Assignment 1

Color Model Program

Begin with the Matrix class from the Java ray tracer, or the the JAMA's Matrix class useful for most of these conversion methods. The JavaDoc for the JAMA Matrix class is available here.

For this assignment, you will implement conversion method from and to RGB and:

CMY - cyan, magenta and yellow
See this HyperGraph page. The Guided Tour of Color Space mentions on pages 13-14 that this "one minus RGB" is only a starting point, and that in practice, conversion requires polynomial arithmetic or 3-D interpolation of lookup tables. However, you should implement the conversion using the "one minus" calculation.
HSV - hue, saturation and value
To implement the conversions, follow the directions given by Wikipedia.

YIQ space
The linear transformation from RGB to YIQ is:

    [ Y ]     [ 0.299   0.587   0.114 ] [ R ]
    [ I ]  =  [ 0.596  -0.275  -0.321 ] [ G ]
    [ Q ]     [ 0.212  -0.523   0.311 ] [ B ]

The linear transformation from YIQ to RGB is:

    [ R ]     [ 1   0.956   0.621 ] [ Y ]
    [ G ]  =  [ 1  -0.272  -0.647 ] [ I ]
    [ B ]     [ 1  -1.105   1.702 ] [ Q ]

CIE XYZ space
The linear transformation from RGB to CIE XYZ is:

   [ X ]   [  0.412453  0.357580  0.180423 ]   [ R ]
   [ Y ] = [  0.212671  0.715160  0.072169 ] * [ G ]
   [ Z ]   [  0.019334  0.119193  0.950227 ]   [ B ]

The linear transformation from CIE XYZ to RGB is:

   [ R ]   [  3.240479 -1.537150 -0.498535 ]   [ X ]
   [ G ] = [ -0.969256  1.875992  0.041556 ] * [ Y ]
   [ B ]   [  0.055648 -0.204043  1.057311 ]   [ Z ].

Negative RGB values mean that the color cannot be represented in RGB space.

CIE L*u*v* space (extra credit)
CIE L*a*b* space (extra credit)

The L* in both these CIE color models is the same. It represents lightness, and ranges from 0 (black) to 100 (white). For CIE L*a*b*, the a* axis runs between red (positive) and green (negative), whereas the b* axis runs between yellow (positive) and blue (negative). For CIE L*u*v*, the u* and v* values are derived directly from the x and y values in CIE XYZ. You can read more about CIE L*u*v* and CIE L*a*b* at Wikipedia.

For all four methods, you will want to convert first to CIE XYZ before converting to the target color space. In addition, all the equations refer to a reference white value, which varies based on viewing angle. You should use the values: