x, y ...

Assume that the world is composed of uniform units of measurement. These units have a horizontal and vertical direction (right/left and up/down).

By naming these directions axes, you can assign them individual names.

As a standard, the right/left axis is known as x and the up/down axis is known as y.

If you give these directions numeric intervals, you can count grid units in either direction. It is then possible to assign points of intersecting intervals by describing them as a set of two numbers (x,y):

The first number describes the horizontal position.

The second number describes the vertical position.

... and z

Introducing a third axis which extends "through" space (front/back) adds the dimension of depth which open up the world of three dimensions.

This new direction adds the letter Z to our numeric set (x,y,z). The concept of three-dimensional space represented in this way is known as Cartesian Space.

Within this representation of space, you need a reference point from which to start counting.

Each axis is represented as a straight line. These perpendicular axes cross each other at one point.

This reference point is called the origin, which is represented by the numeric set (0,0,0).

XYZ Axes

To remember the direction of the x, y, z, axes, use the "right-hand" rule:

Hold up your right hand so that your palm is facing you with your fingers pointing up.

Then extend your thumb to the right, hold your index finger up, and point your middle finger towards you. Your index finger is pointing in the positive y, your middle finger is pointing in positive z, and your thumb is pointing in positive x.

The opposite directions represent negative x, y, and z.

XYZ Coordinates

With the Cartesian coordinate system, you can locate any point in space using the three coordinates.

For example, if x = +3, y = +2, and z = +2, a point would be located to the right of, above, and in front of the point of origin.

Since you are working with a two-dimensional interface that is seen as a flat surface, spatial planes are used to locate points in three-dimensional space.

The perpendicular axes extend as planes: xz, xy, and yz.

These planes correspond to the three parallel projection views.

The objects created by virtual geometry are located at points which can be described in x, y, z, coordinates.

The object's geometry is designated around one point which is called "the centre" of the object.

The object's centre is used as a reference point for positioning the object in relation to the point of origin (the centre of the 3D world).

The Front, Top, Right and Ortho (presented in the Interface section) window views are called parallel projection views. In a parallel projection view, lines do not converge.

The distance between an object and the camera has no influence on the scale of the object. Even if one object is further away, both appear to be the same size.

The fourth view used by default in SOFTIMAGE 3D is the perspective view.

The perspective view simulates the distortion of an object in space. The lines of an object converge to a vanishing point. Objects closer to the camera appear larger and those further away appear smaller.

The perspective view is also the window used to render the final image.

Last updated 04-dec-1998