3-D Coordinate Space

Imagine yourself (as is easy to do) at the very center of the universe. There are six directions ranged about you in three pairs:

• Left and right--the horizontal directions.
• Up and down--the vertical directions.
• Forward and backwards (or front and behind)--for which we have no general name.

Are all these pairs the same to us? Absolutely not. Because of gravity, up and down have a physical meaning quite distinct from left and right or forward and backward. Pasted as we are to the surface of what (for most practical purposes) is a flat plane, we do not have the same freedom to move up and down as we do to move in the other directions.

In an abstract 3-D space, such as that found in a 3-D computer graphics application, there is no gravity, and so there is no natural meaning to up and down, left or right, forward and backwards. We simply have a pure Cartesian space of 3-D dimensions (named for the great philosopher and mathematician Rene Descartes), and call the dimensions X, Y and Z. We choose a point in this space and call it the origin. As the origin, it is the location where X=0, Y=0, and Z=0, and the point is designated as (0,0,0). We run three axes right through this point, the X, Y, and Z axes, each perpendicular to the other two. Now we can designate the exact location of any point in our space relative to the origin. For example, a point at (3,2,1) can be reached by starting at the origin (0,0,0) moving 3 units of length (perhaps inches) in the X direction, then moving 2 units in the Y direction, and finally 1 unit in the Z direction. The numbers are called "coordinates" and therefore the defined space is called a 3-D coordinate space. The coordinates can be negative as well as positive. For example, to find the point at (-3,2,1), we would move down the X axis in the opposite direction as we did before. If the positive direction is left, the negative is right, and so forth.

Although the 3-D coordinate space in a computer application is a mathematical abstraction, our human experience guides it quite a bit. In the vast majority of objects and scenes you will develop, the direction of up and down will be evident and distinct from the other axes. In most applications the X dimension is horizontal to the gravitational sense of the scene. It is the horizon. Positive X values increase to the right, negative values to the left. The Y dimension will typically be vertical, positive coordinates increasing upwards, negative coordinates downward. Z will generally be depth, negative coordinates increasing as you move forward into the scene past the origin, positive coordinates increasing as you retreat backwards from the origin. But these are not hard and fast rules, and in fact, Fractal Design Ray Dream products make the Z axis the vertical one, up and down with respect to the gravitational sense of the scene. And Lightwave 3D orients the positive z axis toward the rear rather than the front.

Comments are welcome