What is Z in a 3D universe?

Question

I'm creating a 3D renderer in Java, which currently can render the wireframe of a cube using Points and lines and rotate the cube, the question is, what should Z be? And what should be set to Z? I'm guessing that the size of the cube should be set to Z?

Thanks for your time! Any answers would be much appreciated.

Answer 1

I think you might be missing some basic school math/geometry here. However, it's actually not that hard to understand.

Imagine a flat plane, e.g. a sheet of paper.

• The first coordinate axis will go straight from left to right and we'll call it X. So X = 0 means your point is on the left border. X = 10 might mean your point is on the right border (really depends on how big you define a unit of 1; this could be in centimeters, inches, etc.). This is already enough to describe some point in one dimension (from left to right).

• Now, we need a second axis. Let's call it Y. It's running from the top border (Y = 0) to the bottom (Y = 10). Now you're able to describe any point on the plane as you've got two positions. For example, (0, 0) would be the top left corner. (10, 10) would be the bottom right corner. (5, 0) would be the center point of the top border, etc.

• What happens if we add yet another dimension? Call it Z. This will essentially be the height of your point above the sheet. For example, Z = 0 could mean your point is sitting on the sheet of painter, while Z = 10 means your point is sitting 10 cm above the paper. Now you use three coordinates to describe a point: (5, 5, 0) is the center of the paper. (5,5,5) is the center of the cube sitting on your paper filling it and being 10 cm high.

When programming in 3D, you can use the same terminology. The only real difference is, that you're using a so called projection/view matrix to determine how to display this 3d positions on screen. The easiest transform could be the following matrix:

1 0 0
0 1 0

Multiplying this with your 3d coordinates you'll get the following two terms:

2d-x = 3d-x 2d-y = 3d-y

This results in you viewing the cube (or whatever you're trying to display) from straight above essentially ignoring the Z axis again (you can't render something sticking out of your display, unless using some kind of 3d glasses or similar technology).

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Overall, it's up to you how you use the coordinates and interpret them. Usually x and y refer to the plane (position on the ground or position inside a 2D world) while z might be the height or the depth (front or back). It really depends on the specific case. But in generic, it's really just another dimension like x and y.

Answer 2

3D means 3 "Dimensions". One dimension is "X", the other "Y", the third "Z". None have a sepcific direction, though it's convenient to conventionally assign a direction, for example "Forward", "Left", and "Up".

Something whose X, Y, and Z values are all equal to 0 resides at the origin, or center of the space. You can write this as (0,0,0) where the order of the parameters are (x,y,z).

A point or vertex at the location (1,0,0) is one unit in the X direction from the origin. So if you moved from (0,0,0) to (1,0,0), you would be moving purely in the X direction.

(0,1,0) is one unit in the Y direction away from the origin.

(0,0,1) is one unit in the Z direction away from the origin.

(1,1,0) is one unit in the X direction and one unit in the Y direction. So if X means "Forward", and Y means "Left", then (1,1,0) is forward-and-left of the origin.

So a basic cube can be defined by the following vertices:

(1,1,-1)
(1,-1,-1)
(-1,1,-1)
(-1,-1,-1)
(1,1,1)
(1,-1,1)
(-1,1,1)
(-1,-1,1)

Answer 3

Z usually means the out-of-plane direction if the current viewport lies in the x-y plane.

Your 3D world has its own coordinate system. You'll transform from 3D world coordinates to viewport coordinates when you render.