/****************************************************************** Java Applet mc.java Modelling and simulation This applet provides a _simulation_ of the example to explain teh idea of Monte Carlo simulation for the determination of the value of Area. ******************************************************************/ import java.applet.*; import java.awt.*; public class mc 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 xBorder = 15; // Basic layout variables int yBorder = 45; int margin = 50; int tableHeight = 200; // int tableWidth = 200; // Define 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 = 0.80; // Set limits for limits of bar graph double barBot = 0.77; 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 = 1.0; // Set limits on the plot double plotMin = 0.0; double plotMid = (plotMax+plotMin)/2; int barMaxPlot = (int) (plotHeight*(plotMax-barTop)/ (plotMax-plotMin)); int barMinPlot = (int) (plotHeight*(plotMax-barBot)/ (plotMax-plotMin)); int barThick = (barMaxPlot==barMinPlot? 1 : barMinPlot-barMaxPlot); int pointerWidth=30; // Bar graph pointer int pointerTop, pointerBot; int power = 5; // Orders of magnitude for the x-axis of the plot int n = 0; // The number of sampling points thrown int hit = 0; // The number of sampling points which is in the figure S int i = 1; // double spX1, spY1; int x1, y1; // Used to draw sampling points 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 estArea, prevEstArea; // Estimates of Area double prob = 1; // Ratio of hits to trys double prev = 1; // Ratio on the previous trial boolean oldScreen = false; boolean begin = false; boolean infigure = false; Thread t; Button b1, b2, b3, b4; public void init() { setLayout(new FlowLayout(FlowLayout.LEFT)); b1 = new Button("Start"); b2 = new Button("Pomaly"); b3 = new Button("Rychlo"); b4 = new Button("Urob"); 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("Urob")) { t.stop(); } else if (o.equals("Pomaly")) { speed = (speed>10? speed-10 : 10); } else if (o.equals("Rychlo")) { speed = speed+10; } return true; } public void run() { while(true) { if(begin) { // Calculate the position of the sampling points... spX1 = Math.random(); spY1 = Math.random(); infigure = false; // Check to see if it is in the figure S ... if( Math.sqrt((spX1-0.5)*(spX1-0.5)+(spY1-0.5)*(spY1-0.5)) < 0.5) { hit++; infigure = true; // break; } n++; prev = prob; h = hit; prob = h/n; prevEstArea = prev; estArea = prob; spX1 = tableWidth*spX1; spY1 = tableHeight*spY1; // Calculation for the plot gx1 = (int)(plotXcorner+Math.log(n)* plotWidth/(power*Math.log(10))); gx2 = (int)(plotXcorner+Math.log(n+1)* plotWidth/(power*Math.log(10))); gy1 = (int)(plotYcorner+(plotHeight/(plotMin-plotMax))* (prevEstArea-plotMax)); if (gy1<=plotYcorner) gy1 = plotYcorner+1; if (gy1==plotYcorner+plotHeight) gy1=gy1-1; gy2 = (int)(plotYcorner+(plotHeight/(plotMin-plotMax))* (estArea-plotMax)); if (gy2<=plotYcorner) gy2 = plotYcorner+1; if (gy2==plotYcorner+plotHeight) gy2=gy2-1; // Calculation for drawing the sampling points x1 = (int) (xBorder+spX1); // x2 = (int) (xBorder+needleX1+2); y1 = (int) (yBorder+spY1); // y2 = (int) (yBorder+needleY1+2); 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) // Setup 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(Color.red); offGraphics.drawRect(0,0, d.width, d.height); 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(" "+barBot+"-", 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 vs. log(number of tries)", plotXcorner+5, plotYcorner+plotHeight+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, tableHeight); offGraphics.drawRect(plotXcorner, plotYcorner,plotWidth, plotHeight); offGraphics.drawOval(tableXcorner, tableYcorner, (int)(tableWidth),(int)(tableHeight)); oldScreen = true; } else { offGraphics.setColor(getBackground()); offGraphics.fillRect(0,0, d.width, yBorder-10); } // Write n and estArea to screen offGraphics.setColor(Color.black); offGraphics.drawString("Current estimate of area: "+estArea, plotXcorner+10, 20); offGraphics.drawString("Number of tries: "+n, 230, 20); offGraphics.drawString("Number of hits: "+hit, 230, 30); offGraphics.setColor(Color.black); // Make sure that none of the sampling points appear outside // the table boundary: x1 = (x1tableXcorner+tableWidth? tableXcorner+tableWidth:x1); y1 = (y1tableYcorner+tableHeight? tableYcorner+tableHeight:y1); if (infigure) { offGraphics.setColor(Color.green); offGraphics.drawOval(x1,y1,1,1); } else { offGraphics.drawOval(x1,y1,1,1); } // Draw the bar graph offGraphics.setColor(Color.gray); offGraphics.fillRect(barXcorner, barYcorner, 20, barHeight); offGraphics.setColor(Color.red); barValue = (int)(barHeight*(estArea-barTop)/(barBot-barTop)); if (barValue<0-pointerWidth/2) barValue=0-pointerWidth/2; if (barValue>barHeight+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); } }