## Color coding

Colors and light are essential to visualization. Most visualization techniques contain a step in which data values are mapped to colors to make the range of the data visible (see the next sections). The interpretation of results produced by these visualization techniques depends crucially on the mapping of data to colors because the human eye is more sensitive to some parts of the visible spectrum of light than to

other parts and the brain may interpret different color patterns differently. Since the mapping of data values to colors involves color coding, we will describe this in some detail. There exist quite a few color coding systems. We discuss here the RGB, CMY, and HSV systems.

The RGB code system is mainly used in television sets and computer screens. Color is determined by the three independent components Red (R), Green (G), and Blue (B). These components correspond with the red, green, and blue cathode ray tubes. Each component has values in the interval [0,1]. A value of 0 corresponds to black and a value of 1 corresponds with full color. For example {R=0, G=0, B=0}is black, {R=1, G=0, B=0}is full red, {R=0, G=1, B=1}is full cyan, and {R=1, G=1, B=1}is white. Every color can be constructed by taking the right combination of the three components. However, the number of values that can be represented by cathode ray tubes for each component in the interval [0, 1] is finite. Most graphical display systems currently use 256 different values, which means that 256**3 = 16,777,216 different colors are supported: more than enough for most applications.

Another color coding system is the CMY system. Color is determined by the three independent components Cyan (C=1-R), Magenta (M=1-G), and Yellow (Y=1-B). It is widely used in the publishing world. The CMY system is related to the RGB system as follows: C=1-R, M=1-B, and Y=1-G. It is clear that these systems are complementary to each other.

The color coding which is used most frequently in visual environments is the HSV system. The three components Hue (H), Saturation (S), and Value (V) have values between 0 and 1. Whereas one can view the volume spanned up by the three independent components of the RGB and CMY color systems as a unit cube, the HSV volume is an inverted cone. The Hue is the angular coordinate in a plane perpendicular to the symmetry axis, where H=0 corresponds to red and an angle of 0 degrees, H=0.33 corresponds to green and an angle of 120 degrees, H=0.66 corresponds to blue and an angle of 240 degrees, and H=1.0 corresponds again to red. The Saturation determines the saturation of the color. Saturation is the radial coordinate in the plane perpendicular to the symmetry axis, so that S=1 corresponds to full saturation and S=0 corresponds to no color (i.e. white), S=0 is situated on the symmetry axis and S=1 corresponds to the maximum radius in the plane, i.e. the boundary of the cone. The Value determines the intensity of the color. Value is the coordinate along the symmetry axis of the cone, where V=0 corresponds to no intensity (i.e. black), and V=1 corresponds to maximum intensity. V=0 is at the top of the cone and V=1 is at the base of the cone. We will not discuss the relation between the RGB and HSV system as it is a complicated one. Interested people are referred to refs. [2] and [3]. HSV is frequently used in visual environments, because the effects of manipulating the components are much more predictable than in RGB and CMY. HSV corresponds to a more natural experience of colors than the other systems provide.

In most visualization techniques, colors from red to blue are used to reveal transitions in some quantity. If one wants to use the complete set of available colors one needs to map the range of values to this complete set. Storing this mapping consumes too much memory.

Therefore, one normally chooses N colors of the available set (typically N=256) and maps the range of values to these N colors. This mapping of the values to colors will be denoted as the colormap in the rest of this report.

It is important to notice that using colors to reveal transitions in quantities can be misleading if there are no transitions at all, e.g. for a monotonically increasing quantity. For the kind of phenomena in which the quantity changes smoothly it is better to use continuously changing schemes like gray scales, saturation scales, and intensity scales. This immediately shows another advantage of the HSV code

system: saturation and intensity are natural variables in the HSV system.