In 3d graphics, what is camera or eye space?

Question

I'm trying to learn 3d graphics programming through "Learning Modern 3D Graphics Programming" by Jason L. McKesson.

I have not really looked at other guides, but this guide seems to emphasize the theory and mathematics behind 3d graphics. Right now, I am stuck on this page:

http://www.arcsynthesis.org/gltut/Positioning/Tut04%20Perspective%20Projection.html

I am not exactly sure what he means by camera space, and why it is necessary to project a 3d world onto a 2d surface. This question is kind of vague, so instead of a full explanation, links that might give me a different way of explaining these concepts would be appreciated as well.

Answer 1

Well, it's necessary to project a 3D world onto a 2D surface since your screen is a 2D surface.

3D graphics works in different "coordinate spaces", and these are converted between to get a final scene.

Imagine for example modelling a city. You might define the bottom left corner of the map as (0, 0), and the top right as (1000000, 1000000). You might also say that as a rule, one point will represent a foot of real space. This representation we will call World Space.

To draw your city, you'll want to import some models of buildings, and place them in the world. So you get your model of a building, but when you're making this model, you don't want to have to worry about the size of the world or where it will be - you maybe will say that the building's bottom left corner is at (0, 0) and its top right is at (1, 1). This representation we will call Model Space. In the world though, the building might be placed at (104, 136) and you might want it to be 1000x1000 pixels, so you will need to translate it to (104, 136) and scale it up 1000x. This is converting it from Model Space to World Space.

Finally, Camera Space is how you move around in the world. If you think about it, moving around in the world could be thought of in two ways (at least): You move around the world, or the world moves around you. So to make movement easy, we'll say that the camera is always at the point (0, 0) facing down some axis. Now if you want to move forward 10 pixels, instead you just move everything back 10 pixels. If you want to rotate, rotate the world instead. So to render the building, first we want to transform it from Model Space to World Space. Now, to actually draw it, we want to know where it is relative to the viewer, so we move it from World Space to Camera Space.

. . .

As an aside, if you want to understand this very well, a good exercise is to write a 3D wireframe renderer, separate from OpenGL. Your only drawing function available is DrawLine(x1, y1, x2, y2) which draws a line on the screen from (x1, y1) to (x2, y2).

Answer 2

why it is necessary to project a 3d world onto a 2d surface

All graphics is just 2D images. 3D graphics is thus a system of producing colors for pixels that convince you that the scene you are looking at is a 3D world rather than a 2D image. The process of converting a 3D world into a 2D image of that world is called rendering.

A projection, for the purposes of rendering, is a way to transform a world from one dimensionality to another. Our destination image is two dimensional, and our initial world is three dimensional. Thus, we need a way to transform this 3D world into a 2D one.

I am not exactly sure what he means by camera space

Before this point, vertex positions were expressed directly in clip space. Recall that the divide-by-W is part of clip space vertex positions. Perspective projection is a way of transforming positions into clip space such that they will appear to be a perspective projection of a 3D world.

This transformation process has well-defined outputs: clip space positions. But what exactly are its input values?

That's camera space.

This is not a space that OpenGL recognizes (unlike clip-space which is explicitly defined by GL); it is purely an arbitrary user construction. However, it can be useful to define a particular camera space based on what we know of our perspective projection. This minimizes the differences between camera space and the perspective form of clip space, and it can simplify our perspective projection logic.