Assignment 6: Conditionals and Colors

a. Write a predicate, (is-color? value), that returns #t when value is either an RGB color or a color name recognized by MediaScript. In all other cases, it should return #f.

You can use the predicates rgb? and color-name?, which are already defined, to help you. You should not use the predicate color?; we want you to write your own version.

b. Write your own version of color-to-rgb, which is a very useful procedure. Your procedure should have the following behavior: If given an RGB color, it returns that color unchanged. If given a color name, it returns the result of calling color-name->rgb on that color name. If given any other type of value, it returns #f.

You should not use the built-in color->rgb procedure; we want you to write your own version.

c. Write a procedure, (type-of value), that returns

d. What result do you obtain by calling type-of with an image as its parameter? Why?

e. What result do you obtain by calling color? with an image as its parameter? Why?

So far the behavior of the RGB transforms you have seen and/or implemented has not explicitly been dependent on qualities of the input color. We can also explore color transforms that involve conditionals.

a. Write an RGB transform (rgb-stronger rgb) that applies rgb-redder to rgb when red is the largest component of rgb, rgb-greener when green is the largest component, or rgb-bluer when blue is the largest component.

b. Write an RGB transform (rgb-weaker rgb) that applies rgb-greener and rgb-bluer to rgb when red is the largest component of rgb, rgb-redder and rgb-bluer when green is the largest component, or rgb-redder and rgb-greener when blue is the largest component.

The previous pair of transforms try to enhance or dampen the most pronounced color in the RGB representation. It may be more useful for us to explore alternate representations of color that are somewhat more intuitive. The HSV (for hue, saturation, and value) representation is one possibility. Hue represents the pure color (e.g., red, blue, yellow, green, or a combination of one of these). Saturation represents the "colorfulness" of the hue in the color. For instance, a completely saturated color would be a pure hue (like red), while a lesser saturated color might appear just as bright but somewhat faded (perhaps rose or pink). Value, then represents the brightness relative to a similarly bright white.

Hue is represented as an angle, or a point on a circle. Thus, the values 0-360 sweep through colors red (0 degrees), yellow (60 degrees), green (120 degrees), cyan (180 degrees), blue (240 degrees), magenta (300 degrees), and back to red (at 360 or 0 degrees).

There are a variety of transformations that can take an RGB color and give an HSV representation. In this problem, we'll focus on just extracting the hue.

Before we describe how to calculate hue, we need some basic values to refer to. Let (R,G,B) refer to the red, green, and blue components of a color, respectively. The chroma of a color, C is the largest of the RGB components minus the smallest of the RGB components. For example, the chroma of (128,64,50) is 128-50, or 78; the chroma of (0,255,0) is 255-0, or 255. The chroma of (255,255,255) is 255-255, or 0.

The raw hue can then be calculated as follows:

The raw hue as given above produces a value between -1 and 6 (corresponding to the 6 cardinal colors described above). If it is negative, we should add 6 to get us back to a positive representation. The final result is converted to the range 0-360 by multiplying by 60 degrees (which is 360/6).

What happens if C is not 0, and two of the components are both the largest? If the formula is well-designed, it shouldn't matter. Hence, you can try the “largest component” tests in order.

Using the algorithm given above, write a procedure (rgb->hue-angle rgb) that takes an RGB color and produces its hue. For example,

> (rgb->hue-angle RGB-RED)
0
> (rgb->hue-angle RGB-YELLOW)
60
> (rgb->hue-angle RGB-GREEN)
120
> (rgb->hue-angle RGB-CYAN)
180
> (rgb->hue-angle RGB-BLUE)
240
> (rgb->hue-angle RGB-MAGENTA)
300
> (rgb->hue-angle RGB-PINK)
7340/21
> (round (rgb->hue-angle RGB-PINK))
350

Note: You may wish to use a let statement or helper procedures to decompose your implementation into managable, meaningful units. Please be sure to give your variables and procedures meaningful names.

Being able to manipulate the hue in a color can actually be quite useful. MediaScheme can convert an HSV color into an RGB with the procedure (hsv->rgb hsv-list), where hsv-list is a three-element list containing the hue, saturation, and value components of a HSV color. MediaScheme can also extract the saturation and value from an RGB color with the procedures (rgb->saturation rgb) and (rgb->value rgb).

Write a procedure (rgb-change-hue rgb hue) that takes an RGB color and a hue value (in the range 0-360) and creates a new RGB color using the given hue with the saturation and value of rgb.

Warning! hsv->rgb only works with exact numbers.

It turns out the making color transforms based on hue can visually interesting.

Original Image	Hue rotated 30 deg	Hue rotated 90 deg

a. Using the procedures you have written so far, write a procedure (rgb-rotate-hue rgb angle) that takes a color produces a new rgb color where the HSV equivalent has a hue rotated by angle degrees, a number between 0-360.

Hint: If the rotated angle is greater than 360, you must subtract 360 to get the proper "wrapped-around" hue angle.

b. Write a concise expression that will rotate the hues in an entire image by 30 degrees.

Warning: When you apply rgb-rotate-hue thousands of times (as you will in an image of non-trivial size), it is likely to take some time. Do your testing on small images.

Create your own RGB color transform that conditionally transforms the hue of input color using a manner of your own choosing. For instance, you may choose to shift colors close to blue more toward green, leaving the rest unchanged.

Include a description of the effect of your transform in English. We should be able to apply your transform using image-variant or image-transform!.