Page 190 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 190
If and , then
Application to Computer Color Models
Colors on computer monitors are commonly based on what is called the RGB color model. Colors in this system are created
by adding together percentages of the primary colors red (R), green (G), and blue (B). One way to do this is to identify the
primary colors with the vectors
in and to create all other colors by forming linear combinations of r, g, and b using coefficients
between 0 and 1, inclusive; these coefficients represent the percentage of each pure color in the
mix. The set of all such color vectors is called RGB space or the RGB color cube. Thus, each color
vector c in this cube is expressible as a linear combination of the form
where . As indicated in the figure, the corners of the cube represent the pure primary colors
together with the colors, black, white, magenta, cyan, and yellow. The vectors along the diagonal
running from black to white correspond to shades of gray.
Sometimes a vector is positioned so that its initial point is not at the origin. If the vector has initial point and
terminal point , then
That is, the components of are obtained by subtracting the coordinates of the initial point from the coordinates of the
terminal point. This may be seen using Figure 3.1.13:
