Games101 review: 3D transformation

Catalog

1. translation 、 The zoom 、 rotate

1.1 translation ： The last column t

1.2 The zoom ： The diagonal to s

1.3 rotate ： Around the y The shaft is special , Because cross multiplication is z×x

1.4 Euler Angle ：roll（ rotate ）、pitch（ Up and down ）、yaw（ about ）

1.5 （ Add ） Four yuan number ：

2. View transformation

2.1 View / The camera changes , The model changes with the view

2.1.0 MVP Transformation ： analogy ： Take photos in reality

2.1.1 The camera / Definition of perspective ： Location 、 Direction of sight 、 Above line of sight ？

2.1.2 View transformation matrix ： First consider the inverse matrix , Then according to the properties of orthogonal matrix ( The inverse = Transposition ) get ​​​​​​​

2.2 Projection transformation ： Orthographic projection 、 Perspective projection

2.2.1 Orthographic projection ： First translate to the origin , Zoom back to the standard coordinate system

2.2.2 Perspective projection ： First think about the properties of homogeneous coordinate point representation , Post thinking collapses into cube orthogonal projection

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1. translation 、 The zoom 、 rotate

1.1 translation ： The last column t

1.2 The zoom ： The diagonal to s

1.3 rotate ： Around the y The shaft is special , Because cross multiplication is z×x

1.4 Euler Angle ：roll（ rotate ）、pitch（ Up and down ）、yaw（ about ）

1.5 （ Add ） Four yuan number ：

2. View transformation

2.1 View / The camera changes , The model changes with the view

2.1.0 MVP Transformation ： analogy ： Take photos in reality

Think about how we take a picture in real life ？

• Put the objects in order （Model Transformation）
• Adjust the position of the camera （View Transformation）
• Taking pictures ！cheese！（Projection Transformation）

2.1.1 The camera / Definition of perspective ： Location 、 Direction of sight 、 Above line of sight ？

Here is the conclusion ： origin 、 For the above Y Axis direction 、 The line of sight is -Z Direction

2.1.2 View transformation matrix ： First consider the inverse matrix , Then according to the properties of orthogonal matrix ( The inverse = Transposition ) get

2.2 Projection transformation ： Orthographic projection 、 Perspective projection

3D to 2D

2.2.1 Orthographic projection ： First translate to the origin , Zoom back to the standard coordinate system

  A simple understanding ： Determine the position of the camera （ origin ） And orientation （－Z Direction , Shang Dynasty Y Axis ）, Directly in Z Drag the model in the axis direction , And pan and zoom it to [-1,1] Within the scope of .

Matrix representation ：

2.2.2 Perspective projection ： First think about the properties of homogeneous coordinate point representation , Post thinking collapses into cube orthogonal projection