Games101 review: linear algebra

Catalog

1. The basics of vectors

1.1 Representation of vectors

1.2 Standardization of vectors （ length ）

1.3 Vector addition ： The rule of connected triangles

1.4 Cartesian coordinate system ： You can use coordinates to represent vectors and lengths , Graphics default column vector

2. Vector multiplication

2.1 Point multiplication ：

2.1.1 The result is a number ;

2.1.2 Obtain the cosine of the included angle ;

2.1.3 Satisfying the commutative law ;

2.1.4 Cartesian coordinate system

2.1.5 Project to another vector

2.1.6 Measure how close two vectors are ; Decompose vectors ; Judge whether the two vectors are in the same direction （ Front and back ） 

2.2 Cross riding

2.2.1 The result is a vector ： Perpendicular to two vectors 、 Right-hand rule

2.2.2 Cartesian coordinate system

 2.2.3 Applications in graphics ： Determine whether one vector is on the left side of another / On the right side

2.3 Rectangular coordinate system

3. matrix

3.1 The transpose of the matrix ：

3.2 Unit matrix

3.3 Matrix representation of point multiplication and cross multiplication ：

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1. The basics of vectors

1.1 Representation of vectors

 

1.2 Standardization of vectors （ length ）

 

1.3 Vector addition ： The rule of connected triangles

 

1.4 Cartesian coordinate system ： You can use coordinates to represent vectors and lengths , Graphics default column vector

 

2. Vector multiplication

2.1 Point multiplication ：

2.1.1 The result is a number ;

2.1.2 Obtain the cosine of the included angle ;

2.1.3 Satisfying the commutative law ;

 

2.1.4 Cartesian coordinate system

 

2.1.5 Project to another vector

2.1.6 Measure how close two vectors are ; Decompose vectors ; Judge whether the two vectors are in the same direction （ Front and back ） 

 

2.2 Cross riding

Determine whether a point is inside a triangle , That is, when rasterizing, judge whether the pixel is inside the triangle

2.2.1 The result is a vector ： Perpendicular to two vectors 、 Right-hand rule

2.2.2 Cartesian coordinate system

 2.2.3 Applications in graphics ： Determine whether one vector is on the left side of another / On the right side

2.3 Rectangular coordinate system

3. matrix

 

3.1 The transpose of the matrix ：

3.2 Unit matrix

3.3 Matrix representation of point multiplication and cross multiplication ：