Geometry was my favorite math class and I was the valedictorian of my class - like I just today found out my son is also.
Seeing 3 dimensions is not my strong suit, which is why I usually do experiments to see how something would look at a different angle. Knowing where the light sources are and where the vantage point is, there are some general principles about where the shadows should fall and what parts of an object should show more or less when the vantage point moves this or that direction.
Ray tracing.