How can I find the offset rotation and position between two objects in 3D?

Question

I have two objects in 3 dimensions, one of them (Child) is attached to the other one (Parent) using the offset between them (XYZ - position and rotation).
Using the Vector3 library, how can I find that Child offsets from the Parent?

Further explanation: let's say we have the parent at position X:0 Y:0 Z:0 with rotations RX:0 RY:0 RZ:0, and there is an attached Child to it with the offset X:10 Y:10 Z:10, RX:90 RY:45 RZ:90 (which is what I want to know). Supposedly, I had the Parent with a different position and rotation, how can I get the offset between it and the Child (which in this case, it should be X:10 Y:10 Z:10, RX:90 RY:45 RZ:90) (in another word, I want the Child position and rotation as the Parent is the center of the map)

I've tried simple math and some other ways on the internet but with no success, since I'm pretty bad at calculating rotations (since vector3 libraries are pretty identical, so as Math libraries, any language should be fine).

Oren · Answer

Transform  A , B;

Vector3 avg_transform_up = (A.up + B.up)/2f;
Vector3 avg_position = (A.position + B.position)/2f;

transform.position = avg_position ;
transform.up = avg_transform_up;

Arthur · Answer

To get the local position, rotation you can decompose the local matrix of the child object. You can calculate the local matrix by multiplying the inverse global matrix of the parent with the global matrix of the child. Like this (example with glm)

Matrix4 invParentMatrix = glm::inverse(GetParent()->GetGlobalMatrix());
 LocalChildMatrix = invParentMatrix * GlobalChildMatrix;

You can also calculate the local position seperatly by using the same inverse parent matrix. Calculating the local rotation is a bit more work and also depends on your implementation.

Matrix4 invParentMatrix = glm::inverse(GetParent()->GetGlobalMatrix());
 LocalChildPosition = invParentMatrix * glm::vec4(GlobalChildPosition, 1.f);

How can I find the offset rotation and position between two objects in 3D?

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