# Welcome to the Physics 1250 Rocket Science Lab!

This lab will guide you through coding up a web-based implementation of the classic video game asteroids. You will need to bring your laptop to the lab or use one of the mac computers in Morril 285. Unfortunately, tablets will probably not work very well unless you have an external keyboard.

This example will use a programming language that is very similar to C and C++ programming. (Note: If you are familiar with C or C++ the main difference you will see is that there is no main() function and instead the draw() function serves this role.)

In the classic game of Asteroids, there is a little ship that flies around in space, very far away from stars and planets so that the gravitational acceleration is zero.

The code is designed to solve the (rather simple) kinematic equations in this case. If we just consider the x-direction forces the equations look like this: $$\sum F_{\rm{net},x} = F_{\rm thrust} = m \, a_x$$ $$\Delta v_x = a_x \Delta t$$ $$v_x = v_{x0} + \Delta v_x$$ $$x = x_0 + v_x \cdot \Delta t$$

The computer program we will work with here computes these equations over and over again, updating $v_x$ and $x$ depending on whether the thrust is turned on or off. Since the thrust is the only force, if it is turned off then $a_x = 0$ and $\Delta v_x = 0$ and the ship just continues with the same $v_x$ velocity. This is how the code works if the ship only moves in the $x$ direction. The equations are essentially the same for the $y$ direction. In the last step of this lab you will modify the code so that the ship can move in the $y$ direction too.

### Step 1. Play around with a 1-dimensional version of Asteroids

Click on this link to the 1D version of the spaceship from asteroids. Push up arrow to see the rocket accelerate. Unfortunately right now the ship can only accelerate in one direction. We will change this step-by-step to make the behavior more similar to the classic asteroids game. If the example doesn't work tell the instructor.

This is the code used to move the ship around in the 1D version. Take a close look at the code and try to get an idea of what each part does:

function draw() {

// Update velocities
vx += deltaVx;

// Update location
x += vx*dt;

// velocity is unchanged if there are no forces
deltaVx = 0;

if (keyIsDown(LEFT_ARROW)) {
theta += 0.0;
}
if (keyIsDown(RIGHT_ARROW)) {
theta += 0.0;
}
if (keyIsDown(UP_ARROW)) {
// Rockets on!
accelx = Fthrust*cos(theta)/mass;
deltaVx = accelx*dt;
}
if (keyIsDown(DOWN_ARROW)) {
// Do nothing
}
if (keyIsPressed && key == ' '){ //spacebar
// Do nothing!
}

// Draw ship and other stuff
display();

} // end draw()


### Step 2. Try out the 1D planetoids code in an editor

Press play there to run the code. It should look the same as it did with the link you were given in Step 1

### Step 3. Edit the source code to let the ship rotate!

After you click duplicate! to make sure that you're working on your own version of the code, change these lines of code:

    if (keyIsDown(LEFT_ARROW)) {
theta += 0.0;
} else if (keyIsDown(RIGHT_ARROW)) {
theta += -0.0;

to look like this:
    if (keyIsDown(LEFT_ARROW)) {
theta += 0.1;
} else if (keyIsDown(RIGHT_ARROW)) {
theta += -0.1;


The asteroids game is now set up so so that only the x-component of the thrust is what accelerates the ship. Notice that allowing the ship to rotate means that we can speed up and slow down the ship because we can rotate the rocket and apply a force that is opposite to the velocity vector. Our asteroids game is already a lot more fun! For reference, the game should now behave like this.

### Step 4. Enable multi-dimensional space travel (i.e. let the ship move in the y direction too)

Now take the code you've written and modify it so that the ship can move in the y direction. It will take a few different changes to get it to work.

#### Step 4a. Change the "Update location" section

Look at the "Update location" section. Right now it looks like this:

// Update location
x += vx*dt;


As you can see, only the x position is updated. The y position is not updated. Change the "Update location" section to this:

// Update location
x += vx*dt;
y += vy*dt;


#### Step 4.b. Change the "Update velocities" section

If you did step 4a correctly, we can now update both the x position and the y position, but only if $v_x$ and $v_y$ are non-zero! This will only happen if we change the "Update velocities" section so that both vx and vy are updated.

Change this:

\\ Update velocities
vx += deltaVx;


to this:

\\ Update velocities
vx += deltaVx;
vy += deltaVy;


#### Step 4.c. Objects in motion move in a straight line unless acted on by a force

Newton realized that objects move in a straight line with constant velocity if there are no forces acting on the object. For our computer program, we need to make sure that the velocity only changes when we push buttons on the keyboard. If we don't push any buttons then the change in velocity ($\Delta v_x$ and $\Delta v_y$) had better be zero.

This is the logic behind this part of the code:

    // velocity is unchanged if there are no forces
deltaVx = 0;


Change this to make sure deltaVy is set to zero too:

    // velocity is unchanged if there are no forces
deltaVx = 0;
deltaVy = 0;


This is an important step because if you do the next step correctly, but you forget to do this the ship will accelerate uncontrollably.

#### Step 4.d. Make sure that acceleration works in the y-direction

If you've done all the steps up to this point correctly, the ship still won't move in the y direction because we haven't told the ship how to accelerate in the y direction when the thrusters are turned on. Nowhere in the program do we set deltaVy equal to anything except zero!

Look closely at this part of the code:

    if (keyIsDown(UP_ARROW)) {
// Rockets on!
accelx = Fthrust*cos(theta)/mass;
deltaVx = accelx*dt;
}


You'll need to change this to something like this:

    if (keyIsDown(UP_ARROW)) {
// Rockets on!
accelx = Fthrust*cos(theta)/mass;
deltaVx = accelx*dt;
accely = ????
deltaVy = accely*dt;
}


It's your job to replace the ???? with something that actually gives the correct acceleration in the y direction. (Hint: it is very similar to the code for accelx but the trig function might be different! Should you use cosine, sine or tangent for the trig function? If you're not sure just try one and see what happens!)

### Step 5. Check that everything works as expected!

If you make all these changes your code should behave like this and your ship should be able to move in 2 dimensions!

Potential pitfall: Which trig function did you use to determine the y-component acceleration?

## Challenges: Choose one or two

### Option: Add Reverse thrusters

This is one of the easier challenges. Notice that your code has a section for when you press the down arrow:

    if (keyIsDown(DOWN_ARROW)) {
// Do nothing
}


Where it says "Do nothing" how would you add code to fire the thrusters in reverse?

Hint: You want to accelerate in the opposite direction of the acceleration you get when the thrusters are turned on.

### Option: Add asteroids to the game

It's not much of an asteroids game without asteroids! Add asteroids to the code which drift at random directions using the ellipse function

drawEllipse(x_asteroid,y_asteroid,width_asteroid,height_asteroid);


Place this just after where it says display(); Then make sure these variables are initialized at the beginning of the program like this:

x_asteroid=200;
y_asteroid=200;
width_asteroid=50;
height_asteroid=50;


It is up to you to make the asteroid move in a random direction with some constant velocity.

Note: to calculate a random direction use the random function to generate a fraction between -1 and 1. For example:

random_number = random(-1,1);


### Option: Add a projectile to the game

You can add another if statement to check to see if you've pressed the spacebar:

    if (keyIsPressed && key == ' ') { // spacebar is pressed
// Do nothing
}


How would you modify the code so that the spacebar shoots a projectile from the nose of the ship? Add two new float variables called xprojectile and yprojectile to the beginning of the program and use the "drawPoint" function to show the position of the projectile:

drawPoint(xprojectile,yprojectile);


Advice: Place this function just after display(); so that it is drawn every time but set xprojectile and y projectile to zero initially so that the point is drawn at the top left corner of the grid and you can't see it. When the spacebar is pressed set the xprojectile and yprojectile equal to the position of the ship. That at least will put a dot on the screen where the ship is. How would you make it move?

### How to get full credit on this assignment!!!

1. Complete steps 1-4 and make absolutely sure that the ship can turn and move in two dimensions

Make sure your program behaves exactly like it does at this link to be sure you did steps 1-4 correctly

2. Complete one of the challenges

Most people choose the reverse thrusters, which is probably the easiest

3. Submit your code before the deadline

Talk to your teacher about where to submit the code