# Correctly combining two Quaternions

• Ed
In summary, the person is asking for help on how to correctly combine two angles representing terrain in order to rotate a software model based on the topography of the ground. They are concerned about the non-commutative nature of quaternions and how it may affect the rotation. They are seeking clarification and assistance.
Ed
Hi folks,

I have a little problem which seems to be melting my brain. I have a (software) model which I wish to rotate based on the topography of the ground. I'm using two angles to represent the terrain - a "North" and "East" elevation (hopefully that's self explanatory).

Once I have the quaternions for these two angles, how to I *correctly* combine them? Unless I'm misunderstanding something, multiplying the quaternions would result in the same effect as performing one rotation and then the other - which I think would be wrong (they're non-commutative, being about perpendicular axes).

Rotations aren't commutative either, which means the quaternions still represent what you want to do.

## 1. What is a Quaternion?

A Quaternion is a mathematical concept used to represent rotations in three-dimensional space. It is similar to a complex number, but with four components instead of two.

## 2. Why is it important to correctly combine two Quaternions?

Correctly combining two Quaternions is important because it ensures that the resulting rotation accurately represents the combination of the two individual rotations. Incorrectly combining Quaternions can lead to errors and distortions in the final rotation.

## 3. How do you correctly combine two Quaternions?

To correctly combine two Quaternions, you can use the quaternion multiplication formula: q = q1 * q2, where q1 and q2 are the two Quaternions to be combined. This will result in a new Quaternion, q, that represents the combination of the two original rotations.

## 4. Can Quaternions be combined in any order?

No, Quaternions must be combined in a specific order in order to accurately represent the combination of rotations. The order in which Quaternions are multiplied matters and depends on the specific application or system.

## 5. Are there any specific considerations when combining Quaternions?

Yes, when combining Quaternions, it is important to ensure that the Quaternions are in their simplest form, also known as being unit Quaternions. This ensures that the resulting rotation is accurate and avoids any potential errors. Additionally, it is important to normalize the resulting Quaternion to maintain its unit length.

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