Posted by dxli on Jan 23, 2016; 11:37am
URL: https://forum.librecad.org/Change-rotation-axis-tp5712839p5712846.html

in general, 3D rotation can not be based only on the projected, because 3D rotation needs 3D information, while the projected contains only 2D.

consider 3D as a linear mapping of 3D space V=(x, y, z), while the only available information is projected V'=(x', y', 0)

V' = P V
R(V') = P R(V)

with R(V) denotes the linear mapping of rotation.

Only if the rotation is in the range space of projection P, P R(V) = R(P V), the rotation can be done using only projected coordinates, i.e. the rotation is around the null space of projection.

in a simple case of isometric projection, the null space is the 3D line, x=y=z, rotation is around this axis is the same as rotation in the projected space.

Evan K wrote

I mis-spoke. I am using the isometric grid. Keep getting the names confused, sorry!