Lecture 2: Review of Linear Algebra
这节课很简单, 简单记录几点.
Cross Product
\[
|| \vec{a} \times \vec{b} || = || \vec{a} || \cdot || \vec{b} || \cdot \sin \theta
\]
\[
\vec{a} \times \vec{b} = \vec{b} \times \vec{a}
\]
-
Cross product is orthogonal to two initial vectors.
-
Direction determined by right-hand rule.
-
Useful in constructing coordinate system(默认右手系)
\[
\vec{x} \times \vec{y} = \vec{z}
\]
\[
\vec{y} \times \vec{z} = \vec{x}
\]
\[
\vec{z} \times \vec{x} = \vec{y}
\]
- 矩阵形式:
- Determin left/right, inside/outside.
比如对于这个三角形, 我们想判断点P是否在三角形内, 我们可以分别计算AP & AB, BP & BC 和 CA & CP的叉积, 如果结果都大于0, 则P在三角形内.