Translating between cartesian and Isometric coordinates

Game Mechanics
#1

Morning all.

my for-fun project at the moment is a basic isomorphic base building tower defense strategy game.

I need to be able to translate between my easy to use 3D Cartesian world system to my 2D Isometric screen projection.

I thought I would create a thread on this, to document my progress and get a bit of discussion going.

UPDATE:

My world cord system will use 3D XYZ coordinates. I need to convert this to the 2D XY cord system that the screen uses to draw.
The goal is to be able to then draw my 3D world in 2D Isometric projection.

I started by Wikipedia-ing that: http://en.wikipedia.org/wiki/Isometric_Projection

The first important point I noticed it that I’ve got the camera angles wrong on my sprite renders :stuck_out_tongue:

After reading through the wiki article, i moved to this page that answers pretty much all my questions.

From this I was able to sketch up the following function for transforming from world to screen cords.


Vector2 cameraOffset;

// these could probably be a constant.  
float a = arctan(1/2); 
float s = 100f; // the edge-width of one cubic cell in the world.

Vector2 World2Screen(float X, float Y, float Z)
{
	float screenX = cameraOffset.X + (X-Z)cos(a)s;
	float screenY = cameraOffset.Y + ((X+Z)sin(a)-Y)s;
	return new Vector2(screenX, screenY);
}

I’ve not had a chance to run this code yet, but any comments, suggestions and constructive crit’ are welcome.

Thanks for reading, have a good day,
Matt

#2

your sin(a) and cos(a) are redundant. You can replace them with a constant.

In this case since you have defined a=arctan(1/2) then sin(a)=1/sqrt(5) and cos=2/sqrt(5).

Its more normal to “cheat” with isometric sets and change the ratios to things that are not irrational.

#3

Hi,

Glad that the forums are back :smiley:

Yes, I realised that most of the processor heavy stuff actualy is constant, so I pre-calculate that, store it as a variable, and use it each time. This is WAYY quicker, obviously :slight_smile:

I dont have my code with me at the moment, but I will post the method I’m now using along with some screens later this evening. What I’m going to work on next is getting a basic particle system going.

The next problem I need to solve is automaticaly finding the center point of the base of a sprite.