color ; plot real stop point1 imag stop point1 'LineWidth' thickness 'Color' color ; plot real stop point2 imag stop point2 'LineWidth' thickness 'Color' color ; end </nowiki></pre> original upload log page en wikipedia Simpsons_method_illustration png 2005-11-23 03 12 Oleg Alexandrov 1186×1072×8 26565 bytes <nowiki></nowiki> 27 124 43 20 kkkkkjjhhgg math Numeric integration graphs Files by User Oleg Alexandrov from en wikipedia |