How to adapt DirectX-style world/view/projection matrices to OpenGL?

Question

I have an application which uses DirectX, and hence a left-handed world-coordinate systen, a view which looks down positive z and a projection which projects into the unit cube but with z from 0..1.

I'm porting this application to OpenGL, and OpenGL has a different coordinate system etc. In particular, it's right-handed, the view looks down along negative z, and the projection is into the real unit cube.

What is the easiest way to adapt the DirectX matrices to OpenGL? The world-space change seems to be easy, just by flipping the x-axis, but I'm not entirely sure how to change the view/projection. I can modify all of the matrices individually before multiplying them together and sending them off to my shader. If possible, I would like to stick with the DirectX based coordinate system as far down the pipeline as possible (i.e. I don't want to change where I place my objects, how I compute my view frustum, etc. -- ideally, I'll only apply some modification to the matrices right before handing them over to my shaders.)

Answer 1

Not tested or anything, just out of the top of my head :

oglProj = transpose(dxProj)
glScalef (1., 1., -1.);  // invert z
glScalef(0.5, 0.5, 1); // from [-1,1] to [-0.5, 0.5]
glTranslatef(0.5, 0.5, 0) // from [-0.5, 0.5] to [0,1]

oglView = transpose(dxView)
glScalef (1., 1., -1.);  // invert z

oglModel = transpose(dwModel)
glScalef (1., 1., -1.);  // invert z

oglModelView = oglView * oglModel

Answer 2

There is an age-old extension for OpenGL exactly for that: GL_ARB_TRANSPOSE_MATRIX. It transposes matrices on GPU and should be available on every video card.