Ankita Kodali

FunctionsChallenge/Functions.pde

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+float findPermutation(float data, float places) {   
+  //change the value of places to use it in the denominator
+  float denominator = data-places;       
+  //set i equal to the denominator value minus one so that every time it goes through the for loop it multiplies by 1 less which simulates the factorial function
+  for (float i=denominator-1; i>=1; i--) {    
+    denominator*=i;
+  }
+  //use the factorial method again for the numerator
+  for (float i=data-1; i>=1; i--) {
+    data=data*i;
+  }
+  //divide the two factorials found
+  float result= data/denominator;
+  //return the result
+  return result;    
+}
+
+float findAcceleration(float vi, float vf, float t) {
+  //use the acceleration equation to find acceleration
+  float acceleration = (vf-vi)/t;
+  //return the value
+  return acceleration;
+}
+void addAcceleration() {
+  //add acceleration to the object
+  for (int i=0; i<count; i++) {
+    //if the acceleration is less than 1...
+    if (a<=1) {
+      //...add acceleration
+      vy[i]+=a;
+    } else { //if not...
+      //...reset the velocity to 1
+      vy[i]=1;
+    }
+  }
+}

FunctionsChallenge/FunctionsChallenge.pde

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+//declare and initialize variables
+float vf, a;
+int count=25;
+//declare arrays
+float []x= new float[count];
+float []y= new float[count];
+float []d= new float[count];
+float []vx= new float[count];
+float []vy= new float[count];
+float []r= new float[count];
+float []g= new float[count];
+float []b= new float[count];
+
+void setup() {
+  //draw canvas
+  size(500, 500);
+  //initialize arrays
+  for (int i=0; i<count; i++) {
+    x[i] = random(width);
+    y[i] = random(height);
+    d[i] = random(80);
+    vx[i] = random(-5, 5);
+    vy[i] = random(-5, 5);
+    r[i] = random(255);
+    g[i] = random(255);
+    b[i] = random(255);
+  }
+}
+
+void draw() {
+  //draw a background
+  background(255);
+  for (int i=0; i<count; i++) {
+    //draw ball
+    noStroke();
+    fill(r[i],g[i],b[i]);
+    ellipse(x[i], y[i], d[i], d[i]);
+    //add velocity
+    x[i] += vx[i];
+    y[i] += vy[i];
+    //bounce ball if it hits walls
+    if (x[i] + d[i]/2 >= width) {
+      vx[i] = -abs(vx[i]);    //if the ball hits the right wall, assign x velocity the negative version of itself
+    } else if (x[i] - d[i]/2 <= 0) {
+      vx[i] = abs(vx[i]);     //if the ball hits the left wall, assign x velocity the positive version of itself
+    }
+    if (y[i] + d[i]/2 >= height) {
+      vy[i] = -abs(vy[i]);
+      y[i] = height - d[i]/2;
+    } else if (y[i] - d[i]/2 <= 0) {
+      vy[i] = abs(vy[i]);
+    }
+  }
+  //initialize variables
+  vf=findPermutation(random(0, 1), random(0, 1));
+  a=findAcceleration(0, vf, 10);
+  //add acceleration to objects
+  addAcceleration();
+}

addAcceleration.md

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+# Name: addAcceleration
+
+## Examples:
+Increase or decrease the speed that the objects move.
+
+## Description:
+Add acceleration to the objects by increasing or decreasing the velocity in each frame.
+
+## Syntax:
+void addAcceleration() {
+  for (int i=0; i<count; i++) {
+    if (a<=1) {
+      vy[i]+=a;
+    } else {
+      vy[i]=1;
+    }
+  }
+
+##Parameters: 
+No parameters
+
+##Returns:
+No return.
+
+##Other notes:
+In my syntax, there is an if statement that will make sure the acceleration doesn't increase too much.

findAcceleration.md

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+# Name: findAcceleration
+
+## Examples:
+In 2 seconds, the ball goes from 3m/s to 5 m/s, determine its acceleration.
+
+## Description:
+If you know the initial and final velocity of an object over a certain amount of time, you can find the acceleration.
+All you have to do is divide the change in velocity by the time.
+
+## Syntax:
+float findAcceleration(float vi, float vf, float t) {
+  float acceleration = (vf-vi)/t;
+  return acceleration;
+}
+
+##Parameters: 
+vi is the initial velocity which, in the example, is 3.
+vf is the final velocity which, in the example, is 5.
+t is the amount of time which, in the example, is 2.
+
+##Returns:
+This function returns a number that represents the acceleration of the object.
+
+##Other notes:
+You can add this value to the velocity that is there to give the object acceleration.

findPermutation.md

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+# Name: findPermutation
+
+## Examples:
+If there were 5 children running in a race, determine how many ways these children could win first, second, and third place. Using the permutation formula will give the answer quicker than trying to list every possibility.
+
+## Description:
+To find the number of ways that certain amount of data can be ordered in a certain amount of places, this function uses the permutation formula. The permutation formla is the factorial of the amount of data divided by the factorial of the data minus the number of places.
+
+## Syntax:
+float findPermutation(float data, float places) {   
+  float denominator = data-places;       //change the value of places to use it in the denominator
+  //set i equal to the denominator value minus one so that every time it goes through the for loop it multiplies by 1 less which simulates the factorial function
+  for (float i=denominator-1; i>=1; i--) {    
+    denominator*=i;
+  }
+   //use the factorial method again for the numerator
+  for (float i=data-1; i>=1; i--) {
+    data=data*i;
+  }
+  float result= data/denominator;  //divide the two factorials found
+  return result;    //return the result
+}
+
+##Parameters: 
+The data parameter tells how many objects can be used to fill the requirement. In the example, this would be the 5 children.
+The places parameter tells how many spaces can be filled by the objects. In the example, this would be the 3 places or 1st, 2nd, and 3rd place.
+If you are using this function to return a random value you can put something like random(0,1) for the parameters in the loop so that you get a random value.
+
+##Returns:
+This function returns the number of ways the data can be put in the places.
+If you are using it to get a random number you will get a random value in return.
+
+##Other notes:
+In my code, I used this functions to return a random value each time it went through the loop.