Color - Computer Graphics: Principles and Practice - page 781

won't matter what color system you're using, in the sense that the results will
be very similar. Verify this in the case of RGB and L ∗ u ∗ v ∗ versions of the colors
( r , g , b )=( 0.7, 0.4, 0.3 ) and ( r , g , b )=( 0.7 +

) , by finding the
50-50 mix of the two colors in both RGB and L ∗ u ∗ v ∗ and comparing. Do this for

− −

,0.4 2 ,0.3

= 0.01, 0.05, and 0.25.
Exercise 28.3: Consider points with Y = 1 and chromaticity values that range
over the entire CIE diagram. Compute the L ∗ u ∗ v ∗ coordinates of these points, and
plot them on axes labeled L ∗ , u ∗ , and v ∗ .
Exercise 28.4: For 400

<λ< 700, consider two monospectral lights, with

Y = 1, one with wavelength + 1; they are separated

by 1 nm in “wavelength space.” Plot their distance in XYZ -space as a function of
λ

λ and one with wavelength λ

; plot their distance in L ∗ u ∗ v ∗ -space as a function of . At what wavelength is

this latter difference largest? Smallest? Note: You'll need to find a table of the
xy -coordinates of the monospectral points on the CIE horseshoe.
Exercise 28.5: No three-color display can faithfully reproduce all color per-
cepts. Suppose you wanted to design a three-primary display with the largest pos-
sible gamut (measured in terms of area on the chromaticity diagram).
(a) Argue why all three primaries should be on the boundary of the horseshoe.
(b) Find the xy -coordinates of the horseshoe boundary and then search for the
optimal location for the three primaries.
(c) Approximately what percentage of the area can you cover with three primaries?
With four? With five?
Exercise 28.6: Derive Equation 28.29 from Equation 28.26.
Exercise 28.7: (a) Suppose that the sensitivities of the receptors in the eye
were not shaped like Gaussian bumps, but were instead triangular, the graph of the
red receptor being an equilateral triangle with base between 600 nm, and 700 nm,
the green having its base between 500 nm and 600 nm, and the blue having its
base between 400 nm and 500 nm (all three equilateral triangles having the same
heights). What would the CIE diagram look like? How many primaries would be
needed for perfect color reproduction?
(b) Suppose instead that the domains overlapped so that red was defined on
[ 500, 600 ] , green on [ 450, 550 ] , and blue on [ 400, 500 ] . What would the chro-
maticity diagram look like? How many primaries would be needed to faithfully
reproduce every color percept?
Exercise 28.8: We said that if you're asked to convert a source that's
18Wm − 2 sr − 1 to nits, it's impossible. Suppose you were told in addition that
it was a blackbody source at a particular temperature. Describe how you could
compute the corresponding number of nits in this case (given a tabulation of the
luminous efficiency function).
Exercise 28.9: Write formulas to convert L ∗ a ∗ b ∗ coordinates for a color back
to the XYZ triple for the color. You may assume that X w , Y w , and Z w are known.
Exercise 28.10: We claimed above that a colorimeter could be used to measure
the XYZ values for each of the red, green, and blue primaries of a display. Suppose,
though, that the colorimeter only produces the CIE xy -values, but you can also
measure the luminances Y r , Y g , and Y b of the full-brightness red, green, and blue
primaries. Express the XYZ coefficients of a color with RGB coefficients r , g , and
b in terms of the observed xy -values and the full-brightness luminosities.
Exercise 28.11: ( Peripheral color perception. ) Stand with one arm pointing
outward, and fixate on a point in front of you. Have a friend place a playing card in
your outstretched hand so that the card faces toward your head. Move your hand

λ