Graphics Rendering Pipeline
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1 Graphic Rendering ipeline Model Modeling Tranformation M Viewing Tranformation Model 2 M 2 3DWorld Scene V 3D View Scene Model n M n 2D Image Raterization 2D Scene rojection
2 Scaling S. ], [ ], [ ;, (, (
3 Scaling S. ], [ ], [ ;, (, ( caling differential : : uniform caling
4 Rotation R φ r φ r φ r φ r. co( in( in( co( ], [ ], [ co( in( in( co( in( co( in( ; co(, (, ( φ
5 General 22 Matri X X [ X X. T, ] [, ] a c b d [( a + c,( b + d ] If a d and b c T Identit Matri X X
6 General 22 Matri If b c X [a, d] : Scaling If b c and a -, d X [-, ] : Reflection
7 General 22 Matri [, ] [, ] [ + c, ] c Shearing in X
8 General 22 Matri b [, ] [, ] [, b + ] Shearing in Y
9 Tranlation ], [ ];, [ ;, (, ( t t T T t t T
10 Homogenou Coordinate Scale/Rotate/Reflect/Shear: X XT Tranlate: X X + T [, ] [,, w ] h Multiple value for the ame point e.g., (2, 3, 6 and (4, 6, 2 are ame point
11 Homogenou Coordinate w (,,w w (/w, /w,
12 Homogenou Coordinate Unifing repreentation for tranformation Tranformation matri from 22 to 33 [, X X X X. T a, w ] [,,] c l [( a + c + b d m l,( b + d + m,]
13 Homogenou Coordinate Tranlation T l m X XT [, ] [ + l, + m]
14 Homogenou Coordinate Scaling/Rotation/Shear T a c b d
15 Homogenou Coordinate Succeive tranlation are additive l m X X After T l 2 m 2 X X After T and T m m l l X m l m l X X Succeive tranlation: T (l, m, T 2 (l 2, m 2
16 Homogenou Coordinate Succeive caling i multiplicative X X After S After S and S 2 Succeive caling: S (,, S 2 ( 2, X X X X X
17 Homogenou Coordinate After R( X Succeive rotation: R(, R(φ co X in X in co X co( + φ X in( + φ After R( and R(φ coφ X inφ in( + φ co( + φ Succeive rotation are additive inφ coφ
18 Compoition of tranformation Rotation about arbitrar point Rotation about origin i known Tranlate uch that become O Rotate (about O Tranlate back to O
19 Compoition of tranformation Rotation about arbitrar point Rotation about origin i known Tranlate uch that become O X X l m O
20 Compoition of tranformation Rotation about arbitrar point Rotation about origin i known Rotate about O co in X X in co O
21 Compoition of tranformation Rotation about arbitrar point Rotation about origin i known Tranlate back to X X l m O
22 Compoition of tranformation Compoite tranformation + in (co in (co co in in co co in in co m n n m X m l m l X X f
23 Compoition of tranformation Reflection about an arbitrar line B C A O
24 Compoition of tranformation Reflection about an arbitrar line Tranlation B C A O
25 Compoition of tranformation Reflection about an arbitrar line Rotation B A C O
26 Compoition of tranformation Reflection about an arbitrar line Reflection O A C B
27 Compoition of tranformation Reflection about an arbitrar line Rotation C O A B
28 Compoition of tranformation Reflection about an arbitrar line Tranlation C O A B
29 Compoition of tranformation Given T and T 2 In general, T T T 2 T2T
30 Rigid Tranformation Square remain quare reerve length and angle Sequence of rotation and tranlation T r r l 2 r r 2 22 m
31 Affine Tranformation reerve parallelim Sequence of rotation, tranlation, caling and hear T a c l b d m Linear tranformation i when no tranlation
32 General Tranformation 33 matri T a c l b d m p q
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