It makes a lot of sense to prefer to think about the real problem. Years ago at school my group wrote a ray tracer from scratch, after a few months we noticed

It makes a lot of sense to prefer to think about the real problem. Years ago at school my group wrote a ray tracer from scratch, after a few months we noticed that the vector class had an inverted scalar operation. The program worked, because we had inverted the entire vector space as we had just fixed the code until it worked. After fixing the vector class most of the other formulas in the program started to look more reasonable :)