TOC
math
向量夹角定义
$$ \cos \theta = \frac{\bar{v} \cdot \bar{k}}{||\bar{v}|| \cdot ||\bar{k}||} $$
缩放矩阵
s1 s2 s3 分为对应你想要缩放的向量分量
$$ \begin{bmatrix} \color{red}{S_1} & \color{red}0 & \color{red}0 & \color{red}0 \ \color{green}0 & \color{green}{S_2} & \color{green}0 & \color{green}0 \ \color{blue}0 & \color{blue}0 & \color{blue}{S_3} & \color{blue}0 \ \color{purple}0 & \color{purple}0 & \color{purple}0 & \color{purple}1 \end{bmatrix} \cdot \begin{pmatrix} x \ y \ z \ 1 \end{pmatrix} = \begin{pmatrix} \color{red}{S_1} \cdot x \ \color{green}{S_2} \cdot y \ \color{blue}{S_3} \cdot z \ 1 \end{pmatrix} $$
位移矩阵
$$ \begin{bmatrix} \color{red}{S_1} & \color{red}0 & \color{red}0 & \color{red}0 \ \color{green}0 & \color{green}{S_2} & \color{green}0 & \color{green}0 \ \color{blue}0 & \color{blue}0 & \color{blue}{S_3} & \color{blue}0 \ \color{purple}0 & \color{purple}0 & \color{purple}0 & \color{purple}1 \end{bmatrix} \cdot \begin{pmatrix} x \ y \ z \ 1 \end{pmatrix} = \begin{pmatrix} \color{red}{S_1} \cdot x \ \color{green}{S_2} \cdot y \ \color{blue}{S_3} \cdot z \ 1 \end{pmatrix} $$
旋转矩阵
弧度转角度：角度 = 弧度 * (180.0f / PI) 角度转弧度：弧度 = 角度 * (PI / 180.0f)
沿x轴旋转：
$$ \begin{bmatrix} \color{red}1 & \color{red}0 & \color{red}0 & \color{red}0 \ \color{green}0 & \color{green}{\cos \theta} & - \color{green}{\sin \theta} & \color{green}0 \ \color{blue}0 & \color{blue}{\sin \theta} & \color{blue}{\cos \theta} & \color{blue}0 \ \color{purple}0 & \color{purple}0 & \color{purple}0 & \color{purple}1 \end{bmatrix} \cdot \begin{pmatrix} x \ y \ z \ 1 \end{pmatrix} = \begin{pmatrix} x \ \color{green}{\cos \theta} \cdot y - \color{green}{\sin \theta} \cdot z \ \color{blue}{\sin \theta} \cdot y + \color{blue}{\cos \theta} \cdot z \ 1 \end{pmatrix} $$
沿y轴旋转：
$$ \begin{bmatrix} \color{red}{\cos \theta} & \color{red}0 & \color{red}{\sin \theta} & \color{red}0 \ \color{green}0 & \color{green}1 & \color{green}0 & \color{green}0 \ - \color{blue}{\sin \theta} & \color{blue}0 & \color{blue}{\cos \theta} & \color{blue}0 \ \color{purple}0 & \color{purple}0 & \color{purple}0 & \color{purple}1 \end{bmatrix} \cdot \begin{pmatrix} x \ y \ z \ 1 \end{pmatrix} = \begin{pmatrix} \color{red}{\cos \theta} \cdot x + \color{red}{\sin \theta} \cdot z \ y \ - \color{blue}{\sin \theta} \cdot x + \color{blue}{\cos \theta} \cdot z \ 1 \end{pmatrix} $$
沿z轴旋转：
$$ \begin{bmatrix} \color{red}{\cos \theta} & - \color{red}{\sin \theta} & \color{red}0 & \color{red}0 \ \color{green}{\sin \theta} & \color{green}{\cos \theta} & \color{green}0 & \color{green}0 \ \color{blue}0 & \color{blue}0 & \color{blue}1 & \color{blue}0 \ \color{purple}0 & \color{purple}0 & \color{purple}0 & \color{purple}1 \end{bmatrix} \cdot \begin{pmatrix} x \ y \ z \ 1 \end{pmatrix} = \begin{pmatrix} \color{red}{\cos \theta} \cdot x - \color{red}{\sin \theta} \cdot y \ \color{green}{\sin \theta} \cdot x + \color{green}{\cos \theta} \cdot y \ z \ 1 \end{pmatrix} $$
欧拉角关于摄像机的计算
front.x = cos(glm::radians(yaw)) * cos(glm::radians(pitch));
front.y = sin(glm::radians(pitch));
front.z = sin(glm::radians(yaw)) * cos(glm::radians(pitch));
观察矩阵
$$ LookAt = \begin{bmatrix} \color{red}{R_x} & \color{red}{R_y} & \color{red}{R_z} & 0 \ \color{green}{U_x} & \color{green}{U_y} & \color{green}{U_z} & 0 \ \color{blue}{D_x} & \color{blue}{D_y} & \color{blue}{D_z} & 0 \ 0 & 0 & 0 & 1 \end{bmatrix} * \begin{bmatrix} 1 & 0 & 0 & -\color{purple}{P_x} \ 0 & 1 & 0 & -\color{purple}{P_y} \ 0 & 0 & 1 & -\color{purple}{P_z} \ 0 & 0 & 0 & 1 \end{bmatrix} $$