# Two points

Between two points we can draw a straight line segment. The division of this segment into a number of equal segments produces a gradient color between the two points (figure 2).

We have seen that the CIELAB  system has three axes of which two correspond to blue-yellow and red-green antagonisms. This way of locating colors is not the most useful. Generally speaking, we prefer to find a hue with a color wheel. The CIE so proposes a polar coordinate system for CIELAB space called CIELCH in which L corresponds to the L of CIELAB, C gives the distance of the color to the achromatic vertical axis of black to white and H the angle of hue expressed in degree. Zero degree corresponds to the red color.

If we use LCH coordinates in a Cartesian system we could transform the circle of hues into one of the axes. Consider then a plane defined by two axes, for example, for the abscissa and the ordinate, H and L or H and C with respectively C or L constant. Two points in this type of plan define a segment that can go through several hues. It is the equivalent of a circle in Cartesian coordinates.

Figure 3 shows a HL plan view with C = 50 and the segment defines by coordinate points [66, 50, 263] and [66, 50, 49]. This segment is divided into ten parts, we therefore have ten intermediate colors.

Figure 4 shows a graphical usage example of this gradient.

We can also confirm the relationship between two colors in exchanging their three coordinates between them. This produces, by coordinated, two other colors which are related to the previous ones and highlight them. Like each color has three coordinates in them exchanging two by two we find six additional colors. In total we have eight colors. These eight colors are the vertices of a parallelepiped rectangle whose faces are parallel to the plans formed by the three axes of the CIELAB orthonormal basis considered  two by two. In Figure 5a there are three square groups of four colors aligned. In each group, both basic colors we exchange the coordinates are placed at the bottom. They are reproduced below each of the new pairs of colors produced by the exchange of one of their coordinates. We see for example that in the group of last four colors on the right the two lower colors are the basic colors and both top colors correspond to a exchange of their L0 coordinate and L1. Figure 5b shows an graphical use example of the 2 basic colors and their 6 paired colors.