I thought that whenever you transform an object to world space, then view space and finally screen space, the last matrix you apply(the projection matrix) normalizes the z values between 0 and 1.
However, I'm getting big z coordinates, which implies that the projection matrix didn't normalize it. Am I doing something wrong? I mean, all I do is:
gl_Position = projection * view * world * gl_Vertex; You are missing a few key points.
After the application of the projection matrix, you have a 4-component vector in clip space (not screen space), which is a homogeneous coordinate system in which clipping will be performed (after your vertex shader).
After clipping, the surviving coordinates are divided by the w component to get normalized device coordinates in (-1, 1). A transformation will then be applied to move from NDC space to window coordinates, where the X and Y coordinates are normalized based on the viewport provided to OpenGL and the Z coordinate is normalized based on the depth range, which is ultimately what gives you your (0, 1) range for depth (unless you use glDepthRange to set a different range).
If you want to access this normalized Z value in your vertex shader, you will need to do the computation manually in the shader (based on the information above).
gl_FragCoord.z should give the window-space (normalized) depth in the fragment shader. \$\endgroup\$ Multiplying a vertex position by the world, view, and projection matrices generates a position in homogeneous coordinates, i.e. (x, y, z, w). Only after dividing by w are the xyz values between -1 and 1 (note: not 0 to 1).
If you're not familiar with homogeneous coordinates, see these other questions on this site: What does the graphics card do with the fourth element of a vector? and Do I need the 'w' component in my Vector class?
