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Geometry book recommendation.

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I'm a second year Computer Science student, and I need to get a decent book on geometry. I have asked my lecturer for a recommendation, but he recommended the notes (which are terse and incomplete, half the work we have done isn't covered by them, and half the notes we haven't covered). We've covered surfaces (planes, half planes, two and one sheeted hyperboloids etc.), SO3(R) matrices (IIRC), intersections, projections, projective space and homogeneous co-ordinates and surfaces in it, transformation matrices and some other things. Is there a book out there that would suit my needs? I already have "Applied Geometry for Computer Graphics and CAD" which covers some but not all of my course, and leaves a lot to be desired when it explains things (it doesn't prove anything, just provides equations and matrices). Thanks.

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You may find Dave Eberly's book, "Geometric Tools for Computer Graphics", handy. As with the other reference you mention, this one doesn't have a complete set of proofs of everything. And it doesn't cover all the obscure analytic surfaces such as the hyperboloid of two cusps. Still, its got a bunch of good stuff in there, and does have proofs of many things, including much of what you listed. You can find a description here:

Geometric Tools: Books

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