I'm writing a book on geometry with a competitive programming approach. I've just started, so I haven't written much at all yet but I'd like to have some early feedback.
My goal is to be easy to understand and practical (quite code-oriented), but also to explain important concepts in depth and try to build intuitions / interesting interpretations, because I think I can bring some things on that front. In what I've written I feel like the "in depth" part is okay but I'm afraid the "easy to understand" part is a bit lacking.
So far I've covered complex numbers, point representation, dot product, cross products and their applications, as the first part of a "Basics" chapter. There will eventually be other chapters, covering things like sweep algorithms, algorithms on convex polygons/hulls, and especially 3D geometry, which I like a lot.
I'd like to have feedback mostly on writing style and on ways in which I can make the explanations more accessible (e.g. adding examples, figures, rephrasing, etc.), but any comment or suggested improvement is welcome. I know I've not written much but there are some concepts in there which I found tricky to explain, so there should be plenty to criticize. :)
Here's the link (I'll update it as I fix things and add sections): https://vlecomte.github.io/cp-geo.pdf