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Computer Graphics

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Title: Computer Graphics


1
Computer Graphics Modeling and Transformations
  • Erik Brisson
  • ebrisson_at_bu.edu

2
Human view of physical world
3
Human view of image
4
Computer graphics paradigm
5
C.G. paradigm with light
6
C.G. basic calculation
7
Resulting image
8
Result is a digital image
9
Model geometry two cuboids
10
Model geometry - approximation
11
Geometric elements in 3D
12
Review from graph paper lecture
Example of hquad hquad, name 2,
2, 2, 4, 4, 4, 4, 2
13
Generalization
Vertices P1 (2, 2) P2 (2, 4)
P3 (4, 4) P4 (4, 2) Face F0 P1,
P2, P3, P4
14
More examples
Vertices P1 (4.0, 2.0) P2 (2.0,
2.0) P3 (2.0, 4.0) P4 (4.0, 4.0)
P5 (6.0, 3.0) P6 (4.0, 1.0) P7
(7.0, 1.0) P8 (8.0, 2.0) Faces F1
P1, P2, P3, P4 F2 P1, P4, P5 F3
P7, P6, P1, P5, P8
15
Computer representation
Vertices 1 4.0, 2.0 2 2.0, 2.0 3
2.0, 4.0 4 4.0, 4.0 5 6.0, 3.0 6
4.0, 1.0 7 7.0, 1.0 8 8.0, 2.0 Faces
1 1, 2, 3, 4 2 1, 4, 5 3 7, 6, 1, 5,
8
16
Note edges
Edges 1 1, 2 2 2, 3 3 3, 4 4
4, 1 5 4, 5 6 1, 5 7 5, 8 8
8, 7 9 7, 6 10 1, 6
17
Translation and rotation in 2D
(B) Rotate by 45 degrees
Translate by (7.0, 4.0) (A)
Translate by (5.0, 1.0)
18
Composition of transformations
Rotate 45 degrees CCW
Translate (2, 0)
19
Composition of transformations
Translate (2, 0)
Rotate 45 degrees CCW
20
Compare
Rotate first Then translate Translate
first Then rotate
21
Rigid body transformations
22
Other transformations - scaling
23
Points in 3D
P1 (4.1, 1.6, 2.8)
24
Geometric elements in 3D
25
Objects in 3D
Vertices P1 (0.0, 0.0, 2.7) P2 (1.0,
0.0, 0.5) P3 (0.998, 0.156, 0.5) P4
(0.951, 0.309, 0.5) P5 (0.891, 0.454, 0.5)
Faces F1 P1, P2, P3 F2 P1,
P3, P4 F3 P1, P4, P5
26
Rotations in 3D
27
Translations in 3D
Sphere translated by (-3.0, 2.0,
-4.5) Blue cube translated by (2.0,
0.0, -4.0) rotated 60 deg around
y-axis Purple cube translated by
(0.0, 0.0, 0.0)
28
Now we can build, move, rotate, and scale
doughnuts
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