The basics of 3-D mountain plotting

In order to describe any object in our three-dimensional world, we must give at least three coordinates. These coordinates are usually labeled X (length), Y (width) and Z (height). This 3-D explanation is no exception. When you want to show an object, you must break it down into a number of points. Each point has its own set of X, Y and Z coordinates, which tells us where the point is located in space.
In addition to the locations of the points, we must ask ourselves how these points are connected to form the sides of the object. The final result will be a "wire-frame" graphic representation of the object (so called because the object looks like it is constructed out of thin wires strung between the individual points of the object). Figure 1 shows the wire-frame representation of a pyramid.

Figure 1

The pyramid in Figure 1 is made up of five points (labeled 1-5) and eight lines. Let's see how we find the coordinates of the points of this pyramid.
First we must draw a top view of the pyramid. A piece of graph paper is best for this. Draw two per- pendicular lines on the paper as in Figure 2. Label the horizontal line X, the vertical line Y and number the lines as shown. These will be the X and Y axes, the first two coordinates in the X-Y-Z group.

Figure 2

Next, draw the top view of the 3-D object and number each point where two or more lines intersect. Figure 3 shows the top view of our pyramid with its five points labeled.

Figure 3

Now draw another set of axis lines and label the horizontal line X and the vertical line Z. This set of axes will be used to draw a side view of the object in order to get the height coordinate (Z) for each point. Figure 4 shows the X-Z axes with the side view of out pyramid. Note that points 2 and 5 are at the same location on the side view, as are points 3 and 4. This is because they have the same X and Z locations.

Figure 4

Now that we've drawn our pyramid, we can write down the coordinates for each point. First let's find the coordinates for point 1.
To find the X coordinate, we can look at either Figure 3 or Figure 4. In either case, the X coordinate for point 1 is 0.
To find the Y coordinate, we look at Figure 3. The Y coordinate for point 1 is also 0.
To find the Z coordinate, look at Figure 4. The Z coordinate for point 1 is 5.
Repeat this procedure for the remaining four points in the pyramid and you should have a list that looks like Figure 5.

Point #	X	Y	Z
1	0	0	5
2	4	4	0
3	-4	4	0
4	-4	-4	0
5	4	-4	0

Figure 5