🗒️ Interpolation (5)

1. 2022.05.01 [Computer Animation] Keyframing and Splines

   Keyframing and Splines What is Motion? Motion is a time-varying transformation from body local system to world coordinate system. (in a very narrow sense) Transformation Rigid Transformation(강체 변환) Rotate + Translate 3x3 orthogonal matrix + 3-vector $T : x → Rx + b$ Affine Transformation(어파인 변환) Scale + Shear + Rigid Transformation 3x3 matrix + 3-vector $T: x → Ax + b$ Homogeneous Transformation..
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. 2022.04.03 [Computer Animation] 2D Rotation and Orientation

   2D 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) Representations for 2D rotations and orientations Turnin..
4. 2022.03.26 [Computer Animation] Linear Interpolation

   Linear Interpolation(선형 보간법) 보간법(Interpolation) : 함수의, 둘 이상의 변숫값에 대한 함숫값을 알고, 그것들 사이의 임의의 변숫값에 대한 함숫값 내지는 그 근삿값을 구하는 계산법 - Oxford Languages 1D Linear Interpolation What is the function, $f(t)$, such that $\begin{matrix} 0 ≤ t ≤ 1 \\ f(0) = 1 \\ f(1) = 5 \end{matrix} ?$ If $f(t)$ is a Linear Equation, $f(t) = at + b$ 2 Unknowns, 2 Equations $\begin{matrix} 1 = a · 0 + b \\ 5 = a · 1 + b \end{matr..
5. 2022.03.03 [Computer Animation] Computer Animation

   Computer Animation Animate to give life to or cause to come alive to make lively; enliven to encourage or inspire to impart motion to; move to action or work to record on film or video tape so as to give movement to => an animated cartoon Animatronics Animation + Electronics 특수 효과 기술의 일종으로, 생물을 모방한 로봇을 사용하여 촬영하는 기술 Animation A way of making a movie by using a series of drawings, computer graphic..