3D mathematical basics: graphics and Game Development

Chapter 4 vectors of Chapter 4

4.1 vector-a mathematical definition vector -- mathematical definition

4.1.1 vectors vs. scalars vector and scalar

"Velocity" and "displacement" are vector quantities, while "speed" and "distance" are
Scalar quantities

 

4.1.2 dimension of the vector dimension vector

4.1.3 notation Method

Row vs. column vectors row vector column vector

 

4.2 vector-a geometric definition 4.2 vector- ry Definition

4.2.1 what does a vector look like? Arrows, including size and direction

4.2.2 position vs. Displacement 4.2.2 position and displacement

4.2.3 specifying vectors 4.2.3 Vector Expression

The numbers in a vector measure signed displacements in each dimension

Indicates the directed displacement of each dimension.

 

4.2.4 vectors as a sequence of displacements 4.2.4 represent vectors as displacement sequences.

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.

Split into parallel components of the axis. When the displacement of these components is combined, it represents the displacement of the vector.

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

Different sequences correspond to different paths on the vector axis alignment box (AABB.

 

4.3 vectors vs. Points

A "point" specifies a position, and a "vector" specifies
Displacement

 

4.3.1 relative position

Reference Frame Reference System

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 chapter 5th vector operations

Normalized Vectors

5.8 vector addition and subtraction

Vector Addition isCommutative), But vector sub-
Traction is not.

 

5.10 vector dot product

Dot Product (also known as the inner product ).

Point multiplication, also called Inner Product

 

 

5.11 vector Cross Product

Cross Product or outer product cross multiplication, Outer Product

A × B.

The operation A · B × C is known as the triple product

anticommutative: A × B =-(B × A).