Create Rainbow Program

Author: SubhanshuMG

Rainbow Program

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+import java.awt.Color;
+
+public class Rainbow { 
+
+    public static void main(String[] args) { 
+
+        int N = Integer.parseInt(args[0]);
+        int SIZE = 1000;
+        StdDraw.setCanvasSize(SIZE, SIZE/2);
+        StdDraw.setXscale(0, SIZE);
+        StdDraw.setYscale(0, SIZE/2.0);
+        StdDraw.enableDoubleBuffering();
+
+        // sky blue background
+        Color skyblue = new Color(48, 144, 199);
+        StdDraw.clear(skyblue);
+
+        // simulate N incident light rays
+        for (int i = 0; i < N; i++) {
+
+            // generate random (x, y) uniformly in unit circle centered at (0, 0)
+            double r = Math.random();                       // impact parameter
+            double theta = Math.random() * 2 * Math.PI;     // between 0 and 2*pi
+            double x = Math.sqrt(r) * Math.sin(theta);
+            double y = Math.sqrt(r) * Math.cos(theta);
+
+            float c  = (float) Math.random();               // random hue of rainbow
+            double n = 1.33 + 0.06 * c;                     // refraction index
+
+            double thetaI = Math.asin(r);                   // angle of incidence
+            double thetaR = Math.asin(r / n);               // angle of refraction
+            double thetaP = 4*thetaR - 2*thetaI;            // primary rainbow angle
+            double thetaS = 6*thetaR - 2*thetaI - Math.PI;  // secondary rainbow angle
+
+            // intensities of principle and secondary 
+            double p = Math.pow(Math.sin(thetaI - thetaR) / Math.sin(thetaI + thetaR), 2);
+            double s = Math.pow(Math.tan(thetaI - thetaR) / Math.tan(thetaI + thetaR), 2);
+            double intensityP = 0.5 * (  s*(1-s)*(1-s) +   p*(1-p)*(1-p));
+            double intensityS = 0.5 * (s*s*(1-s)*(1-s) + p*p*(1-p)*(1-p));
+
+            // plot primary rainbow
+            float saturation = (float) Math.min(intensityP / 0.04, 1.0);
+            StdDraw.setPenColor(Color.getHSBColor(c, saturation, 1.0f));
+            double xp = (SIZE/2.0 * thetaP * 3 / Math.PI * x / r) + SIZE / 2.0;
+            double yp = (SIZE/2.0 * thetaP * 3 / Math.PI * Math.abs(y) / r);
+            StdDraw.point(xp, yp);
+
+            // plot secondary rainbow
+            saturation = (float) Math.min(intensityS / 0.02, 1.0);
+            StdDraw.setPenColor(Color.getHSBColor(c, saturation, 1.0f));
+            double xs = ( SIZE/2.0 * thetaS * 3 / Math.PI * x / r) + SIZE / 2.0;
+            double ys = (-SIZE/2.0 * thetaS * 3 / Math.PI * Math.abs(y) / r);
+            StdDraw.point(xs, ys);
+
+            // display every 1000 iterates
+            if (i % 1000 == 0) {
+                StdDraw.show();
+                StdDraw.pause(10);
+            }
+        }
+
+        StdDraw.show();
+    }
+
+}