Functional Problem Solving (CSC 151 2014F) : Labs
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Summary: In this laboratory, you will explore some of the issues that pertain to writing your own procedures.
a. Review How Scheme Evaluates Expressions (Take 2).
b. Start GIMP and enable the DBUS Server. Then start DrRacket.
c. Save a copy of procedures-lab.rkt
, which contains most of the code from the reading.
d. Open the file in DrRacket. Review the file to see what values and procedures are included. (You may find it easiest to look at the list provided by using the DrRacket
menu. Finally, click .If things go wrong, see our instructions for running the CSC 151 software. Ask for help if you need it.
Recall that in the lab on numeric
values, you explored the use of the min
and max
procedures to compute a bounded value:
> (define bounded-val (min (max val lower) upper))
This code assumed that val
, lower
, and
upper
had already been defined. It would be helpful to
create a subroutine, instead, so that we can easily limit any real number
to fall within any bounds.
Take the code given above and encapsulate it in a procedure named
bound
. This procedure should take three
parameters: val
,
lower
, and upper
. As a
reminder, the general form of a procedure definition is
(define procedure-name (lambda (formal-parameters) body))
Here is an example of some output from the bound
procedure:
>(bound 5 0 10)
5
>(bound 5 10 20)
10
>(bound 0.7 -1 1)
0.7
>(bound 1.01 -1 1)
1.0
>(bound -8.3 -1 1)
-1.0
Now that we can draw circles using
, it will be helpful to write
procedures that generate other simple shapes. Let's start with squares.
circle
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 (hshift-drawing 20 (vshift-drawing 30 (scale-drawing 25 drawing-unit-square))))
Now, let's think about how to generalize this.
a. Write a procedure, (
that creates a drawing of a square. (We couldn't call this procedure
centered-square
edge-length
center-x
center-y
)
, 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
square
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 (hshift-drawing (+ (/ 30 2) 17)) (vshift-drawing (+ (/ 30 2) 42) (scale-drawing 30 drawing-unit-square)))
Of course, we can also generalize this code.
Write a procedure (
that creates a drawing of a square of the
specified edge length, with the left side of the square at
drawing-of-square
edge-length
left
top
)left
and the top side at top
.
In part a of the previous exercise, you started with existing code, generalized the code by replacing particular values with names/parameters, and then turned the generalized code into a procedure. You've certainly improved the code. At the same time, you've also made something that others might consider a “derivative work”. Hence, you have a responsibility to consider whether or not to cite the original.
a. Suppose that you decided to cite the original. Write a comment that gives appropriate details. (The original comes from this lab, which was created by Janet Davis, Samuel A. Rebelsky, and Jerod Weinman.)
b. Suppose you wrote the code for centered-square
with another
student, perhaps for a previous lab. In writing the
drawing-of-square
procedure, should you cite the code
for centered-square
? Why or why not?
c. Suppose you wrote the code for centered-square
alone,
but wrote drawing-of-square
with another student. Should
you cite the code for centered-square
? Why or why not?
One deficiency of the
procedure
from the reading and of the circle
centered-square
and
drawing-of-square
procedures you've just written
is that they don't allow you to specify the color of
the circle or square.
Rewrite the
procedure to
take a color as a parameter. For example,
circle
(circle 20 10 10 "blue")
Write a procedure,
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
(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.
As you may recall, the
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.
add-right-neighbor
a. Write a procedure,
(
that combines a drawing with
a duplicate neighbor that is 75% of the size of the original drawing.
add-smaller-right-neighbor
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,
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
drawing
)
(add-nearer-right-neighbor red-eye)
We now have procedures that pair an image with a smaller right neighbor and a nearer right 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-smaller-right-neighbor (add-nearer-right-neighbor red-eye))
b. (add-nearer-right-neighbor (add-smaller-right-neighbor red-eye))
c. (add-smaller-right-neighbor (add-smaller-right-neighbor red-eye))
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.
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, (
that renders the drawing on
a "large enough" image, then shows the image. Once we've written
that procedure, we can more easily check drawings, as in the
following.
check-drawing
drawing
)
>
(check-drawing (rectangle 20 10 50 80))
How can we find out how large the image needs to be? We can
ask a drawing where its lower right hand corner is using the
drawing-bottom
and
drawing-right
procedures.
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.
As you may recall, one potentially confusing aspect of the
procedure is that it not
only scales the drawing, it also scales the distance of the drawing
from the top-left corner.
scale-drawing
Write a procedure, (
, 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.
alternate-scale
amt
drawing
)
If you're not sure how to approach this problem, you may want to read the notes on this exercise.
a. Write a procedure, (
that creates a compound
drawing with four copies of drawing (one shifted right, one
shifted down, and one shifted down and right).
two-by-two
drawing
)
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.
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 (hshift-drawing 50 (vshift-drawing 50 (drawing-group (scale-drawing 100 drawing-unit-circle) (scale-drawing 90 (recolor-drawing "yellow" drawing-unit-circle)) (vshift-drawing 10 (hscale-drawing 60 (vscale-drawing 40 drawing-unit-circle))) (hscale-drawing 60 (vscale-drawing 40 (recolor-drawing "yellow" drawing-unit-circle))) (vshift-drawing -15 (drawing-group (hshift-drawing 18 (drawing-group (hscale-drawing 30 (vscale-drawing 15 (recolor-drawing "white" drawing-unit-circle))) (hscale-drawing 15 (vscale-drawing 15 (recolor-drawing "blue" drawing-unit-circle))))) (hshift-drawing -18 (drawing-group (hscale-drawing 30 (vscale-drawing 15 (recolor-drawing "white" drawing-unit-circle))) (hscale-drawing 15 (vscale-drawing 15 (recolor-drawing "green" drawing-unit-circle)))))))))))
In Extra 4, 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.)
In Exercise 6, 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.
We would recommend that your procedure have the form
(define rectangle (lambda (left top width height color) ..._))
The alternate scaling algorithm is fairly straightforward: