I am writing a paper which includes a fair bit of (euclidean and projective) geometry. I would like to be able to create some nice illustrations to accompany the proofs, and I'm hoping there is some software that could make this easier.
In particular, I want to draw spheres, planes, straight lines, arrows, and if possible some free-form lines. I would prefer to be able to draw these without needing to specify equations, kind of like in Microsoft Powerpoint. It would also be nice if I could rotate the drawing in 3D to be able to see it from different perspectives.