Find X/Y/Z rotation angles from one position to another

Question

I am using a 3D engine called Electro which is programmed using Lua. It's not a very good 3D engine, but I don't have any choice in the matter.

Anyway, I'm trying to take a flat quadrilateral and transform it to be in a specific location and orientation. I know exactly where it is supposed to go (i.e. I know the exact vertices where the corners should end up), but I'm hitting a snag in getting it rotated to the right place.

Electro does not allow you to apply transformation matrices. Instead, you must transform models by using built-in scale, position (that is, translate), and rotation functions. The rotation function takes an object and 3 angles (in degrees):

E.set_entity_rotation(entity, xangle, yangle, zangle)

The documentation does not speficy this, but after looking through Electro's source, I'm reasonably certain that the rotation is applied in order of X rotation -> Y rotation -> Z rotation.

My question is this: If my starting object is a flat quadrilateral lying on the X-Z plane centered at the origin, and the destination position is in a different location and orientation where the destination vertices are known, how could I use Electro's rotation function to rotate it into the correct orientation before I move it to the correct place?

I've been racking my brain for two days trying to figure this out, looking at math that I don't understand dealing with Euler angles and such, but I'm still lost. Can anyone help me out?

Answer 1

First do the translation to bring one corner of the quadrilateral to the point you'd like it to be, then apply the three rotational transformations in succession:

If you know where the quad is, and you know exactly where it needs to go, and you're certain that there are no distortions of the quad to fit it into the place where it needs to go, then you should be able to figure out the angles using the vector scalar product.

If you have two vectors, the angle between them can be calculated by taking the dot product.

Answer 2

Can you tell us more about the problem? It sounds odd phrased in this way. What else do you know about the final orientation you have to hit? Is it completely arbitrary or user-specified or can you use more knowledge to help solve the problem? Is there any other Electro API you could use to help?

If you really must solve this general problem, then too bad, it's hard, and underspecified. Here's some guy's code that may work, from euclideanspace.com.