2D_Colorplan.html IM

2D Graphs to Color Planes

Again we are going to use Fig3 as your example. Each point on the line top line of Fig 3 represents how tall the plant is at a certain amount of water and 14 hours of sunlight per day. The higher the point is on the y-axis (which equals plant growth), the taller the plant is. If a color bar is placed along the y-axis, so that the maximum value of plant growth is equal to red, and the minimum value is equal to purple, then each point of the line can be presented by a color.

Figure5- Color bar indicated plant growth equals a color.

Figure6 - Each point of the top graph is equal to a color.

A point at the top of the curve is colored red, since red stands for a maximum value, the point no longer needs to be on a curve for the viewer to know that it is a maximum value. The color takes the place of the need for the y-axis, because the color now represents height just as the y-axis did. The line can then be compressed into a single horizontal line of color. Red represents where the curve used to be height, and the purple represents where the curve used to be low.

Figure 7- The color line below the graph represents
the plant growth at 14 hours of sun per day.

Color can be similarly substituted for each point on the other four graphs. The five lines of color are stacked on top of each other in a square. The colors represent plant growth, the x-axis is still the amount of rain per week, but the y-axis is now the amount of sunlight per day.

Figure8 - The color represents plant growth,
with the amount of water on the x-axis and
amount of sun on the y-axis.

The following movie shows the process of going from a 2D graph (family of curves) into a single plane of color.

A Color Plane = A Surface Graph

What is a surface graph?

A surface graph of a function shows two independent variables on two axises, i.e. x-axis and y--axis, and a dependent variable on the z-axis. This graph differs from the type of 3D graph we will examine, because one of the axises is the dependent variable. The 3D graph will examine has an independent variable on each axis.

Example of a surface graph:

Figure9 - The surface plot of the Gaussian distribution function, e^(-(x^2+y^2)). The x and y axises are the x and y values of the function from 0 to 40, and the z axis is the resulting value of the function with a range from 0 to 1.

A color plane can be changed into a surface graph.

A color plane, like Fig8, can be converted into a surface graph. If the color plane is laid down like the floor of a room, each color point on the graph would be like a small tile on the floor. If the color is changed back into height; the height would range from the floor to the ceiling of the room, and would represent the z-axis. A red tile which represents maximum plant growth would be given the maximum height value, meaning that tile would be close to the ceiling of the room. A purple tile would which represents the lowest amount of plant growth would be given the lowest amount of height meaning that it would still be on the floor. A green tile would be suspended half way between the floor and ceiling. The surface created by raising each of these color tiles to a corresponding height would create a surface graph.

A color plane has two independent variables on two axises; a surface graph also has two independent variables on two axises. In a surface graph the dependent variable is represented by a third axis, and in a color plan the dependent variable is represented by color instead of another axis.

In the next section we are going to add another axis (independent variable) to the color plane and get a 3D image of color, that has independent variables on each axis.

Last revised July 2, 1996
http://www.sv.vt.edu/class/surp/surp96/laughlin/stat/3D_tutor/2D_Colorplan.html