🗒️ Quaternion (3)

1. 2022.05.01 [Computer Animation] Quaternion Catmull-Rom Spline

   Quaternion Catmull-Rom Spline Quaternion(사원수) Operations Unit Quaternion Algebra Unit Quaternion space is closed under multiplication and inverse, but not closed under addition and subtraction Rotation Quaternion Exp and Log Scale Quaternion Catmull-Rom Spline Quaternion Bezier Quaternion Bezier Curve Linear Combination of quaternion? De Casteljau by Slerp by De Casteljau Algorithm Multi-linear ..
2. 2022.04.10 [Computer Animation] Slerp(Spherical Linear Interpolation)

   Slerp(Spherical Linear Interpolation) Interpolation betwee two orientations, $o_{a}$ and $o_{b}$? $o_{a}$ and $o_{b}$ can be represented by Euler-angles 3x3 matrices quaternions How can them be interpolated? Is the linear interpolation applicable? When the axis-angle is known, $o_{a} → o_{b}$ Rotation between two orientations? Rotation between two SO(3) matrices, $m_{a}$ and $m_{b}$ $m_{r} = m_{..
3. 2022.04.10 [Computer Animation] 3D Rotation and Orientation

   3D Rotation and Orientation Orientation vs. Rotation Rotation Circular movement Orientation The state of being oriented. Given a coordinate system, the orientation of an object can be represented as a rotation from a reference pose. Analogy (point : vector) is similar to (orientation : rotation) Both represent a sort of (state : movement) What is 3D Rotation? Many different ways to describe Rota..