File:Simpsons method illustration.png

Beskrivelse[redigér]

BeskrivelseSimpsons method illustration.png	Simpson's method illustration. Done by myself (Oleg Alexandrov 23:17, 12 August 2007 (UTC)).
Dato	23. november 2005 (original upload date)
Kilde	Transferred from en.wikipedia to Commons.
Forfatter	Oleg Alexandrov at engelsk Wikipedia
Andre versioner	En vektorversion af dette billede (SVG) er tilgængelig. Det bør bruges i stedet for punktgrafikbilledet når det er fordelagtigt. File:Simpsons method illustration.png → File:Simpsons method illustration.svg For mere information om vektorgrafik: Læs om overgangen til SVG på Commons. Se også information om MediaWikis understøttelse af SVG-billeder. På andre sprog Alemannisch ∙ Bahasa Indonesia ∙ Bahasa Melayu ∙ British English ∙ català ∙ čeština ∙ dansk ∙ Deutsch ∙ eesti ∙ English ∙ español ∙ Esperanto ∙ euskara ∙ français ∙ Frysk ∙ galego ∙ hrvatski ∙ Ido ∙ italiano ∙ lietuvių ∙ magyar ∙ Nederlands ∙ norsk bokmål ∙ norsk nynorsk ∙ occitan ∙ Plattdüütsch ∙ polski ∙ português ∙ português do Brasil ∙ română ∙ Scots ∙ sicilianu ∙ slovenčina ∙ slovenščina ∙ suomi ∙ svenska ∙ Tiếng Việt ∙ Türkçe ∙ vèneto ∙ Ελληνικά ∙ беларуская (тарашкевіца) ∙ български ∙ македонски ∙ нохчийн ∙ русский ∙ српски / srpski ∙ татарча/tatarça ∙ українська ∙ ქართული ∙ հայերեն ∙ বাংলা ∙ தமிழ் ∙ മലയാളം ∙ ไทย ∙ 한국어 ∙ 日本語 ∙ 简体中文 ∙ 繁體中文 ∙ עברית ∙ العربية ∙ فارسی ∙ +/−

Licensering[redigér]

Dette værk er blevet udgivet som offentlig ejendom af dets skaber, Oleg Alexandrov at engelsk Wikipedia. Dette gælder i hele verden. I nogle lande er dette ikke juridisk muligt. I så fald: Oleg Alexandrov giver enhver ret til at anvende dette værk til ethvert formål, uden nogen restriktioner, medmindre sådanne restriktioner er påkrævede ved lov.Public domainPublic domainfalsefalse

Source code[redigér]

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

Oprindelig oplægningslog[redigér]

• 2005-11-23 03:12 Oleg Alexandrov 1186×1072×8 (26565 bytes)

[[File:--27.124.43.20