Assignment 5: A Miscellany of Image Models

As you learned in the reading on transforming images, once we have a function that transforms a color to another color, we can apply that function to each pixel in an image with image-variant. For example, if kitty is an image, we can make a slightly darker version of that image with

> (define darker-kitty (image-variant kitty rgb-darker))

Often, it is useful to see what effect each of a variety of color transformations have on an image. For example, given a starting image, we might want one copy that is slightly darker, one copy that is slightly lighter, one copy that is slightly redder, and one copy that is slightly greener.

In essence, our algorithm might be expressed as

For each color-transformation
  Use image-variant to apply that transformation to the image
  Use image-show to show the resulting image

Express that algorithm in Scheme in as concise a form as possible.

(define image-show-variants
  (lambda (image list-of-transformations)
    ...))

One common technique for manipulating images is to “flatten” the colors in the image, using a much more restricted scale. For example, we might ensure that the components are each multiples of 16, 32, or 64. (Well, we'll use 255 instead of 256 for the highest multiple.)

How do we convert each component to the appropriate multiple? Consider the case of multiples of 32. If we divide the component by 32, round, and then multiply by 32, we'll get the nearest multiple of 32. For example,

> (* 32 (round (/ 11 32)))
0
> (* 32 (round (/ 21 32)))
32
> (* 32 (round (/ 71 32)))
64
> (* 32 (round (/ 91 32)))
96
> (* 32 (round (/ 211 32)))
224
> (* 32 (round (/ 255 32)))
256

a. Document and write a procedure, (rgb-flatten rgb base) that flattens rgb by converting each component of rgb to the nearest multiple of base.

b. Write the most concise expression you can to show four flattened versions of an image, using a base of 16 (first image), 32 (second image), 64 (third image), and 128 (fourth image). (You may use the image-show-variants procedure you wrote for problem 1 and the rgb-flatten procedure you wrote for problem 2.a.)

Write a procedure, (turtle-polygon! turtle side-length sides ), that uses a turtle to draw a regular polygon with the specified number of sides, with each side of the specified length.

For example,

(turtle-polygon! t 100 3)

(turtle-polygon! t 100 4)

(turtle-polygon! t 60 5)

(turtle-polygon! t 40 6)

Your procedure should return the turtle to its original position and angle.

Note: The sum of the interior angles of a polygon with N sides is (N-2)*180.

Write a procedure, (turtle-spin-polygon! turtle side-length sides angle copies), that draws the given number of copies of the specified polygon, with the turtle turned an angle of angle between polygons.

For example,

(turtle-spin-polygon! t 50 4 15 10)

(turtle-spin-polygon! t 50 4 20 5)

(turtle-spin-polygon! t 50 4 5 20)

(turtle-spin-polygon! t 50 4 -30 5)

Write a procedure, (turtle-scale-polygon! turtle initial-side-length sides scale-factor copies), that draws the given number of copies of the specified polygon, with each copy drawn with a side length scale-factor times the the previous side length.

For example, if the initial side length is ten, and the scale factor is two, this procedure would draw polygons with side lengths 10, 20, 40, 80, 160, ....

Similarly, if the initial side length is 100, and the scale factor is 0.9, the procedure would draw polygons with side lengths 100, 90, 81, 72.9, ....

Here are some visual issues.

(turtle-scale-polygon! t 1 5 2 8)

(turtle-scale-polygon! t 1 5 1.2 30)

(turtle-scale-polygon! t 100 5 0.9 20)

In the lab on iteration, we saw that it was possible to use for-each and the GIMP tools procedures to build compound images similar to those we built using map and the “drawings as values” model, but with the added benefit that we could stroke rather than select. In that example, we explored the following code.

> (define world (image-show (image-new 200 200)))
> (image-select-nothing! world)
> (for-each (lambda (left top)
              (image-select-ellipse! world ADD left top 12 10))
              (map (l-s * 10) (iota 20))
              (map (l-s * 9) (iota 20)))
> (image-stroke! world)
> (image-select-nothing! world)

Write a set of instructions to stroke the outside of a figure like the following (which we created in the reading on homogeneous lists). Your instructions should not cut off the bottom edge of the figure.

Hint: You may want to see how we created that image, and then think about how we can use selection tools to simulate the parts of the drawing.