1. COSC 1P02 Introduction to Computer Science 3.1 Cosc 1P02 Week 3 Lecture slides Birthdays are good for you. Statistics show that the people who have the most live the longest. (Rev. Larry Lorenzoni)

2. COSC 1P02 Introduction to Computer Science 3.2 Review  Memory Representation of:  Value variables  Reference variables  Assignment of reference variables  Tiling patterns

3. COSC 1P02 Introduction to Computer Science 3.3 Dealing with Complexity  Limits on composition  Can only go so deep before the nesting becomes un- manageable.  Requires separate index variables for each loop  Repetition of code  Duplicating code in a program is a bad thing  Increases complexity unnecessarily  More work.  Abstraction  Divide and conquer  Break problems into chunks  Let the process (code) be independent from operation of calling the code.  E.g. Yertle.forward(40); runs magic code to move yertle.

4. COSC 1P02 Introduction to Computer Science 3.4 Two Squares  Consider drawing two squares at different places on the screen  repeated code  increased possibility of error  Drawing a square could be considered an operation (like drawing a line)  drawing a line done by a method ( forward )  write a method to draw a square ( drawSquare )  Example

5. COSC 1P02 Introduction to Computer Science 3.5 Methods  Method declaration  syntax  name  verb  body  Method call  syntax  Method execution  current code suspended  body of method executed  current code continues

6. COSC 1P02 Introduction to Computer Science 3.6 Eight Squares Revisited eightSquares2.java  Composition via methods  use method call instead of nesting  Example  Reduced complexity  Can think of drawing a square as a basic operation  don’t have to worry about how it is done  code for EightSquares simpler  don’t have to worry about different index variables

7. COSC 1P02 Introduction to Computer Science 3.7 Scope  Declarations occur at different places  in class  in method  in for statement  Scope  Where are names defined in declarations useable?  Rule  in class – from { in class header to } at end of class  includes methods names  in method – from { in method header to } at end of method  in for – body of for (statements between { } )  Example  Composition via nesting vs via methods  non-interference

8. COSC 1P02 Introduction to Computer Science 3.8 Eight Squares2 public class EightSquares2 { private Turtleyertle;// turtle for drawing private TurtleDisplayer display; public EightSquares2 ( ) { int i; yertle = new Turtle(); display = new TurtleDisplayer(yertle); for ( i=1 ; i<=8 ; i++) { drawSquare(); yertle.right(PI/4); }; };// constructor private void drawSquare() { yertle.penDown(); for (int i=1 ; i<=4 ; i++) { yertle.forward(40); yertle.right(PI / 2); }; yertle.penUp(); };// drawSquare public static void main ( String args[] ) { new EightSquares2(); }; }// EightSquares2 This i is local and visible to entire constructor Visible within for loop only Modification of i in drawSquare does not affect the i in the constructor Declared at the class level, visible over entire class.

9. COSC 1P02 Introduction to Computer Science 3.9 What is an Object  An Object has 2 parts  Memory  What it remembers  State information  Data  Behaviour  What an object can do  Actions which can be performed  A Class defines what an object is:  Instance Variables represent the memory  Methods define the behaviour

10. COSC 1P02 Introduction to Computer Science 3.10 Object Creation  New causes an object to be created from the template (class)  E.g. new Turtle();  An Object is initialized when it is created.  Initial memory and behaviour are set  New causes the constructor to run to create the object  Constructor  Is a method (initial behaviour)  Has the same name as the class  New causes the constructor to execute.

11. COSC 1P02 Introduction to Computer Science 3.11 Constructors, Methods & Objects  Methods are executed by an object  who is executing drawSquare ?  no object specified  Turtle (yertle) doesn't know how  main method  is a method declaration  every Java program must have ate least one class (called the main class) that has a main method  Execution begins in body of main method  body includes object creation ( new )  creates a new EightSquares object  on creation object executes its constructor  Local method call  when no object specified method is executed by same object as is executing the method call (e.g. the EightSquares object)  drawSquare() is shorthand for this.drawSquare()

12. COSC 1P02 Introduction to Computer Science 3.12 Eight Squares public class EightSquares2 { private TurtleDisplayer display; // display to draw on private Turtle yertle; // turtle to do drawing /** The constructor draws 8 squares in a pattern. */ public EightSquares2 ( ) { display = new TurtleDisplayer(); yertle = new Turtle(30); display.setTurtle(yertle); yertle.penDown(); for ( int i=1 ; i<=8 ; i++ ) { drawSquare(); yertle.right(PI/4); }; yertle.penUp(); display.close(); }; // constructor /** This method draws a square with the current turtle position as the * top-left corner. */ private void drawSquare ( ) { yertle.penDown(); for ( int i=1 ; i<=4 ; i++ ) { yertle.forward(40); yertle.right(PI/2); }; yertle.penUp(); }; // drawSquare public static void main ( String[] args ) { new EightSquares2(); }; EightSquare2 object is created Constructor creates object, identified as by same name as the class Method drawSquare is called, control is passed to the method. Method code is executed Control is passed back from where it was called. Rest of code is executed. When constructor finishes then control goes back to main.

13. COSC 1P02 Introduction to Computer Science 3.13 Eight Squares One More Time  Constructor is meant to initialize an object  Separate initialization from operation  Puts object into a known state.  write operations as methods  e.g. Turtle  Example  constructor simply creates display, turtle and connects them  method draw performs the operation to draw the eight squares  draw is executed by the EightSquares object created in main  E.g. new EightSquares3().draw();  New EightSquares3() creates an object returning a reference .draw then calls the behavior of the new object.

14. COSC 1P02 Introduction to Computer Science 3.14 Hexagon Revisited  Complex scene with many figures  hard to keep track of where drawing begins & ends  Centre figure on a point with a size of the figure (rather than a side)  method to draw figure starts from center & leaves pen in center  i.e. leaves turtle in same state as it started  Turtle state becomes independent from drawing.  Geometry of a hexagon  Drawing a hexagon  move out from center  position down first side  draw sides  return to center & pen orientation  Example

15. COSC 1P02 Introduction to Computer Science 3.15 Geometry of a Hexagon - Half of this angle is then  /6 Facts about Polygons The size of the interior angle is 2  / the number of point. - For a Hexagon this would be 2*  /6. By taking half of the interior angle we create a right angled triangle. We can now calculate the opposite side using standard trigonometry. - For our Hexagon this would be r*sin  /6 - For any polygon this would be r*sin  /sides The entire side would be 2 * this quantity. - For a Hexagon 2*r*sin  /6 - For a Polygon 2*r*sin  /sides We need to calculate the initial angle of rotation. If this is the angle    /2-  Then to opposite angle is  /2-   /2-  Which is also this angle We now can do some simple subtraction  -(  /2-  ) gives us the angle we are looking for. This reduces to  /2+  This angle To get subsequent angles of rotation. We can note that these angles are the same. So….  -2(  /2-  ) = 2  For a hexagon this becomes  /3  /2- 

16. COSC 1P02 Introduction to Computer Science 3.16 Expressions  Computations specified by expressions  like algebraic expressions in Mathematics  written on one line  Composed of  operators  constants  variables  functions  Evaluation order  by priority, left to right  parentheses to force order

17. COSC 1P02 Introduction to Computer Science 3.17 Two Hexagons  Consider drawing two hexagons of different size  Size of hexagon fixed in method  different methods for different sizes?  essentially identical code  differs only by value of radius  Allow the method to vary depending on value of radius  Example  radius is parameter

18. COSC 1P02 Introduction to Computer Science 3.18 Two Hexagon. public TwoHexagon ( ) { display = new TurtleDisplayer(); yertle = new Turtle(); display.setTurtle(yertle); }; // constructor private void draw ( ) { yertle.moveTo(-75,75); drawHexagon(40); yertle.moveTo(75,-75); drawHexagon(60); display.close(); }; // constructor private void drawHexagon ( double radius ) { //Rest of code next page Radius take on the value 40 Rest of drawHexagon executes using radius, on method completion drawHexagon returns Radius take on the value 60

19. COSC 1P02 Introduction to Computer Science 3.19 Two Hexagon.. private void drawHexagon ( double radius ) { double angle; // exterior angle between sides of hexagon double side; // length of side of hexagon angle = 2 * PI / 6; side = 2 * radius * sin(PI/6); yertle.forward(radius); yertle.right(PI/2+PI/6); yertle.penDown(); for ( int i=1 ; i<=6 ; i++) { yertle.forward(side); yertle.right(angle); }; yertle.penUp(); yertle.left(PI/2+PI/6); yertle.backward(radius); }; // drawHexagon The value of radius is then used in the method.

20. COSC 1P02 Introduction to Computer Science 3.20 Parameters  Allows a method to be generalized over one or more values  radius for drawHexagon  Parameter (formal parameter)  declared in method header  behaves like a local variable within method body  scope is method body  is initialized to value of argument at call  Argument (actual parameter)  an expression that produces a value of the declared type  constant  variable  expression  Method execution  value of argument computed  calling code suspended  value of argument copied to parameter  body of method executed  calling code continues

21. COSC 1P02 Introduction to Computer Science 3.21 Polygons  Code for drawing all regular closed figures (polygons) similar  move out from center  rotate to facing down first side  for each side  draw side  rotate to next side  move back to center  Geometry of a polygon  Code would depend on two values: radius and number of sides  method with two parameters  Example  Note: number of times in for loop now a variable  index i counts from 1 to value of nSides

22. COSC 1P02 Introduction to Computer Science 3.22 Polygons private void draw ( ) { yertle.left(PI/2); // facing up so point of polygon is at top yertle.moveTo(-75,75); drawPolygon(5,20); yertle.moveTo(75,75); drawPolygon(6,30); yertle.moveTo(75,-75); drawPolygon(7,40); yertle.moveTo(-75,-75); drawPolygon(8,50); display.close(); }; // draw private void drawPolygon ( int nSides, double radius ) { double angle; // exterior angle between sides of polygon double side; // length of side of polygon angle = 2 * PI / nSides; side = 2 * radius * sin(PI/nSides); yertle.forward(radius); yertle.right(PI/2+PI/nSides); yertle.penDown(); for ( int i=1 ; i<=nSides ; i++) { yertle.forward(side); yertle.right(angle); }; yertle.penUp(); yertle.left(PI/2+PI/nSides); yertle.backward(radius); }; // drawPolygon When the method is called each actual parameter is assigned to its formal parameter Formal parameters are then used in the method body.

23. COSC 1P02 Introduction to Computer Science 3.23 The end