Assignment 6: Conditionals and Colors

Due: 10:30 p.m., Tuesday, 16 October 2012

Summary: You will explore some novel color transforms.

Purposes: To practice conditionals and have some fun with representations of colors and their transforms.

Expected Time: Two to three hours.

Collaboration: We encourage you to work in groups of size two. You may, however, work alone or work in a group of size three. You may discuss this assignment with anyone, provided you credit such discussions when you submit the assignment.

Submitting: Email your answer to . The subject of your email should have the form CSC151-02 Assignment 6: Conditionals and Colors and should contain your answers to all parts of the assignment. Scheme code should be in the body of the message.

Warning: So that this assignment is a learning experience for everyone, we may spend class time publicly critiquing your work.


Problem 1: Types

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.

Problem 2: Hue Transforms

The previous transform tries to enhance 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. As we learned in the reading on design and color representing colors in terms of hue, saturation, and value, the HSV 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.

As shown below, 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 (red, green, blue) refer to the red, green, and blue components of an RGB color, respectively. The chroma of a color 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:

  • (green-blue)/chroma if red is a largest component
  • ((blue-red)/chroma) + 2 if green is a largest component
  • ((red-green)/chroma) + 4 if blue is a largest component
  • if chroma=0 the hue is undefined, because all the components are the same and we would have a gray. In this case, one convention is to set the hue to 0.

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 chroma 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)
> (rgb->hue-angle RGB-YELLOW)
> (rgb->hue-angle RGB-GREEN)
> (rgb->hue-angle RGB-CYAN)
> (rgb->hue-angle RGB-BLUE)
> (rgb->hue-angle RGB-MAGENTA)
> (rgb->hue-angle RGB-PINK)
> (round (rgb->hue-angle RGB-PINK))

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.

Problem 3: Changing Hue

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. Thus you may need to use inexact->exact.

Problem 4: Hue-Based Transforms

It turns out that making color transforms based on hue be 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 and 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, be sure to wrap around properly (e.g., using modulo) to get the correct hue angle.

b. Write an expression as concisely as possible that will rotate the hues in an entire image (say, called picture) 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.

Problem 5: Conditional Hue Transforms

Create your own RGB color transform that transforms the hue of its input color conditionally 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!.

Optional Bonus Problem: Generating Color Schemes

For extra credit, design, document, and implement a Color Scheme Generation Toolkit. Your toolkit should consist of a suite of related procedures. Each procedure will take an RGB color as a parameter and produce a list of colors forming a coherent color scheme. Some procedures may need to take additional parameters: You decide what those parameters will be. You will find the procedures related to hue, saturation, and value very useful.

You should at least write procedures to do the following:

  • Pair a color with its true complement on the color wheel.
  • Generate an analogous color scheme based on the given color.
  • Generate a list of tints of a color.
  • Generate a list of shades of a color.
  • Generate a list of colors according to at least one other color scheme, based on the reading on design and color, the Color Scheme Designer, or another source of color schemes used by artists and designers.

Important Evaluation Criteria

We will evaluate your work on the correctness, clarity, and conciseness of your code, and on the creativity of your response to the last problem.


The HSV hexagon is adapted from an original by Jacob Rus.

Jerod Weinman

Copyright 2007-2012 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.

Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License .