Jump to content
  • Advertisement
Sign in to follow this  
CulDeVu

Vector Multiplication

This topic is 2218 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

Hey everyone!

I was learning about quaternions the other day and I noticed something interesting about quaternion multiplication.

The component-wise form of Q3=Q1*Q2 is
w3=w1*w2 - v1.v2
v3 = v1*w2 + v2*w1 + v1Xv2

I noticed it looked very similar to a simple algebraic expansion of the form (a + b)(c + d).

Well if you look at the multiplication as a multiplication of their components you get:

(w1 + v1)(w2 + v2) = w1*w2 + w1*v2 + w2*v1 + (v1)(v2)

If you cancel terms from the first set of equations:

(v1)(v2) = v1Xv2 - v1.v2

What type of multiplication is this?

Thanks,
CulDeVu

Share this post


Link to post
Share on other sites
Advertisement
If you write the quaternions as 4D vectors with basis 1, i, j, k, then the multiplication is simply defined using the distributive law you used in your post with rules i^2 = j^2 = k^2 = -1 and i*j = k, j*k = i, k*i = j (the other products follows from these identities). Since the scalar-vector representation of the quaternions is equivalent to this representation, it is clear that the product in that representation should resemble the application of the distributive law. That product is simply the quaternion product of two imaginary quaternions. The result is indeed a non-imaginary quaternion having both a scalar and vector component.

Share this post


Link to post
Share on other sites
Sign in to follow this  

  • Advertisement
×

Important Information

By using GameDev.net, you agree to our community Guidelines, Terms of Use, and Privacy Policy.

We are the game development community.

Whether you are an indie, hobbyist, AAA developer, or just trying to learn, GameDev.net is the place for you to learn, share, and connect with the games industry. Learn more About Us or sign up!

Sign me up!