/ic/ - Artwork/Critique

>>4395246
Hey bro, I had a really tough time with this problem too. It's really fundamental to doing anything useful with perspective and yet NO ONE covers it.
This pic explains one nice idea for how to do it. The core is, All you really have to do is treat each plane of the cube as its own rotation problem. Rotate each plane by the exact same amount and you've rotated the cube. And of course, all you really need to do is to rotate one plane and find its orthogonals and then it's easy to construct the rest of the cube. You need one plane of the cube to be parallel to a plane with known orthogonals (and the ground plane is one such plane) and then you need to construct an ellipse representing the rotation you want to do on a cube edge in that plane (Marshall and others give examples of simple rotations like that). There are a few techniques that would let you use the same ellipse to rotate the known orthogonal by the same amount, or you can just do what this pic does, and realize that (an equivalent orthogonal parallel to) the rotated orthogonal must be tangent to the rotation ellipse at the point where your rotated cube edge intersects the ellipse.
Repeat on the other cube edge parallel to your first one. Now you have two orthogonals. The point where they intersect is the vanishing point for all lines orthogonal to your rotated cube face. Now you have your new rotated set of axes and you can continue on your way.
This pic looks a little informal but it can easily be formalized with real vanishing points. Let me know if any of this is confusing and I'll draw an example for you.

>>4393208
Start from a plane where you know the orthogonals, e.g. the ground. And find the tangent of the ellipse that lets you rotate from the ground to your arbitrary surface. Do this twice for two different points on the surface and where they intersect is the vanishing point of all orthogonals.

>>4385500
does pic related illustrate what you are talking about?