Games101 review: Transformation

Catalog

1. Two dimensional transformation

1.1 Zoom transform （Scale）

1.2 shear （Shear）

1.3 rotate （Rotate）

1.4 symmetry （Reflection）

2. Homogeneous coordinates

2.0 Solution of homogeneous coordinates ： Add a dimension w

2.1 Translation transformation ： In matrix form

2.2 Homogeneous coordinate matrix （ Affine transformation ）： Various transformations can be written in the same form

3. Transformation combination ： The order matters!（ Because matrix multiplication does not satisfy the commutative law ） From right to left

4. Transformation decomposition ： Move to the origin first

5. Three dimensional transformation

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1. Two dimensional transformation

No matter how complex the transformation is , Just find the one-to-one correspondence between any point , You can write the matrix

 

1.1 Zoom transform （Scale）

1.2 shear （Shear）

1.3 rotate （Rotate）

 

1.4 symmetry （Reflection）

 

2. Homogeneous coordinates

2.0 Solution of homogeneous coordinates ： Add a dimension w

 

  among w The significance of will be added later

2.1 Translation transformation ： In matrix form

2.2 Homogeneous coordinate matrix （ Affine transformation ）： Various transformations can be written in the same form

 

 

3. Transformation combination ： The order matters!（ Because matrix multiplication does not satisfy the commutative law ） From right to left

4. Transformation decomposition ： Move to the origin first

 

5. Three dimensional transformation