Common geometric transformation matrices

Reference : http://wenku.baidu.com/view/193f8a8fbceb19e8b8f6baf6.html

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Common geometric transformation matrices: translation (translate), rotation (rotate), scaling (scale), and simple compositing, such as rotation around a specified point, scaling

Multiplicative reference Http://blog.csdn.net/chunyexiyu/article/details/44671737-Matrix matrix multiplication for matrix recombination

Two-dimensional transformation matrices:

Two-dimensional translational Vec (Tx, Ty)

1 0 Tx

0 1 Ty

0 0 1

Two-dimensional rotation :

[Email protected] [Email protected] 0

[Email protected] [Email protected] 0

1 1 1

Two-dimensional amplification

Sx 0 0

0 Sy 0

0 0 1

Rotate around the vertex (Xr, Yr)

[Email protected]        [Email protected] Xr ([email protected]) + [email protected]

[Email protected]        [Email protected] Yr ([email protected]) –[email protected]

0 0 1

( Transform step: Pan to Origin, rotate- and-pan recovery )

Zoom in around a specified point (xr,yr)

Sx 0 Xr (1-SX)

0 Sy Yr (1-sy)

0 0 1

( transform step : pan to Origin, Zoom, Pan recovery )

Three-dimensional transformation matrix:

Panning Vec (Tx, Ty, Tz)

1 0 0 Tx

0 1 0 Ty

0 0 1 Tz

0 0 0 1

Rotate around the Z axis

[Email protected] [email protected] 0 0

[Email protected] [email protected] 0 0

0 0 1 0

0 0 0 1

Rotate around X axis

1 0 0 0

0 [email protected] [email protected] 0

0 [email protected] [email protected] 0

0 0 0 1

Rotate around the Y -axis

[email protected] 0 [email protected] 0

0 1 0 0

[email protected] 0 [email protected] 0

0 0 0 1

Three-dimensional rotation of the specified point (Xr, Yr, Zr) in general

1. pan to Origin

2. rotate to an axis x| y| Z

3. rotate around the axis

4. inverse matrix processing of rotation recovery -2

5. translation Recovery -1 inverse matrix processing

Three-dimensional scaling

Sx 0 0 0

0 Sy 0 0

0 0 Sz 0

0 0 0 1

Center scale around any point (Xr, Yr, Zr)

Sx 0 0 Xr (1-SX)

0 Sy 0 Yr (1-sy)

0 0 Sz Zr (1-sz)

0 0 0 1

( step : pan to Origin, Zoom, Pan recovery )

The wrong cut, for example, to cut a matrix into a parallelogram

x is a dependent axis

1 0 0 0

B 1 0 0

C 0 1 0

0 0 0 1

y is a dependent axis

1 A 0 0

0 1 0 0

0 C 1 0

0 0 0 1

z axis is a dependent axis

1 0 A 0

0 1 B 0

0 0 1 0

0 0 0 1

Composite

1 A1 A2 0

B1 1 B2 0

C1 C2 1 0

0 0 0 1

Geometric transformation function corresponding to OpenGL

Gltranslate/glroate/glscale/glloadidentity/glloadmatrix/glmarixmode

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Common geometric transformation matrices