CSC151.02 2010S Functional Problem Solving : Labs

Laboratory: Writing Your Own Procedures


Summary: In this laboratory, you will explore some of the issues that pertain to writing your own procedures.

Preparation

a. Review How Scheme Evaluates Expressions (version 2).

b. Make a copy of procedures-lab.scm, which contains most of the code from the reading.

c. Review the file to see what values and procedure are included. (You may find it easiest to look at the list provided by the Index button in MediaScript.

Exercises

Exercise 1: Sanity Checks

a. Verify that the four basic values look as they are described in the corresponding reading.

> (image-show (drawing->image black-circle 200 100))
> (image-show (drawing->image purple-ellipse 200 100))
> (image-show (drawing->image blue-i 200 100))
> (image-show (drawing->image red-eye 200 100))

b. Try some of the transformers. For example,

> (image-show (drawing->image (variant-1 black-circle) 200 100))
> (image-show (drawing->image (variant-1 (variant-1 black-circle)) 200 100))
> (image-show (drawing->image (add-right-neighbor red-eye) 200 100))

c. Try the circle constructor.

> (image-show (drawing->image (circle ___ ___ ___) 200 100))

d. Verify that square correctly squares the numbers 5, 10, -3, 1.2, and 0.05.

Exercise 2: Drawing Squares

Now that we can draw circles using circle, it will be helpful to write procedures that generate other simple shapes. Let's start with squares.

How do we create a drawing of a square? It depends on how we want to describe the square. If we are centering the square on a particular point, we need to know (1) the x coordinate of the center, (2) the y coordinate of the center, and (3) the edge length of the square. We can then scale the unit square by the edge length and shift it horizontally by the x coordinate of the center and vertically by the y coordinate of the center. Suppose we are drawing a square with edge length 25, centered at (20,30). We might write

(define my-square
  (drawing-hshift
   (drawing-vshift
    (drawing-scale drawing-unit-square 25)
    30)
   20))

Now, let's think about how to generalize this.

a. Write a procedure, (centered-square edge-length center-x center-y) that creates a drawing of a square. (We couldn't call this procedure square, because we'd already used that name for the procedure that squares numbers.) You should be able to generalize the code above, and base your procedure on the circle procedure.

b. However, most of us don't like to draw our squares centered on a particular point. We'd rather specify the left edge and the top edge. How can we do that? Suppose we want to draw a square of side-length 30, with the left edge at 17 and the top edge at 42. We first scale the unit square by 30. That means that the left edge, which was at -1/2, is now at -15 (that is, -1/2 * 30). The top edge, similarly, is also at -15. To get the left edge at 17, we need to shift it horizontally by 32 (that is, 15 + 17). To get the top edge at 42, we need to shift it vertically by 59 (that is, 15 + 42).

In Scheme, we might write

(define another-square
  (drawing-hshift
   (drawing-vshift
    (drawing-scale drawing-unit-square 30)
    (+ (/ 30 2) 42))
   (+ (/ 30 2) 17)))

Of course, we can also generalize this code. Write a procedure (drawing-of-square edge-length left top) that creates a drawing of a square of the specified edge length, with the left side of the square at left and the top side at top.

Exercise 3: Drawing Circles, Revisited

One deficiency of the circle procedure from the reading and of the centered-square and drawing-of-square procedures you've just reading is that they don't allow you to specify the color of the circle or square.

Rewrite the three procedures to take a color as a parameter. For example,

(circle 20 10 10 "blue")

Exercise 4: Drawing Rectangles

Write a procedure, rectangle that creates a drawing of a rectangle. You should do your best to figure out appropriate parameters. Here is a sample call, using the parameters we find most natural.

(rectangle 20 10 50 80 "yellow")

If you'd like to know what we thought were appropriate parameters, you can look at the notes on this exercise.

Exercise 5: Rendering Drawings

For each of the procedures above, you've likely tested your procedure by applying it to some drawing, rendering that drawing to some image, and then showing the image. For example,

> (image-show (drawing->image (rectangle 20 10 50 80) 200 100))

Write a procedure, (check-drawing drawing) that renders the drawing on a 200x100 image and then shows the image. Once we've written that procedure, we can more easily check drawings, as in the following.

> (check-drawing (rectangle 20 10 50 80))

Exercise 6: Fun with Neighbors

As you may recall, the add-right-neighbor procedure makes a copy of a drawing, places the copy immediately to the right of the original drawing, and combines the two into a new drawing.

a. Write a procedure, (add-smaller-right-neighbor drawing) that combines a drawing with a duplicate neighbor that is 75% of the size of the original drawing.

(add-smaller-right-neighbor red-eye)

As you write this procedure, you will find it useful to examine the code for add-right-neighbor

b. Write a procedure, add-nearer-right-neighbor drawing) that combines a drawing with a duplicate neighbor of the same size, but that overlaps 20% (so that the left end of the neighbor is 20% left of the right end of the original).

(add-nearer-right-neighbor red-eye)

c. Write a procedure, add-narrow-right-neighbor drawing) that combines a drawing with a duplicate neighbor immediately to the right, with the neighbor the same height, but half the width of the original.

(add-narrow-right-neighbor red-eye)

d. Write a procedure, add-bottom-neighbor drawing) that builds a duplicate neighbor that is immediately below the drawing.

(add-bottom-neighbor red-eye)

e. Write a procedure, (add-larger-bottom-neighbor drawing) that builds a 25% larger neighbor that is immediately below the drawing.

Exercise 7: Combining Transformations

We now have procedures that pair an image with a smaller right neighbor and a larger bottom neighbor. What happens if we combine these transformations? For each of the following, predict what the image will look like and then render it to check your prediction.

a. (add-larger-bottom-neighbor (add-smaller-right-neighbor red-eye))

b. (add-smaller-right-neighbor (add-larger-bottom-neighbor red-eye))

c. (add-smaller-right-neighbor (add-nearer-right-neighbor red-eye))

d. (add-smaller-right-neighbor (add-smaller-right-neighbor red-eye))

e. (add-narrow-right-neighbor (add-narrow-right-neighbor red-eye))

f. (add-smaller-right-neighbor (add-narrow-right-neighbor red-eye))

g. (add-narrow-right-neighbor (add-smaller-right-neighbor red-eye))

For Those With Extra Time

If you have extra time, you may find it useful to do any of the following exercises. (You need not do them in order.) You may also choose to do one of the explorations.

Extra 1: Drawing Eyes

In the reading, we defined a drawing that looks a bit like a red eye. Write your own procedure, drawing-eye, that builds a drawing of an eye, based on the values of its parameters. What parameters should it have? Certainly, the color of the iris. However, you might find other parameters useful, too.

Extra 2: An Alternate Scaling Mechanism

As you may recall, one potentially confusing aspect of the drawing-scale procedure is that it not only scales the drawing, it also scales the distance of the drawing from the top-left corner.

Write a procedure, (alternate-scale drawing), that scales a drawing, but does not move the drawing. That is, the scaled drawing has the same left edge and the same top edge as the original drawing.

If you're not sure how to approach this problem, you may want to read the notes on this exercise.

Extra 3: Grids of Images

a. Write a procedure, (two-by-two drawing) that creates a compound drawing with four copies of drawing (one shifted right, one shifted down, and one shifted down and right).

b. Write a procedure that takes the result of two-by-two and scales it by 50%, so that the resulting drawing is the same width and height as the original.

c. Using this new procedure, build a four-by-four grid of one of the original images, or one of your own choosing.

Explorations

For each of these explorations, you may find the following drawing an appropriate starting point. You might also start with a house or other drawing you've designed. You might even start with a simple shape.

(define sample
  (drawing-hshift
   (drawing-vshift
    (drawing-group
     (drawing-scale 
      drawing-unit-circle 
      100)
     (drawing-scale 
      (drawing-recolor drawing-unit-circle "yellow") 
      90)
     (drawing-vshift
      (drawing-hscale
       (drawing-vscale 
        drawing-unit-circle
        40)
       60)
      10)
     (drawing-hscale
      (drawing-vscale
       (drawing-recolor drawing-unit-circle "yellow")
       40)
      60)
     (drawing-vshift
      (drawing-group
       (drawing-hshift
        (drawing-group
         (drawing-hscale
          (drawing-vscale
           (drawing-recolor drawing-unit-circle "white")
           15)
          30)
         (drawing-hscale
          (drawing-vscale
           (drawing-recolor drawing-unit-circle "blue")
           15)
          15))
        18)
       (drawing-hshift
        (drawing-group
         (drawing-hscale
          (drawing-vscale
           (drawing-recolor drawing-unit-circle "white")
           15)
          30)
         (drawing-hscale
          (drawing-vscale
           (drawing-recolor drawing-unit-circle "green")
           15)
          15))
        -18))
      -15))
    50)
   50))

Exploration 1: Multiple Neighbors

In Exercise 5, each of the expressions takes one drawing and turn it into four drawings. Explore other ways to use this kind of replication to build an interesting image. (You might also think about ways to create eight, sixteen, or even more copies of the image.)

Exploration 2: More Interesting Neighbors

In the Exercise 4, you developed a number of procedures that pair an image with a neighbor. Create a few variants of those procedures that change the neighbor in an “interesting” way. For example, you might scale it differently horizontally and vertically, you might have it overlap the original figure, you might shift it both horizontally and vertically.

Notes on the Exercises

Notes on Exercise 4: Drawing Rectangles

We would recommend that your procedure have the form

(define rectangle
  (lambda (left top width height color)
    ..._))

Return to the exercise.

Notes on Extra 2: An Alternate Scaling Mechanism

The alternate scaling algorithm is fairly straightforward:

  • Shift the drawing back to the origin. (The top and left should both be 0.)
  • Scale the shifted drawing.
  • Shift the scaled drawing back to the original place. (The top and left should match the top and left of the original drawing.)

Return to the exercise.

Creative Commons License

Samuel A. Rebelsky, rebelsky@grinnell.edu

Copyright (c) 2007-10 Janet Davis, Matthew Kluber, Samuel A. Rebelsky, and Jerod Weinman. (Selected materials copyright by John David Stone and Henry Walker and used by permission.)

This material is based upon work partially supported by the National Science Foundation under Grant No. CCLI-0633090. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/2.5/ or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA.