Buffon needle (Java and MATLAB)

Source: Internet
Author: User
Tags value of pi

 

 

Java code

 

/*************************************** * ************************** Java Applet buff. java March 1998-Michael J. hurben this applet provides a _ simulation _ of the famous Buffon's needle experiment. buffon's needle is a Monte Carlo Simulation for the determination of the value of pi. **************************************** * *************************/import Java. applet. *; import Java. AWT. *; Public Class buff extends applet implements runnable {dimension offdimension, D; // variables used to create an image offimage; // offscreen image via the update () graphics offgraphics; // method, to reduce flicker int needlelength = 20; int numrows = 10; int xborder = 15; // basic layout variables int yborder = 45; int margin = 50; int tableheight = needlelength * numrows; // int tablewidth = 200; // def INE size of table int tablexcorner = xborder; // where needles are thrown int tableycorner = yborder; // int barwidth = 20; // define size of bar graph int barheight = tableheight; int barxcorner = xborder + tablexcorner + tablewidth + margin; int barycorner = tableycorner; double bartop = 3.24; // set limits for limits of bar graph double Barbot = 3.04; double barmid = (bartop + Barbot)/2; int barvalue; // Dynamic value of the bar graph int plotwidth = 200; // define size of plot int plotheight = tableheight; int plotxcorner = barxcorner + margin + barwidth + xborder; int plotycorner = tableycorner; double plotmax = 4; // set limits on the plot double plotmin = 2; double plotmid = (plotmax + plotmin)/2; int barmaxplot = (INT) (plotheight * (plotmax-bartop)/(plotmax-plotmin); int barminplot = (INT) (ploth Eight * (plotmax-Barbot)/(plotmax-plotmin); int hire ick = (barmaxplot = barminplot? 1: barminplot-barmaxplot); int pointerwidth = 30; // bar graph pointer int pointertop, pointerbot; int power = 5; // orders of magnqueue for the x-axis of the plot int n = 0; // The number of needles thrown int hit = 0; // The number of needles which hit lines int I = 1; // double needlex1, needlex2, needley1, needley2; double deltax, deltay; int ysign; final double pivalue = 2.0 * Math. atan( 1.0); int X1, x2, Y1, Y2; // used to draw needles int GX1, GX2, gy1, gy2; // used to make the plot int speed = 20; // sets speed with try-Catch Block double H = 0; // double version of the number of hits double estpi, prevestpi; // estimates of PI double prob = 1; // ratio of hits to trys double Prev = 1; // ratio on the previous trial Boolean oldscreen = false; Boolean begin = false; thread t; button B1, B 2, B3, B4; Public void Init () {setlayout (New flowlayout (flowlayout. left); b1 = new button ("START"); b2 = new button ("slower"); B3 = new button ("faster "); b4 = new button ("done"); add (B1); add (B2); add (B3); add (B4); t = new thread (this); T. start ();} public Boolean action (event E, object O) {If (O. equals ("START") {n = 0; hit = 0; oldscreen = false; begin = true;} else if (O. equals ("done ")){ T. Stop ();} else if (O. Equals ("faster") {speed = (speed> 10? Speed-10: 10);} else if (O. equals ("slower") {speed = speed + 10;} return true;} public void run () {While (true) {If (BEGIN) {// calculate the position of the needle ends... needlex1 = tablewidth * Math. random (); needley1 = tableheight * Math. random (); deltax = needlelength * Math. sin (2 * pivalue * Math. random ()-pivalue); deltay = math. SQRT (needlelength * needlelength-deltax * deltax); needlex2 = needlex1 + d Eltax; ysign = (math. Random () <0.5? -1: 1); needley2 = needley1 + ysign * deltay; // check to see if it crosses a line... for (INT yline = 0; yline <= needlelength * numrows; yline + = needlelength) {If (needley1 <= yline & needley2> = yline) | (needley1> = yline & needley2 <= yline) {hit ++; break ;}} n ++; Prev = prob; H = hit; prob = H/N; prevestpi = 2/Prev; estpi = 2/prob; // calculation for the plot GX1 = (INT) (plotxcorner + math. log (n) * plotwid Th/(Power * Math. log (10); GX2 = (INT) (plotxcorner + math. log (n + 1) * plotwidth/(Power * Math. log (10); gy1 = (INT) (plotycorner + (plotheight/(plotmin-plotmax) * (prevestpi-plotmax); If (gy1 <= plotycorner) gy1 = plotycorner + 1; if (gy1 = plotycorner + plotheight) gy1 = gy1-1; gy2 = (INT) (plotycorner + (plotheight/(plotmin-plotmax )) * (estpi-plotmax); If (gy2 <= plotycorner) gy2 = plotycorner + 1; if (gy2 = plotycorner + Plotheight) gy2 = gy2-1; // Calculation for drawing the needles X1 = (INT) (xborder + needlex1); x2 = (INT) (xborder + needlex2); Y1 = (INT) (yborder + needley1); y2 = (INT) (yborder + needley2); repaint () ;}try {thread. currentthread (). sleep (speed);} catch (interruptedexception e) {}} public void paint (Graphics g) {d = size (); Update (g );} public void Update (Graphics g) {If (offgraphics = NULL) // se Tup an off-screen image | (D. Width! = Offdimension. width) // via the update () method. | (D. height! = Offdimension. Height) // {offdimension = D; offimage = createimage (D. Width, D. Height); offgraphics = offimage. getgraphics ();} If (! Oldscreen) {offgraphics. setcolor (getbackground (); offgraphics. fillrect (0, 0, D. width, D. height); offgraphics. setcolor (color. gray); offgraphics. fillrect (plotxcorner, plotycorner + barmaxplot, plotwidth, barminplot-barmaxplot); offgraphics. drawstring ("+ barmid +"-", barXcorner-45, barycorner + barheight/2); offgraphics. drawstring ("+ bartop +"-", barXcorner-45, barycorner + 5); offgraphics. drawstring ("" + B Arbot + "-", barXcorner-45, barycorner + 3 + barheight); offgraphics. drawstring ("-" + plotmax, plotxcorner + plotwidth + 2, plotycorner + 5); offgraphics. drawstring ("-" + plotmin, plotxcorner + plotwidth + 2, plotycorner + plotheight + 5); offgraphics. drawstring ("-" + plotmid, plotxcorner + plotwidth + 2, plotycorner + plotheight/2 + 5); offgraphics. drawstring ("estimate. log (number of tries) ", plotxcorner + 5, plotycorner + plothei Ght + 20); // draw lines which relate the bar graph and the plot... offgraphics. drawline (barxcorner + barwidth + 5, barycorner, plotXcorner-5, barmaxplot + plotycorner); offgraphics. drawline (barxcorner + barwidth + 5, barycorner + barheight, plotXcorner-5, barminplot + plotycorner); // draw tabletop and the plot axes offgraphics. setcolor (color. blue); offgraphics. drawrect (tablexcorner, tableycorner, tablewidth, Tab Leheight); offgraphics. drawrect (plotxcorner, plotycorner, plotwidth, plotheight); for (I = 1; I <tableheight/needlelength; I ++) {offgraphics. drawline (tablexcorner, tableycorner + needlelength * I, tablexcorner + tablewidth, tableycorner + needlelength * I);} oldscreen = true;} else {offgraphics. setcolor (getbackground (); offgraphics. fillrect (0, 0, D. width, yBorder-10);} // write N and estpi to screen offgrap Hics. setcolor (color. black); offgraphics. drawstring ("current estimate of Pi:" + estpi, plotxcorner + 10, 20); offgraphics. drawstring ("Number of tries:" + N, 220, 20); offgraphics. setcolor (color. black); // make sure that none of the needles appear outside // The table boundary: X1 = (x1> tablexcorner + tablewidth? Tablexcorner + tablewidth: X1); x2 = (X2> tablexcorner + tablewidth? Tablexcorner + tablewidth: X2); Y1 = (Y1> tableycorner + tableheight? Tableycorner + tableheight: Y1); y2 = (Y2> tableycorner + tableheight? Tableycorner + tableheight: Y2); X1 = (x1barheight + pointerwidth/2) barvalue = barheight + pointerwidth/2; pointertop = (barvalue-pointerwidth/2 <0? 0: barvalue-pointerwidth/2); pointerbot = (barvalue + pointerwidth/2> barheight? Barheight: barvalue + pointerwidth/2); offgraphics. fillrect (barxcorner, barycorner + pointertop, barwidth, pointerbot-pointertop); // center line in the pointer offgraphics. setcolor (color. gray); If (barvalue <0) barvalue = 0; If (barvalue> barheight) barvalue = barheight; offgraphics. drawline (barxcorner, barycorner + barvalue, barxcorner + barWidth-1, barycorner + barvalue); // Finally, draw the plot offgraphics. setcolor (color. red); offgraphics. drawline (GX1, gy1, GX2, gy2); G. drawimage (offimage, 0, 0, this );}}

MATLAB

% Buffon test % for get the PI % Aris 2006.3.25% L is the length of needel % N is the numtest function buffonpi = buffon_test (L, n) winnum = 0; for I = 1: N center_l = Rand * l/2; % the location of the center of the L sta = Rand * PI/2; temph = (l/2) * sin (STA); If temph> center_l winnum = winnum + 1; end buffonpi = 2 * n/winnum;

Contact Us

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

  • Sales Support

    1 on 1 presale consultation

  • After-Sales Support

    24/7 Technical Support 6 Free Tickets per Quarter Faster Response

  • Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.