3 ms·

While a related but more advanced topic, I still can't quite intuit quaternions. But of course we're all fortunate to not need to understand them completely to

by th0ma5 7y ago

While a related but more advanced topic, I still can't quite intuit quaternions. But of course we're all fortunate to not need to understand them completely to use them.

colinthompson 7y ago
3Blue1Brown has a great video on quaternions: https://www.youtube.com/watch?v=d4EgbgTm0Bg https://www.youtube.com/watch?v=d4EgbgTm0Bg
- th0ma5 7y ago
  Yeah, I have seen this... Still pretty mind boggling though :P
m1el 7y ago
Here's how I think about quaternions: 1) using complex numbers: A unit complex number (having its length/magnitude/absolute value equal to 1) form a circle, this circle corresponds to all 2d rotations The result of multiplying two unit complex number corresponds to combination of two 2d rotations. You can apply the rotation to a point in complex plane by multiplying that point by unit complex number that corresponds to a rotation Quaternions are the same as complex numbers, but instead of having one imaginary part they have three, and they have slightly different rules of multiplication. Quaternions of magnitude one form a 4d sphere, this 4d sphere corresponds to all 3d rotations. The result of multiplying two unit quaternions corresponds to combination of two 3d rotations. You can apply the rotation to a point in 3d space using slightly different multiplication. 2) not using complex numbers Ine of the ways to represent 3d rotations is to choose an axis direction and and angle of rotation (surprisingly, this can represent all 3d rotations) A unit quaternion representing this rotation will have its three imaginary parts ijk equal to sin(angle)*(axis direction vector), and the real part equal to cos(angle) There are funny rules about how you can multiply these quaternions, and this multiplication will produce a quaternion that represents the rotation.

3 ms·

While a related but more advanced topic, I still can't quite intuit quaternions. But of course we're all fortunate to not need to understand them completely to

by th0ma5 7y ago

While a related but more advanced topic, I still can't quite intuit quaternions. But of course we're all fortunate to not need to understand them completely to use them.

colinthompson 7y ago
3Blue1Brown has a great video on quaternions: https://www.youtube.com/watch?v=d4EgbgTm0Bg https://www.youtube.com/watch?v=d4EgbgTm0Bg
- th0ma5 7y ago
  Yeah, I have seen this... Still pretty mind boggling though :P
m1el 7y ago
Here's how I think about quaternions: 1) using complex numbers: A unit complex number (having its length/magnitude/absolute value equal to 1) form a circle, this circle corresponds to all 2d rotations The result of multiplying two unit complex number corresponds to combination of two 2d rotations. You can apply the rotation to a point in complex plane by multiplying that point by unit complex number that corresponds to a rotation Quaternions are the same as complex numbers, but instead of having one imaginary part they have three, and they have slightly different rules of multiplication. Quaternions of magnitude one form a 4d sphere, this 4d sphere corresponds to all 3d rotations. The result of multiplying two unit quaternions corresponds to combination of two 3d rotations. You can apply the rotation to a point in 3d space using slightly different multiplication. 2) not using complex numbers Ine of the ways to represent 3d rotations is to choose an axis direction and and angle of rotation (surprisingly, this can represent all 3d rotations) A unit quaternion representing this rotation will have its three imaginary parts ijk equal to sin(angle)*(axis direction vector), and the real part equal to cos(angle) There are funny rules about how you can multiply these quaternions, and this multiplication will produce a quaternion that represents the rotation.