GAMES101-02线性代数复习

A Swift and Brutal Introduction to Linear Algebra

图形学依赖：
Basic mathematics

• Linear algebra,calculus,statistics
  Basic physics
• Optics,Mechanics
  Misc
• Signal processing
• Numerical analysis数值分析
  And a bit of aesthetics

一、Vector

Magnitude (length) of a vector written as ||a||
Unit vector

• A vector with magnitude of 1
• Finding the unit vector of a vector (normalization): a^ = a/||a||
• -Used to represent directions

//默认向量为列向量，即上图A所示。

点乘

用途：快速得出向量夹角

点乘在图形学作用：
Find angle between two vectors
(e.g. cosine of angle between light source and surface)Finding projection of one vector on another

• Measure how close two directions are
• Decompose a vector
• Determine forward /backward
  
  判断向量a和向量b基本一致，与向量c基本相反。
  金属高光，镜面反射等

叉乘

（右手螺旋定则）决定方向

相同向量叉乘得到零向量

作用：

• Determine left / right
• Determine inside / outside
  衍生：判断点是否在三角形内部

二、Matrix

ln Graphics, pervasively used to represent

• transformations- Translation, rotation,shear，scale
  (more details in the next lecture)

矩阵乘法得先能乘才可以。

没有任何交换律

转置特点

单位矩阵