[TA frost wolf \u may- hundred talents plan] 1.2.3 MVP matrix operation

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1.2.3 MVP Matrix computing

1.2.3.1 Learning goals

• take 3D The object is transformed into 2D Plane
• Prepare for the use of various spaces

1.2.3.2 MVP Definition of matrix

MVP The matrices are ：

• Model Model
• View Observe
• Projection Projection

Five coordinates ：
Vertex coordinates start in local space （Local Space）, This is called local coordinates （Local Coordinate）, It will then change to world coordinates （World Coordinate）, Observation coordinate （View Coordinate）, Cut coordinates （Clip Coordinate）, And finally in screen coordinates （Screen Coordinate） The form ends .

1.2.3.3 M： Model space to world space

Model space takes itself as the origin , World space has an origin independent of the model itself .
There are three steps to transform from model space to world space （ The order cannot be changed ）：

1. The zoom
2. rotate
3. translation
   The corresponding matrix transformation is carried out in turn to obtain the transformation matrix .
   M Representation of matrix （ The rotation here only includes the rotation around y The rotation of the shaft , Do you need to add information about other axes ？）：
   

1.2.3.4 V: From world space to visual space

Visual space ： A space coordinate system centered on a camera .

From world space to camera space
↓
Pan the entire viewing space , Make the camera origin coincide with the elder martial sister's coordinate origin , And make the coordinate axes coincide
↓
The camera rotates first in world space , Retranslated
↓
In order to make the camera coincide with the world coordinates , Using inverse transformation

The transformation process ：

1. Pan the world space
2. Rotate world space
3. z The component is reversed （ The reason of left-handed coordinate system ）
   According to the above method, the transformation matrix is obtained by matrix transformation

V A matrix representation of a matrix ：

1.2.3.5 P: Visual space to crop space

Be careful ：

• Not a real projection , Prepare for projection
• Purpose ： Determine whether the vertex is within the scope of the courseware
• P matrix ： Yes x, y, z Scale the component , use w The component is the range value . If x,y,z It's all in range , Then the point is in the clipping space .
  There are two ways of projection ：
• Perspective projection
• Orthographic projection

1.2.3.6 P： Perspective projection

P A matrix representation of a matrix ：

The meaning of each parameter of perspective projection is shown in the figure below ：


Use the above P matrix , The coordinates of the transformed visual cone are shown in the figure ：

It can be obtained. , If a vertex is within the visual cone , Then its transformed coordinates must meet ：x,y,z Both in -w To w Within the scope of .

1.2.3.7 P： Orthographic projection

Relevant schematic diagram of orthogonal projection and its parameter interpretation ：

Orthographic projection P A matrix representation of a matrix ：

summary

Model space 、 World space 、 The difference of visual field space ：

1. Model space is centered on the model itself , The origin of the coordinate axis is the origin of the coordinate , By scaling 、 rotate 、 translation **（Model matrix ）** Set the model coordinates （Model Coordinate） Change to world coordinates （World Coordinate）
2. World space is centered on the whole scene , By translation and rotation **（View matrix ）**, as well as z The inverse of the component will set the world coordinates （World Coordinate） Convert to observation coordinates （View Coordinate）
3. The visual field space takes the camera as the origin center , Through the projection matrix **（Projection matrix ）** Observe the coordinates （View Coordinate） To crop coordinates （Clip Coordinate）