Summary Computer Graphics (210244)

📦
3D Transformation and Projection
Translation
Scaling
Rotation
About Z Axis
About X Axis
About Y Axis
Reflection
About XY Plane
About XZ Plane
About YZ Plane
About Any Plane
Shear
About XY Plane
About YZ Plane
About XZ Plane
Projection
Parallel Projection
Orthographic Parallel Projection
Axonometric Orthographic Projection
Trimetric Projection
Dimetric Projection
Isometric Projection
Multiview Orthographic Projection
Oblique Projection
Perspective Projection
One-point/Single Perspective Projection
Two-point Perspective Projection
Three-point Perspective Projection



Translation
⎡1 0 0 0⎤
0 1 0 0
T =
0 0 1 0
⎣ tx ty tz 1⎦


Scaling
⎡ Sx 0 0 0⎤
0 Sy 0 0
T =
0 0 0
⎣0 1⎦
Sz
0 0


Rotation
About Z Axis


⎡ ⎤

3D Transformation and Projection 1

, ⎡ cos θ sin θ 0 0⎤
−sin θ cos θ 0 0
Rz =
0 0 1 0
⎣ 0 0 0 1⎦

About X Axis

⎡1 0 0 0 ⎤
0 cos θ sin θ 0
Rx =
0 −sin θ 0
⎣0 ⎦
cos θ
0 0 1

About Y Axis
⎡ cos θ 0 −sin θ 0⎤
0 1 0 0
Rz =
0 0
⎣ 0 1⎦
sin θ cos θ
0 0


Reflection
About XY Plane

⎡1 0 0 0⎤
0 1 0 0
RFz =
0 0 −1 0
⎣0 0 0 1⎦

About XZ Plane

⎡1 0 0 0⎤
0 −1 0 0
RFy =
0 0 1 0
⎣0 0 0 1⎦

About YZ Plane
⎡−1 0 0 0⎤
0 1 0 0
RFx =
0 0 1 0
⎣0 0 0 1⎦

About Any Plane

⎡ 1 0⎤ ⎡ ∣N ∣ 0⎤ 1
⎡ 0⎤ ⎡ ∣N ∣ 0⎤ ⎡ 1 0⎤
λ n1 −n1 n2 −n1 n3
0 0 0 ∣N ∣ 0 0
λ
λ∣N ∣ λ∣N ∣ 0 0
−n1 n2 n3 n2 −n2
0 1 0 0 λ∣N ∣ ∣N ∣
0 0 1 0 0 0 n3
0 0 1 0 0
RT = −n1 n3
λ
−n2
λ λ
0 0 1 0 0 0 −1 0 n1 n2 n3
0 0 0 1 0
⎣−x0 1⎦ ⎣ 0 ⎣0 1⎦ ⎣ 0 ⎦ ⎣ 1⎦
n3
0
⎦
λ∣N ∣ λ ∣N ∣ ∣N ∣ ∣N ∣ ∣N ∣
−y0 −z0 0 0 1 0 0 0 0 1 x0 y0 z0


Shear
About XY Plane
⎡ ⎤

3D Transformation and Projection 2