1.4 Super Procedures and Sub Procedures

Transcription

1 1.4 Super Procedures and Sub Procedures Here is a new problem: Write a procedure to draw a equilateral triangle of side 40. Your procedure should look something like this: To TRIANGLE REPEAT 3[ FD 40 RT 120] Type: POTS POTS - stands for Print Out Titles. This list all the procedures in the workspace. This stands for Print Out Titles. It shows you what procedures you have defined in the workspace. You should have Square and Triangle defined. Now we want to define a new procedure called house. The output will look like the following: Notice that this procedure is made up of triangle and square. Therefore we are going to define a Superprocedure House with Subprocedures: Square and Triangle. This might be a first try: TO HOUSE SQUARE TRIANGLE

2 Draft - T. Giambrone MAT 306- September 12, Page 2 But there is a problem because the output looks like this: So we need to put some glue moves in to glue the two procedures together. Try to edit house to make it successful. TO HOUSE SQUARE FD 40 RT 30 TRIANGLE NOTE : I put the glue moves all on the same line to keep them together. This will make it easier to debug a procedure in the future. You can put as many commands on a single line as long as they are separated by a space. I also have the glue outside square or triangle procedure so I can still use these procedures in other projects. Problem Use house and PU &PD to define a new procedure Neighborhood that looks something like the following: Don't be surprised if it takes several tries. Here is one that works: TO NEIGHBORHOOD PU LT 90 FD 120 RT 90 PD REPEAT 4[ HOUSE PU LT 30 BK 40 RT 90 FD 60 LT 90 PD ]

3 Draft - T. Giambrone MAT 306- September 12, Page Structured Programming Now we are ready for a big project. We will write a procedure to do the following: On the surface it looks a bit intimidating. This is were structure programming and structured problem solving come together. Lets look at the problem this way: To Sail To Sail To Rudder To Hull Now the problem is to write three procedures and glue them together.

4 Draft - T. Giambrone MAT 306- September 12, Page 4 The picture drawn on graph paper will help you get started. Consider each of the grids 10 turtle steps. TO HULL LT 90 FD 160 RT 45 FD 28 RT 135 FD 180 RT 90 FD 20 LT 180 NOTE: That I turned the turtle is in the same place it started and facing in the original position. This will help me keep track of where the turtle is when I put these procedures together. Now Hull is complete. Resize your turtle window so the hull fits on the screen without wrapping. We will see later how to do this from within the program. TO SAIL FD 100 RT 150 FD 80 RT 120 FD 70 RT 120 FD 60 LT 30 BK 83

5 Draft - T. Giambrone MAT 306- September 12, Page 5 NOTE: I returned the turtle to its original position and original orientation. This will make glueing the procedures together easier. Now we need to RUDDER TO RUDDER REPEAT 2 [FD 5 RT 90 FD 30 RT 90] FD 5 RT 90 FD 30 REPEAT 2 [FD 5 RT 90 FD 30 RT 90] RT 90 FD 30 LT 180 REPEAT 2 [FD 5 RT 90 FD 30 RT 90] FD 25 LT 90 FD 30 RT 90 Now TO BOAT TO BOAT HULL PU FD 20 LT 90 FD 140 RT 90 PD SAIL PU RT 90 FD 110 LT 90 PD SAIL PU RT 90 FD 10 LT 90 FD 5 PD RUDDER PU BK 25 RT 90 FD 20 LT 90 PD In general when you write a subprocedure, have the turtle return to the begining point with the begining orientation. Now it is your turn. Construct a procedure to draw the following castle.

6 Draft - T. Giambrone MAT 306- September 12, Page 6 The structure of your castle should look something like this: Castle Tower Frame Door Rectangle Triangle Lookout Square 1.6 VARIABLES Let's return to our square procedure: TO SQUARE REPEAT 4[ FD 40 RT 90] If we want to change this procedure to draw a square of side 100, we could do so by just changing the 40 to 100. In fact, to vary the side of the square we need only to change the input for the FD command. Here is how we do it.

7 Draft - T. Giambrone MAT 306- September 12, Page 7 General form for a variable : (variable name) The (:) means "The contents of". A variable in LOGO can be a number, a word or a list of words or numbers. Lets return to square. To make it variable we will type TO VSQUARE :SIDE REPEAT 4[ FD :SIDE RT 90] Now type VSQUARE <RETURN> You got an error message that said: "VSQUARE needs more inputs" This is because it is not expecting you to accompany the procedure with a number. Try typing VSQUARE 60 <RETURN> Now try using your VSQUARE procedure to draw the following: Problem Write procedures for VTRIANGLE, and VHOUSE You can also use an arithmetic expression for and input. Try typing VSQUARE 6*7, LOGO will compute the expression and do a square of Using several variables. You can have as many inputs as you what. Suppose you want to write a variable procedure to draw a rectangle. This procedure will need two inputs: TO VRECTANGLE :LENGTH :WIDTH

8 Draft - T. Giambrone MAT 306- September 12, Page 8 REPEAT 2[ FD :LENGTH RT 90 FD :WIDTH RT 90] Now we type: VRECTANGLE The numbers must be on the same line and separated by a space. Problem: Change your Castle procedure to draw different size castles 1.8 TURTLE TRIP THEOREM. You have written procedures for triangle and square. The procedures have looked something like the following: REPEAT 3[ FD 40 RT 120] REPEAT 4 [ FD 40 RT 90 ] Notice that in these procedure the number in front of the repeat bracket tells us the number of sides for each procedure and the number following the RT is the turn for the shape. Let s explore the turns for any regular polygon by using the following procedure: TO POLY :SIDES :TURN REPEAT :SIDES [ FD 40 RT :TURN] -Now type : POLY CG POLY 4 90 CG You got the triangle and the square. Let s explore with POLY by filling out the following chart: Number of sides Angle of the turn

9 Draft - T. Giambrone MAT 306- September 12, Page Some of these will be easier to find than others. Try to look at the table and find a pattern to help you out. This is called the turtle trip theorem. In general, if the turtle takes a trip and returns facing the same direction the turtle has gone 360 degrees or a multiple of 360 degrees. This makes the standard theorem that the sum of the exterior angles of a polygon equals 360 much easier to see. List push the mathematics a little further.. Consider the following hexagon: The extra lines are shown to indicate the exterior angles. What are the angles? Can you tell what the interior angle should be? Why? The exterior angle is 60 degrees and the interior angle is or 120 degrees because the two angles form a straight line. Now here is a new problem.

10 Draft - T. Giambrone MAT 306- September 12, Page 10 Problem 1.4 What is the central angle for this hexagon? Remember: the sum of the angles of a triangle is 180 degrees. Can you generalize these three ideas for any polygon?