My final purpose is to compute the distance of a point from a plane. The problem is that I have to transform the plane coefficient with the modelview matrix, so I thought I had to use the inverse transpose to compute the transformed normal but that is really cpu expensive. Is there another way to achieve the same result?

# transforming planes

I assume you want to transform your clipping planes into object space in order to perform clipping in object space? If so, I think there is no other way around it. You could do the clipping in view space but then again, you would have to transform all the vertices into view space first. But itâ€™s still faster to do culling in object space and transform only visible vertices than transform all vertices into view space. And of course bounding boxes or spheres speed things up.