Chapter 4 Vectors 第4章 向量

4.1 Vector — A Mathematical Definition  向量——数学定义

4.1.1 Vectors vs. Scalars  向量和标量

“velocity” and “displacement” are vector quantities, while “speed” and “distance” are

scalar quantities

 

4.1.2 Vector Dimension 向量的维度

4.1.3 Notation 记法

Row vs. column vectors 行向量列向量

 

4.2 Vector — A Geometric Definition 4.2 向量——几何定义

4.2.1 What Does a Vector Look Like? 箭头，包含大小和方向

4.2.2 Position vs. Displacement  4.2.2 位置与位移

4.2.3 Specifying Vectors 4.2.3 向量的表达

The numbers in a vector measure signed displacements in each dimension

代表各个维度的有向位移

 

4.2.4 Vectors as a Sequence of Displacements  4.2.4 将向量表示为位移序列.

break the vector into its axially aligned components.

When these axially aligned displacements are combined, they

cumulatively define the displacement defined by the vector as a whole.

分解成轴平行的分量。当这些分量的位移组合起来，就代表了这个向量的位移。

The different orderings correspond to different routes along the axially aligned bounding box con-

taining the vector.

不同顺序对应向量轴对齐包围盒（AABB）上的不同路径。

 

4.3 Vectors vs. Points

A “point” specifies a position, and a “vector” specifies a

displacement

 

4.3.1 Relative Position

reference frame 参考系

4.3.2 The Relationship Between Points and Vectors

When you think of a loca-

tion, think of a point and visualize a dot.When you think of a displacement, think of a vector and

visualize an arrow.

 

 

chapter 5 Operations on vectors 第5章 向量运算

Normalized Vectors

5.8 Vector Addition and Subtraction

vector addition is commutative（交换律）, but vector sub-

traction is not。

 

5.10 Vector Dot Product

dot product (also known as the inner product).

点乘，也叫内积

 

 

5.11 Vector Cross Product

cross product or outer product  叉乘，外积

a×b.

The operation a·b×c is known as the triple product

anticommutative: a×b= –(b×a).