Geometric modelling tends to need a lot of detailed work for two main reasons.

Firstly, you probably have a variety of analytic shapes to represent — things like lines and circles in 2D or cubes and spheres in 3D. Even seemingly simple questions, like whether two such shapes intersect or not, can require a significant amount of logic to calculate the answer. That logic will often be specific to the exact combination of shapes you have, because the number of freedoms and nature of any symmetries in the shapes you’re working with can mean you would use completely different algorithms for superficially similar situations.

Secondly, while you’re probably going to implement a lot of analytic calculations, in realistic models you’re probably going to end up using numerical methods as well. That can be because you need to work with geometry like Bézier curves or NURBS surfaces that has many freedoms. It can be because even if you start with convenient analytic shapes, new geometry that you derive from those shapes, for example by offsetting a single shape or by combining details from multiple shapes as in constructive solid geometry, won’t in general have an analytic shape itself.

By the time you allow for the numerous different types of constraint that you might want to enforce between different types of geometry and the numerous different ways you can construct new geometry from geometry you already have, the scale of the problem explodes. And on top of that, almost everything you do is going to have numerical sensitivity issues, and all but the simplest algorithms are going to need detailed, careful analysis to make sure you really have covered all the possibilities. In this field, “edge case” and “corner case” are literal terms and not just figures of speech!

To give a practical example, without looking up how to do it, could you confidently calculate whether two arbitrary cuboids are completely separate or they touch or intersect somewhere? As another example, given an arbitrary parametric surface, a sphere in a position just resting on that surface, and the constraint that the surface of the sphere must remain tangent to the parametric surface without intersecting it anywhere, how would you calculate the path the centre of the sphere will follow if you introduce gravity to start the sphere rolling in a certain direction along the surface?

These are relatively simple problems in the field, but each already has some subtlety that leaves the “obvious” solutions incomplete. Solve a few thousand problems like that, each unique and with its own calculation strategy, and now you’re starting to get a practically useful geometric modelling system. (You’ve also probably had a team of dozens of mathematicians and developers working on it for decades.)