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Example/Collision_ex/Collision_ex.pde

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+ArrayList ps;
+
+void setup() {
+   size(400, 600);
+   //Creates a array list of 50 new particles
+   ps = new ArrayList<Particle>();
+   for(int i =0;i<50;i++)
+   {
+      ps.add(new Particle());
+   }
+   //Changes the Coefficent of resitution to .6
+   Vector.setCoRes(.6);
+}
+
+void draw() {
+   background(50);
+   fill(255);
+   stroke(0);
+   ellipse(width/2,400,200,200);
+   //shows all the particles in the array on the screen and updates them
+   for(int i=0;i<ps.size();i++)
+   {
+      ((Particle)ps.get(i)).show();
+      ((Particle)ps.get(i)).update();
+      //deletes and creates a new particle if it has gone off the screen
+      if(((Particle)ps.get(i)).y>height)
+      {
+         ps.remove(i);
+         i--;
+         ps.add(new Particle());
+      }
+   }
+}
+//The particle class utalizes the Vector class when it collides with a surface
+class Particle
+{
+  //a particle is defined by a postion, velocity, and acceleration.
+   float x;
+   float y = 0;
+   float yA =.5;
+   float yV = 0;
+   float xV = 0;
+
+   Particle()
+   {
+     //randomizes the starting x postion of the particle
+      x= random(0,width);
+
+   }
+
+   void show()
+   {
+      //draws a red circle where the particle's postion is
+      fill(255,0,0);
+      ellipse(x,y,15,15);
+   }
+
+   void update()
+   {
+     //updates the particle's postion and velocity
+      x+=xV;
+      y+=yV;
+      yV+=yA;
+
+      //checks to see if the particle's postion is withi the circle
+      if(Math.pow(100,2)>=Math.pow(x-(width/2),2)+Math.pow(y-400,2)
+      )
+      {
+         //Finds the slope of the circle at the point the particle hit the circle by takign the derivative of the circle
+         float m= (width-2*x)/(2*y-800);
+         //creates a vector based on the particle's velocity
+         Vector v = new Vector(xV,yV);
+         //the vector collides with the surface of the circle
+         v.collide(m);
+         //makes the particle's x and y velocity equal to the vectors x an y velocity
+         xV = (float)v.getX();
+         yV = (float)v.getY();
+         //changes the y postion of the particle to the outer rim of the circle so the particle does not get stuck inside the circle
+         y=(float) -Math.sqrt(Math.pow(100,2)-Math.pow(x-(width/2),2))+400;
+      }
+
+
+
+
+   }
+}

Example/Collision_ex/Vector.java

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+/*
+ * Created by:Scott Turro
+ * Date:October 29th, 2017
+ * Version 1.0
+*/
+class Vector
+{
+   //Private instance feilds
+   //x is the x value of the vector, and y is the y value of the vector
+   double x;
+   double y;
+
+   /* Coefficent of resitution. 
+    * On a scale of 0-1.
+    * 0 will make objects lose all veloctiy when they collide, 
+    * 1 will make objects bounce with 100% of their original velocity. 
+   */
+   static double coRes = 1;
+
+   //tX is the x value of the vector, and tY is the y value of the vector
+   Vector(double tX, double tY)
+   {
+      x = tX;
+      y = tY;
+   }
+   //returns the x value of the vector
+   double getX()
+   {
+      return x;
+   }
+   //returns the y value of the vector
+   double getY()
+   {
+      return y;
+   }
+   //CHanges the direction and velocity of the vector when it collides with a surface with the slope m.
+   void collide(double m)
+   {
+     double tY, tX;
+     tX=coRes*(x*m*m+2*y*m+x)/(1+m*m);
+     tY=-coRes*(-y*m*m-2*x*m+y)/(1+m*m);
+     x = tX;
+     y = tY;
+   }
+   //Changes the Coefficent of Restitution for all objects.
+   static void setCoRes(double temp)
+   {
+      coRes=temp;
+   }
+
+
+}

srcCode/Vector.java

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+/*
+ * Created by:Scott Turro
+ * Date:October 29th, 2017
+ * Version 1.0
+*/
+class Vector
+{
+   //Private instance feilds
+   //x is the x value of the vector, and y is the y value of the vector
+   double x;
+   double y;
+
+   /* Coefficent of resitution. 
+    * On a scale of 0-1.
+    * 0 will make objects lose all veloctiy when they collide, 
+    * 1 will make objects bounce with 100% of their original velocity. 
+   */
+   static double coRes = 1;
+
+   //tX is the x value of the vector, and tY is the y value of the vector
+   Vector(double tX, double tY)
+   {
+      x = tX;
+      y = tY;
+   }
+   //returns the x value of the vector
+   double getX()
+   {
+      return x;
+   }
+   //returns the y value of the vector
+   double getY()
+   {
+      return y;
+   }
+   //CHanges the direction and velocity of the vector when it collides with a surface with the slope m.
+   void collide(double m)
+   {
+     double tY, tX;
+     tX=coRes*(x*m*m+2*y*m+x)/(1+m*m);
+     tY=-coRes*(-y*m*m-2*x*m+y)/(1+m*m);
+     x = tX;
+     y = tY;
+   }
+   //Changes the Coefficent of Restitution for all objects.
+   static void setCoRes(double temp)
+   {
+      coRes=temp;
+   }
+
+
+}