assignment 9: balls and bumpers - radboud...

Assignment 9: Balls and Bumpers

Algorithmic Thinking and Structured Programming (in Greenfoot)© 2017 Renske Smetsers-Weeda & Sjaak Smetsers1

ContentsIntroduction 1

Learning objectives 1

Instructions 1

Theory 29.1 Smooth movements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.2 The resolution of the world . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.3 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39.4 Getter methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39.5 Setter methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49.6 Colliding with a bumper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49.7 Implementing how moving balls collide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59.8 Collision with different masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Challenges 69.1 Getting started with Balls and Bumpers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69.2 Changing the cell size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69.3 Changing the resolution of the world . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69.4 Exploring the Vector class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79.5 Setting up the Ball class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79.6 The ball starts rolling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79.7 Bounce back . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89.8 Adding bumpers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89.9 Bounce off of bumpers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99.10 Moving balls colliding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99.11 Different sized balls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99.12 Balls with different masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Reflection 11

1Licensed under the Creative Commons Attribution 4.0 license: https://creativecommons.org/licenses/by/4.0/

https://creativecommons.org/licenses/by/4.0/

Balls and Bumpers Assignment 9

Saving and Handing in 12

Algorithmic thinking and structured programming (in Greenfoot) 2


IntroductionIn the following challenges we will continue to giveyou less code and tips in advance. For the largestpart, you will design and implement the scenario onyour own.In this assignment you will make a pinball ma-chine. In order to do that, you will simulate themovement of one or more balls in a two-dimensionalspace.The simulation is in a Greenfoot world, so it itbounded (a ball can’t fall out of the world). A ballmoving in a straight line will eventually hit one ofthe borders. After that, it will bounce back.And what happens when there are more balls in-volved in the game, and one ball hits another? Or ifthere are other obstructions in the world where theball can bounce into? That makes it a bit more complicated!The simulation will be as realistic as possible. To do this you will use and implement collision lawsthat you learned in Physics: the law of conservation of energy and the law of conservation of momen-tum.

Learning objectivesAfter completing this assignment, you will be able to:

• make a (2-dimensional) simulation for a real (3-dimensional) situation;• use and apply formula’s from another subject (or field).

InstructionsFor this assignment you will need:

• scenario ’BallWorldScenario9’: to be downloaded from the course website2.Throughout the assignment you will also need to answer some questions. The following must be handedin:

• All flowcharts: use pencil and paper, or go to https://www.draw.io/;• Your code• The reflection sheet: complete and hand it in.You must discuss all other answers with a programming partner. Jot down a short answer on (theassignment) paper.

2http://course.cs.ru.nl/greenfoot/


https://www.draw.io/

http://course.cs.ru.nl/greenfoot/


There are three types of challenges:Recommended. Students who need more practice or with limited programming experienceshould complete all of these.Mandatory. Everyone must complete these.Excelling. More inquisitive tasks, designed for students who completed 2 star tasks and areready for a bigger challenge.Students who skip 1-star challenges should complete all 3-star challenges.

Theory

Theory 9.1: Smooth movementsTo make the simulation realistic, the balls have to move smoothly over the screen. This isn’t possible inMimi’s wereld (which exists only out of 12-by-12 cells), as you will see the ball (or actor) jump from onecell to the next. This results in jerking movements. To simulate smoother movements, the world needsto be made up of many more, smaller, cells.Theory 9.2: The resolution of the worldThe cell-size that we want to use for this simulation is 1-by-1. Every cell is made up of just one pixel.As pictures are often more than one pixel, pictures will cover multiple cells. The following figure showsthe difference between a world with a high and a low resolution.

Figure 1: World with a low resolution. Figure 2: World with a high resolution.With a higher resolution, more cells are needed for the simulation. Mimi’s world, with just 12-by-12cells is much too small for such a simulation. Possibly a 600-by-600 cell world would be more realistic.Using class-constants to define the resolution makes it easy to change the size later on, if you are notsatisfied with the way it looks.

Indicating the world’s resolution

The resolution is indicated in the call of the World-constructor. Here, the hight and width of the cell-sizeis given.Example

Here is an example on how to indicate the resolution in the extension of World-class:public class BallWorld extends World

{private static final int WIDTH = 600;private static final int HEIGHT = 500;private static final int CELLSIZE = 1 ;



/**

* Create the world of balls.

* This world has a size of WIDTH by HEIGHT cells

* each cell consists of CELLSIZE pixels

*/

public BallWorld ( ) {super ( WIDTH , HEIGHT , CELLSIZE ) ;

}}

Theory 9.3: VectorsThe Vector class has been given. Vectors can be represented in two different ways:

a) The Cartesian form: as a pair of distances, expressed as x and y components;b) The Polar form: as a pair with a direction component and a distance (length) component.

This figure shows the same vector being represented in both manners://

Figure 3: Vector in its Cartesian form. Figure 4: Vector in its Polar form.In some cases, it is more convenient to use the Cartesian form. In other cases, the Polar form maybe favorable. The Java-implementation makes use of both formats. Internally, the Vector-object isconstantly updated automatically.

Theory 9.4: Getter methodsAnother object can use a public accessor method (a so-called getter method) to ask for the value ofan object’s private instance variable. Not every instance variable has a public getter method. Gettermethods are only written if they are useful, that is to say, if the values need to be shared with otherobjects.Naming conventions of a getter method

How to name a getter method depends on the result which the method returns.• If the result is a boolean , choose ’is....’, for example boolean isHatched ( ) ;• Otherwise, choose a name as ’get...’, for example int getNrOfEggsHatched ( ) .

Here, the variable name is written instead of ’...’.Example code for a getter method

Because instance variables are private , other objects can’t access its value. Another object can ask itsvalue by using a getter method.Below is an example of a public getter method for the private myNrOfEggsHatched variable. Byadding this getter method, another object can call the method to ask how many eggs have been hatched:



public int getNrOfEggsHatched ( ) {return myNrOfEggsHatched ( ) ;

}

This is a public method. Thus, another object can call this getNrOfEggsHatched ( ) method to ask howmany eggs have been hatched. Note that another object can’t change the value of the variable by callingthis method, another object can only ask its value.Theory 9.5: Setter methodsThe value of a private instance variable can be changed by another object using a public mutatormethod (a so-called setter method).Tip: Use setter methods sparingly. Only add them to a class if they are really needed. That keeps thevariables better protected, and thus it’s safer.Example code for a setter method

For this example, assume MyDodo has an instance variable private int eggsToHatch with which Mimican keep track of how many eggs she has to hatch.Only she knows how many eggs she has to hatch (the variable is private). A snake may come alongand eat an egg. In that case, Mimi can get a message from the snake telling her there is one less egg tohatch. Mimi then changes the value of myEggsToHatch herself (she decreases it by one). We don’t trustthe snake to change the value of myEggsToHatch directly because he would immediately set its value to0. The snake’s intention is to eat all the eggs; he doesn’t want Mimi to hatch any eggs at all. So, we don’ttrust the snake with the variable myEggsToHatch and keep it private .The following setter method can be called by another object in order to change one of MyDodo ’s vari-ables:public void setOneEggLessToHatch ( ) {

myEggsToHatch−−; // decrease value by one

}

Because the method setOneEggLessToHatch ( ) is public , another object can use setOneEggLessToHatch ( )to decrease the value of the variable myEggsToHatch by only one. Another object is now given the ’power’to change the value by one, but not to immediately set it to 0. Obviously, calling setOneEggLessToHatch ()many times will lead myEggsToHatch to equal 0. However, we could keep track of how often another ob-ject calls a method and take adequate measures. In the case of the egg-eating-snake, after he eats 5eggs we could set a snake trap. Whatever the case, the variable can not be changed without MyDodoknowing about it.Theory 9.6: Colliding with a bumperFor balls to bounce off of bumpers properly, it can be useful to take a step back and analyse exactlywhat needs to happen if a ball bumps into a bumper. Actually, whether a ball bounces into a boundaryor a bumper doesn’t make a difference: only the direction component of the velocity changes. Withbumpers, the same happens. The following figure depicts this:



• The ball (whose center is at (x1, y1)) collides with the bumper (whose center is at (x2, y2)) at anangle θ.• To determine the effect of the collision on the ball, we need to calculate L, the component of theballs’ speed ~v in the direction of the bumper. This can be done in a simple manner by roating thevector ~v clockwise over an angle −θ. L is then equal to the x component of the rotated vector.• Due to the collision, the x component has to be inverted. The final speed is calculated by rotatingthe changed vector over the angle θ again.

Theory 9.7: Implementing how moving balls collideImplementing how balls collide into each other is actually very similar to the collisions of the balls withthe bumpers. The only difference is that the ball may collide into a moving ball (rather than an objectthat is standing still). In that case, the velocities of both balls will change.Laws of conservation of energy

Using the laws of conservation of energy, you can calculate that when balls of the same mass collidehead-on, they exchange each others velocity.So, if the first ball has a velocity of v1 and the second ball has a velocity of v2, then, after the collision,the first ball will have a velocity of v2 and the second ball with have a velocity of v1.However, generally, balls will not collide exactly head-on. Just as when a ball hits a bumper, theremay be an angle with which it collides. This angle of incidence, θ, is calculated in the same way as withthe balls and bumpers.Theory 9.8: Collision with different massesIf one ball collides into a ball with another mass (originally standing still) in a head-on collision, thenew velocity of the balls can be calculated using the law of conservation of energy.Here, the first ball has a mass ofm1 and speed of v. The second ball has a mass ofm2 (and no velocitybecause it is standing still). The new velocities, u1 for the first ball and u2 for the second ball can becalculated as follows:

u1 =m1 −m2

m1 +m2v u2 =

2m1

m1 +m2v



Challenges

Challenge 9.1: Getting started with Balls and BumpersWe are going to get started with the Balls and Bumpers simulation. You will be given three Java classesin advance. We will add these to the scenario.

a) Make your own new scenario for the Balls and Bumpers simulation. Come up with an appropriatename.b) Add the three given Java classes to the scenario:

i) Exit Greenfoot.ii) Download the classes: BallWorld , Vector and SmoothMover .

iii) Copy-paste these three classes in the folder that belongs to the scenario which you have justmade.c) Open the scenario again.d) Have a look at the class diagram. The three classes should appear in the Greenfoot project-window.As you can see, the Vector class is shown at the bottom of the class-window, and not as one of the

Actor classes. This is because it is not an Actor. This is because no Vector objects will appearin the world on their own. The SmoothMover class is a helper-class, which is an extension of theActor class. We will get into more details later.

e) Compile the scenario. There is no point in running the scenario yet. For that, you must programfirst!Please read Theory 9.1: Smooth movements.

Please read Theory 9.2: The resolution of the world.

Challenge 9.2: Changing the cell sizeSmaller cells need to be used to simulate smooth movements. The cell-size is indicated using pixels:dots on the screen. In Mimi’s world the cells are made up of 60-by-60 pixels. And in ”The egg-hoarder(Sokoban)” in assignment 8, the cells were made a little smaller so that all the levels could fit on thescreen without a problem. The corresponding cell-size was 50-by-50 pixels. The cell-size is specifiedin Madagaskar .

a) Open the scenario for assignment 8 (”The egg-hoarder (Sokoban)”).b) Have a look at Madagaskar ’s code. Can you find where the cell-size is specified?c) And where is the cell-size used?d) Why is this in capital letters? Do you remember what this was called? Tip: have a look back atTheory 7.1.



Challenge 9.3: Changing the resolution of the worldChange the resolution of the Balls and Bumpers scenario:

a) Open the code belonging to BallWorld .b) Adjust the code as explained in Theory 9.2.

Please read Theory 9.3: Vectors.

Challenge 9.4: Exploring the Vector classWe now explore the methods in the given Vector class so that you can use them later on.

a) Open the Vector class.b) Have a look at the 2 constructors in this class.

i) What is the difference between these constructors?ii) When making a new Vector instance, how do you ensure the correct constructor is called?

c) Which operations have been defined for vectors? What do these operations do?

Challenge 9.5: Setting up the Ball classIn order to show a ball on the screen, you obviously need a Ball class. You will now develop and im-plement the Ball class. As a ball needs to roll smoothly over the screen, this will be a sub-class of theSmoothMover (we will have a look at this class later). First, we add the Ball class to the scenario. To doso, follow the next steps:

a) Extend the SmoothMover class with a class called Ball:i) In the class diagram, right-click on the SmoothMover and select New subclass ....

ii) Choose a name and picture for your ball.iii) Click on OK.

b) Compile your scenario. Probably, you will get an error because your Ball constructor doesn’t callthe SmoothMover constructor. Solve this as follows:i) In the Ball constructor, use super to call the constructor which you are extending.

ii) Give super the same parameters as the SmoothMover constructor expects. You have seen sucha call before, when you were extending the World class. Have a look at the BallWorld for someexample code.iii) Compile the scenario again.

c) It is useful to keep track of the ball’s radius.i) Add an appropriate instance variable.

ii) Determine the radius from the picture which you choose for the ball.iii) Attain the picture using getImage ( ) . The width can then be determined using getWidth ( ) .Use the Greenfoot documentation to figure out how to use these methods.

Please read Theory 9.4: Getter methods.Please read Theory 9.5: Setter methods.



Challenge 9.6: The ball starts rollingThe Ball class is now a sub-class of the SmoothMover . We will now have a look at the SmoothMover classin more detail.

a) Open the code for the SmoothMover class.b) Near the top you will see three instance variabels:

• myXCoord and myYCoord of the type double : to keep track of the position of a SmoothMover ;• myVelocity of the type vector : to keep track of the velocity.

c) In the previous assignments, to determine the position of Mimi or an egg, we used coordinates.For this we used the getX ( ) and getY ( ) methods from Actor.i) What is the difference between myXCoord ’s type and the return-type of getX ( )?

ii) Why would we now prefer to use myXCoord?d) The class’s constructor expects the initial SmoothMover ’s velocity expressed in Polar form. (Tip:see Theory 9.3)e) Using the method move, the SmoothMover moves one step.

• If (x, y) is the current position of the ball, and it’s velocity is ~v, then its new position is (x +vx, y + vy).

• As you can see, this uses the Cartesian form of vector ~v. (Tip: see Theory 9.3)f) For each of the other methods, have a look at the getter methods belonging to the instance vari-ables (Tip: see Theory 9.4).

Challenge 9.7: Bounce backWe now want to simulate how a ball bounces off other objects. Because this is pretty complex, we willbreak the implementation down into several steps. We start with a simple implementation of the Ballwhich we then extend, step-by-step, until it works perfectly. We start by checking if the ball bumps intosomething which it needs to bounce off of, and then we implement the bouncing itself.

a) Open the code for Ball.b) First, in the act ( ) method call a move ( ) .c) Compile and run the scenarion.d) Something should be happening. Describe what you see.e) The ball moves around, but doesn’t take into account that the world is bounded. In Mimi’s worldwe saw that an Actor can’t step out of the world. Write a method which checks if a world-boundaryhas been reached. Tip: Compare the distance from the boundary to the center of the ball with theball’s radius.f) Write a method which makes the ball bounce back off a boundary:

i) Describe precisely what happens to a vector when the ball bounces straight back. Tip: thedirection changes, but it’s speed remains the same.ii) Write a method void handleWallCollision ( ) that checks if a world boundary has beenreached, and if so, adjusts the velocity of the ball accordingly.



Challenge 9.8: Adding bumpersWe now add obstacles to the scenario. In a pinball machine, these are called bumpers. For these, weadd a class called Bumper :

1. Bumper-objects are round and can’t move. Decide which class you should extend with your newBumper-class.

2. Extend the Actor class with a Bumper-class.3. Which instance variable would be useful to add to the Bumper class? Tip: Have a look at Challenge9.5 part c).4. Add this instance variable and initialize it appropriately.5. Which class is responsible for making the balls bounce back? That is to say, determines how itbounces back? Having figured that out, what is left over for the Bumper? Tip: The definition of

Bumper may be extremely simpel.Please read Theory 9.6: Colliding with a bumper.

Challenge 9.9: Bounce off of bumpersWe work-out the steps for simulating bouncing off the bumpers step by step.

a) Add a method void handleBumperCollision ( ) to the Ball class, which does the following:i) First checks if the ball collides with a bumper. How do you determine if the ball hits a bumper?Tip: You can get all the bumper-objects using the world method getObjects ( Class cls ) .This will give you a list of bumpers. For each bumper, determine if the ball is near enough.

ii) If the ball hits a bumper, the next steps must be executed:1) Determine the angle θ. Tip: Create a new vector with its starting point at the center ofthe ball, and endpoint at the center of the bumper. Now, figure out how you could easilyobtain θ from this.2) Rotate the velocity of the ball over the angle −θ;3) Invert the x−component of this velocity;4) Rotate the velocity again, this time over the angle θ.

b) In the act ( ) methode belonging to the Ball class, call void handleBumperCollision ( ) .c) Run and test your scenario. Does it work as you would expect it to?

Please read Theory 9.7: Implementing how moving balls collide.

Challenge 9.10: Moving balls collidingWe now modify the code so that two balls can collide at a particular angle:

a) Figure out how to calculate the new velocities of the colliding balls. Tip: use the rotations againto determine the correct components of each of the speeds, and exchange these between the twoballs.b) For the above, write a method void handleBallCollision ( ) . Call this method in the act ( )method.c) Run and test your scenario.



Challenge 9.11: Different sized ballsModify your code so that the simulation works with different sized balls. A few tips:

• In Greenfoot you can create your own image for a ball (in the next step you will transform this into apicture of a ball). Connect this image to your actor using the Greenfoot class GreenfootImage . Thenuse the constructor public GreenfootImage ( int width , int height ) to make a rectangularimage where the ball fits in perfectly. How large are its width and height?• Draw a circle. It’s easiest to color in the circle first, and then draw its border.

– First choose the color of the ball. Use setColor ( Color c ) to choose the pen color for coloringin the ball.– Use the GreenfootImage method fillOval (int x , int y , int width , int height ) to colorin the circle. Have a look at the Greenfoot API to understand how to use the parameters.– If you want to give the circle a black border, you need to first change the color of the pen (back)to black. After that you can draw a border using drawOval ( int x , int y , int width , int height ) .– Use Greenfoot . getRandomNumber (int limit ) to create a random-sized or random-coloredball.

Please read Theory 9.8: Collision with different masses.

Challenge 9.12: Balls with different massesIn this challenge we will make the simulation more realistic (and complex) by allowing balls with dif-ferent masses.

a) Just like in the previous challenge, both balls are moving and we don’t need to consider a perfecthead-on collision. You can describe this general case as a 1-dimensional case using a rotation anda transformation. Determine exactly how this happens. Tips:i) First, represent the velocity of the first ball(~v1) with respect to the second ball (with velocity~v2). This is done by a simple subtraction: ~v1 − ~v2.

ii) Rotate this result over an angle −θ.iii) Use the formula in Theory 9.8 to calculate the velocities after the collision.iv) Convert everything back to the original situation.

b) Write these steps out in Java code.c) Test your program.d) Now modify the code so that the mass coincides with the size of the ball. The larger the ball, theheavier it is.e) Test your modifications.



ReflectionIn this assignment you practiced using list to store values. You also learned about the for-each-loop totraverse lists and how to use a list to store (Egg) objects. One of the most important steps in becominggood at anything is to evaluate and reflect on what you did and how it went:ResultI know my solution works because . . .I am proud of my solution because . . .I could improve my solution by . . .

MethodMy approach was good because . . .What I could do better next time is . . .

Fill the following table with smileysindicating how things went. I can do itI did it a bit but didn’t fully get itI didn’t get it at all

I can make a (2-dimensional) simulation for a real (3-dimensional) situ-ation;I can use and apply formula’s from another subject (or field).



Saving and Handing inYou have just finished the assignment. Save your work! You will need this for future assignments. In theGreenfoot menu at the top of the screen, select ’Scenario’ and then ’Save’. You now have all the scenariocomponents in one folder. The folder has the name you chose when you selected ’Save As ...’.Handing inHand in the following:

• Your code;• Flowcharts: paste (photo’s of) your flowcharts in a Word document;• The reflection sheet: complete and hand it in.


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