everyone! I am hoping to get some direction and book recommendations. I am an artist and have been learning from an art teacher a little about the role that geometry played for the Old Masters and the artists that lived before them thousands of years ago. Something he has said to me is, “Every drawing problem is actually a geometry problem.” I am starting to see the connection when thinking about linear perspective, how light and shadow fall on 3d objects, how rectangular and triangle grids can be used to transfer images accurately, and orthographic views of the human figure being used to design sculptures. It’s incredibly interesting to me but the amount of subjects related to this are overwhelming.
One problem that really interests me is related to cross sections of the human body. Medical imaging works by taking images of the human body in sagittal, coronal, and transverse planes. By looking at and accurately drawing the curved outline created from images taken in all 3 planes, you could draw a kind of topological map of the surface of the human body, similar to a mesh in 3D modeling, which would be incredibly helpful for artists to help them draw, paint, and sculpt the human body with a lot of detail. An extension of this problem would be drawing that “3D mesh” in perspective, from different angles, in different lighting conditions, etc. I’ve attached some images to help illustrate the things I am talking about. I'm not currently in college but I’ve attended college for a couple of years (as a finance major, not math) and I’m having a hard time figuring out what subjects are most relevant and which ones are unnecessary. Some subjects that I’ve come across that might be relevant are: proofs, descriptive geometry, projective geometry, plane and solid geometry, differential geometry, algebraic geometry, linear algebra, and calculus. This sounds like a really difficult geometry problem, one that I have absolutely no idea where to even begin with. But I would like to try because this is fascinating to me. A related problem is figuring out how to pose Leonardo Da Vinci’s stick figures in any way, in any perspective.
I began learning simple geometric constructions using a compass but felt very dissatisfied since it wasn’t explained why or how the constructions worked. So, I’ve recently begun working through “Euclid’s Elements,” and “Geometry: Euclid and Beyond,” by Hartshorne and I’m finding it challenging but fun. I’m using a compass and a straight edge to understand each proof as well as I can. My question to y'all is, what other subjects would I need to study if I was interested in understanding and solving problems related to: linear perspective, plane and solid geometry, orthographic projection, and the problems previously mentioned? Understanding the why, not just the how, is what I am after. If you have recommendations for the subjects I should learn to understand and tackle these problems, as well as any book recommendations that someone with minimal math background could work through on their own, that would be greatly appreciated. This is my first post so I hope I left enough context!
Different views of projected figure drawing
Albrecht Durer's cross sectional anatomy
