Introduction to the 3D space

In a 3D space, we need to recreate the basic elements which allow us to perceive the world.
We need to create  
 
  • a space objects which exist in that space
  • create an atmosphere for the space, such as lighting conditions and
  • point of view (perspective)
Space in 3D
In 2 dimensional space, we utilize 2 axes to represent images: x,y
 
  • The X axe represents the horizontal alignment
  • The Y axe represents the vertical alignment

In a computer based system we calculate pixel positions using x and y coordinates.

Cartesian Space

In a 3 dimensional system, we are still using a 2 dimensional screen but we use 3 D coordinates to change the perception of an object.
 

One essential concept that a first-time user of 3D computer graphics should understand is the notion of working within a virtual three dimensional space using a two-dimensional user interface.

To represent pictorial reality, 3D computer software uses the classical Euclidean/Cartesian mathematical representation of space. To represent the geometry of an object, the software uses the Cartesian coordinate system based on three perpendicular axes x,y,z intersecting at one point. This reference point is called the origine. You can find it by looking at the centre of the grid in any of the display windows

 
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, then extend your thumb to the right, hold your index finger up, and point your middle finger towards you. Your thumb is pointing in positive x, your index finger in positive y, and your middle finger in positive z. The point of origin is 0, 0, 0. The opposite directions represent negative x, y, and z.

  A small icon representing the three axes and their directions is shown in the corner of each window in. the SOFTIMAGE 3D display.
 

XYZ Coordinates

With the Cartesian coordinate system, you can locate any point in space using three coordinates. For example, if x = +6, y = -6, z = +6, a point would be located to the right of, below, and in front of the origin.
 

XZ, XY, YZ Planes

Since you are working with a two-dimensional interface, spatial planes are used to locate points in three-dimensional space.

The perpendicular axes extend as spatial planes: xz, xy, and yz. In the SOFTIMAGE 3D display, these planes correspond to three of the parallel projection windows: Top, Front, and Right.
 

Imagine that the xz, xy, and yz planes are folded together like tile top, front, and right side of a box.

This helps give you to keep a sense of orientation when you are working within the parallel projection windows.
Global and Local Coordinate Systems
The xyz coordinate system can be global or local.
 

Global Coordinates

When you place an object in 3D space, it is inside a world. The reference point of that world is called the origin (also known as the centre of the world). It is located at the centre (0, 0, 0) of the reference grid in the windows. Accordingly, the xyz coordinates locating the object in relation to the origin are called global coordinates.
 

Local Coordinates

A local coordinate system is thought of in terms of an object's own point of reference, which is its own centre. This centre also has three axes: x, y, and z. They are represented by colour-coded vectors: red for x, green for y, and blue for z.

(TIP) An easy way to remember the colour coding is RGB = XYZ.
  The centre of an object is only a reference - it is not necessarily in the middle of the object because it can relocated (as well as rotated and scaled).
 
So, how do you model in a 3d environment?