I think 3D geometry has a lot of quirks and has so many results that un_intuitively don’t hold up. In the link I share a discussion with ChatGPT where I asked the following:
assume a plane defined by a point A=(x_0,y_0,z_0), and normal vector n=(a,b,c) which doesn’t matter here, suppose a point P=(x,y,z) also sitting on the space R^3. Question is:
If H is a point on the plane such that (AH) is perpendicular to (PH), does it follow immediately that H is the projection of P on the plane ?
I suspected the answer is no before asking, but GPT gives the wrong answer “yes”, then corrects it afterwards.
So Don’t we need more education about the 3D space in highschools really? It shouldn’t be that hard to recall such simple properties on the fly, even for the best knowledge retrieving tool at the moment.
Back in 2001, I wrote my own 3D graphics engine, down to the individual pixel rendering, shading, camera tracking, Z buffer, hell even error diffusion dithering for 256 color palettes.
And I still don’t know half the terms you just used.
I do know points, polygons, vectors, normals, roll, pitch, yaw, Lambert’s Law shading, error diffusion feedback…
And my Calculus 2 teacher admired my works and told me I had the understanding of a Calculus 4 student.
impressive, I’d like to ask abou stuff like how long it took you and stuff. But in this discussion I’d like to mention that I didn’t use any complicated terms, only orthogonal projection (middle school) and perpendicularity (elementary school).