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Render the Depth Buffer

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Hello everybody, I currently render the depth buffer in my application by copying it to a texture, clearing the screen and drawing a fullsize quad to display it. (2 passes) Somehow, this strikes me as an ugly way to go about and do it. Is it possible to just access the depth buffer in a GLSL shader and change the fragment color to it? This would allow me to do all this in one pass.
// draw the mesh to fill the depth buffer
for (unsigned int i = 0; i < meshes.size(); i++)
	if (!visible[i]){continue;}
// copy depth buffer to texture
glBindTexture(GL_TEXTURE_2D, depthTexture);
glCopyTexSubImage2D(GL_TEXTURE_2D, 0, 0, 0, 0, 0, 512, 512);

// clear screen
// enable texturing and bind the depth texture
glBindTexture(GL_TEXTURE_2D, depthTexture);
// overlay texture to fullsizequad

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In the pixel shader you can use gl_FragCoord as an input, and if it's in screenspace then the z coord should be depth. Then draw that as a color output?

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