Assignment 3

1.

The outline of the fin shows the various wavelengths – the pure colours shown in the spectrum.

wavelength versus x/y

wavelength vs y

wavelength vs z/y

wavelength vs x

wavelength vs z

x represents the percentage of red in the wavelength
y represents the percentage of green in the wavelength
z represents the percentage of blue in the wavelength

2.

Given C1(x1,y1), C2(x2,y2) and C(x,y) are ordered pairs within the chromaticity diagram. C1 and C2 form a line segment and C is a point on this line segment.

Length of C1C=SQRT( (x1-x)^2 + (y1 – y)^2)

Length of C1C2 = SQRT( (x1-x2)^2 + (y1 – y2)^2)

%C2 = (length of C1C)/(length of C1C2)*100%
%C1=100-%C2

I did this question using ratios before I saw Mike’s message on Facebook. I was not able to do #3 using this strategy.

Using Mike’s strategy, I got

My equations are
a + b = 1
x = ax1 + bx2
y = ay1 + by2

My solutions for a and b are:

a = (xy2-x2y)/(x1y2-x2y1)
b = (xy1-x1y)/(x2y1-y1x2)

3.

Using Mike’s strategy again,
My equations are:
a + b + c = 1
x = ax1 + bx2 + cx3
y = ay1 + by2 + cy3

My solutions for a, b and c are:

a = [x(y3-y2)+x2(y-y1)+x3(y1-y)]/[y1(x1-x2) +y2(x3-x1)+y3(x2-x3)]
b = [x(y3-y2)+x2(y-y1)+x3(y1-y)]/[y1(x3-x2)+y2(x1-x3)+y3(x2-x1)]
c = [x(y2-y1)+x1(y-y2)+x2(y1-y)]/[y1(x2-x3)+y2(x2-x1)+y3(x1-x2)]

I did this manually so I hope I didn’t make any mistakes as I don’t feel like doing it again (enjoyable though it was)!

4.

a) I started with the RGB components of the image.

Red Component

Green Component

Blue Component

Black: (C,M,Y)=(1,1,1)-(R,B,G)
(C,M,Y)=(1,1,1)-(0,0,0)
(C,M,Y)=(1,1,1)

Similarly,

Red: (C,M,Y)=(0,1,1)
Yellow: (C,M,Y)=(0,0,1)
Green: (C,M,Y)=(1,0,1)
Cyan: (C,M,Y)=(1,0,0)
Blue: (C,M,Y)=(1,1,0)
Magenta: (C,M,Y)=(0,1,0)
White: (C,M,Y)=(0,0,0)

Cyan Component

Magenta Component

Yellow Component








6.
b) In GIMP, choose
Colours
Components
Channel mixer
Switch the percentages on the red and blue channels.

The above image looks good to me as there is still white in the middle. If there is a problem, please let me know.

I am tired and can’t think about HSI right now. I will finish other questions after sleep.