IVR Chapter Recap Computer Graphics
Questions about the lecture 'Introduction to Virtual Reality' of the RWTH Aachen Chapter Recap Computer Graphics
Questions about the lecture 'Introduction to Virtual Reality' of the RWTH Aachen Chapter Recap Computer Graphics
Set of flashcards Details
| Flashcards | 28 |
|---|---|
| Language | English |
| Category | Computer Science |
| Level | University |
| Created / Updated | 03.02.2017 / 07.06.2017 |
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How does translation1 works?
P translated1 to P’ via vector t with p’=p+t // Does not affect vectors
How does translation2 works?
P translated2 to P’ via matrix T with p’=T*p
How is T of translation2 defined?
T defined as diagonal 1 matrix with last column vector t
How does scaling works?
P scaled to P’ via diagonal matrix S with p’=S*p
How does rotation works?
P rotated to P’ via matrix R with p’=Ri*p and i axis
How is R of rotation defined?
R is defined as i-th row with 1 and 0 and rest (cos sinxz; siny cos)
How does shearing works?
P sheared to P’ via matrix D with p’=D*p
How is D of shearing defined?
D is defined as diagonal 1 and dij shearing to i from j
What is the problem of concatenation?
Concatenation of matrices is not always possible due to translation1 but possible with translation2
What has to be considered transforming normal vectors?
Normal n transformed n’ regarding M*(p1-p2) with n’=(M-1)T*n
How does rotation of coordinate frames works? [3]
1. Rotating a coordinate frame A into another B by R with [uB,vB,wB]=R4x3 with R4x3 is sub-matrix of R
2. eB Is origin of A measures in B
3. M_A→B = [uB,vB,wB,eB]
How does users define cameras by parameters in camera transform? [3]
1. Eye position e 2. gaze vector g and 3. view-up vector t
What is the definition of the base vectors of camera coordinates? [4]
1. w=-g/|g|
2. u=t*w/|t*w|
3. v = w*u
4. Camera looks along -z
How does transforming from world B into camera space A works?
MB→A = (MA→B)-1 = R-1*T-1 = [u;v;w;0,0,0,1]*[1,0,0,-ex;0,1,0,-ey;0,0,1,-ez;0,0,0,1]
Which are the steps of viewport transform? [2]
1. From canonical view volume to window dimensions with V_S
2. From window dimensions to viewport or pixel coordinates with V_T
What are the parameters of viewport transform? [2]
1. n_x is number of horizontal pixels
2. n_y is number of vertical pixels
What are the matrices of viewport transform? [3]
1. V_S is 4x4 with diagonal 1 and V_S_11=n_x/2 and V_S_22=n_y/2
2. V_T is 4x4 with diagonal 1 and V_T_14=n_x-1/2 and V_T_24=n_y-1/2
3. V = V_T*V_S // Merge of both matrices
Which are the steps of orthographic projection? [2]
1. From orthographic view volume to scaled view volume with O_S
2. From scaled view volume to canonical view volume with O_T
What are the parameters of orthographic projection? [6]
1. l is x of left clipping plane
2. b is y of bottom clipping plane
3. c is z of near clipping plane
4. r is x of right clipping plane
5. t is y of top clipping plane
6. f is z of far clipping plane
What are the matrices of orthographic projection? [3]
1. O_S is 4x4 with diagonal 1 and O_S_11=2/r-l O_S_22=2/t-b and O_S_33=2/n-f
2. O_T is 4x4 with diagonal 1 and O_S_14=-(r+l/r-l) O_S_24=-(t+b/t-b) and O_S_34=-(n+f/n-f)
3. O = O_T*O_S // Merge of both matrices
What are the matrices of perspective projection? [2]
1. F is 4x4 with F_11=F_22=n F_33=n+f F_34=-nf F_43=1
2. P=O*F is 4x4 with P_11=2n/r-l P_22=2n/t-b P_13=-(r+l/r-l) P_23=-(t+b/t-b) P_33=n+f/n-f P_34=-(2nf/n-f) P_43=1
What can be deduced from a camera resolution?
[perspective projection.CG recap]
Aspect ratio a=r/t
What can be deduced from a symmetric frustsum?
[perspective projection.CG recap, 2]
1. t=-b and 2. r=-l
What can be deduced from a vertical FoV with theta?
[perspective projection.CG recap]
tan(theta/2) = t/|n|
How can we create a time dependent transformation for a point around an axis?
[CG, 2]
1. M(t) = Rz(t)*T
2. Rz with pz substituted by phiz(t)=omegaz*t
What is needed for a rotating sphere?
[scene graph.CG]
T*S*R // No T if on axis and no S if radius is 1
What is needed for an arm?
[scene graph.CG]
R*T
Which information is not necessary for further objects?
[scene graph.CG, 2]
1. Scaling and rotation of spheres
2. Only transformations and arm-rotations is necessary
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