3.Transformations

Question 1

How is the camera simulated in OpenGL

Answer 1

By transformations on the model

Question 2

If the transformation that moves the default camera to the desired position is Tc, what is the transformation that moves the object to the right position?

Answer 2

Tc^-1

Question 3

How does opengl know how to compute this?

Answer 3

gluLookAt(E,C,V)

Question 4

What kind of geometrical transformation is x’=x*sx?

Answer 4

Scaling

Question 5

What transformation is x’=x+tx

Answer 5

Translation

Question 6

What transformation is rotation in 2d about origin?

Answer 6

x’ =xcos9-ysin9
y’ = xcos9+ysin9
z’=z

Question 7

How is rotation in 2d about an arbitrary point achieved?

Answer 7

1. Translate by -coordinates of arbitrary point
2. Do rotation about origin
3. Translate by +coordinates of arbitrary point

Question 8

Is rotating then shifting the same as shifting then rotating?

Answer 8

NOPE non-commutativity of matrix transformations

Question 9

What does “homogenous coordinates” mean?

Answer 9

have SAME representation for Translation, Scale & Rotation (3d about z) (x,y,z,w)
Vertices -> Points
Matrices -> Transformations

Question 10

Why do we introduce w’?

Answer 10

Translation: You can’t represent it in 3x3
SOLUTION: point->(x,y,z,1), Matrix-> 4x4

Question 11

In which direction is P’ = P*T transformation read?

Answer 11

Right to left

Question 12

If I show you the rotation matrix, how can you tell about which axis it is?

Answer 12

If it’s about x axis x row won’t have cos/sin terms

Question 13

How many transformation matrices in OpenGL?

Answer 13

PVM: Modelling, Viewing (Camera) and Projection matrix

Question 14

Rotation about an arbitrary 3d axis

Answer 14

M1:origin
M2:XY plane
M3:X axis
M4:ROTATION
M3^-1
M2^-1
M1^-1