CS200 Final Practice questions with
complete solutions passed
Find the 3 x 3 homogeneous coordinate matrix that maps the axis-aligned rectangle with vertices:
(12, 0), (-4, 0), (-4, -20), (12, -20)
in this order to the axis-aligned rectangle with respective vertices:
(3, 4), (19, 4), (19, -18), (3, -18)
A geometric solution is required. - correct answer ✔✔Transformation = T<11, -7> * H<-1, 11/10> * T<-4,
10>
| -1, 0, 15 |
| 0, 1.1, 4 |
| 0, 0, 1 |
We are to use texture mapping with the object on the left so that the vertices of the object map to the
points in texture space as indicated on the right. What are the texture coordinates associated to the
vertices labeled 0 and 3? - correct answer ✔✔Object-Texture Transformation:
T<0.2, 0.2> * H<0.02, 0.08>
| 0.02, 0, 0.2 |
| 0, 0.08, 0.2 |
| 0, 0, 1 |
Vertex 0 :
Object Coords = (2, 0)
Text Coords = (0.24, 0.2)
, Vertex 1 :
Object Coords =
(4, 6)
Text Coords =
(0.28, 0.68)
Recall that the standard square is the axis-aligned rectangle centered at the origin with sides of length 2.
Let R be the rectangle with width 10 and height 20, centered at the point (25, -15), and rotated by the
angle θ with respect to the horizontal, where θ is such that cos θ = 4/5 and sin θ = 3/5.
a) Find the 3x3 homogeneous coordinate matrix that maps the standard square to rectangle R.
b) Let R' be the rectangle obtained by scaling rectangle R by 3 with respect to the point (8, -7). Find the
3x3 homogeneous coordinate matrix that maps the standard square to R'. - correct answer ✔✔a) T<25, -
15> * R<θ = cos^-1(4/5)> * H<5, 10>
| 4, -6, 25 |
| 3, 8, -15 |
| 0, 0, 1 |
b) M1 = u * M0
u = T<8, -7> * H<3> * T<-8, 7>
| 3, 0, -16 |
| 0, 3, 14 |
| 0, 0, 1 |
M1 =
| 12, -18, 59 |
| 9, 24, -31 |
complete solutions passed
Find the 3 x 3 homogeneous coordinate matrix that maps the axis-aligned rectangle with vertices:
(12, 0), (-4, 0), (-4, -20), (12, -20)
in this order to the axis-aligned rectangle with respective vertices:
(3, 4), (19, 4), (19, -18), (3, -18)
A geometric solution is required. - correct answer ✔✔Transformation = T<11, -7> * H<-1, 11/10> * T<-4,
10>
| -1, 0, 15 |
| 0, 1.1, 4 |
| 0, 0, 1 |
We are to use texture mapping with the object on the left so that the vertices of the object map to the
points in texture space as indicated on the right. What are the texture coordinates associated to the
vertices labeled 0 and 3? - correct answer ✔✔Object-Texture Transformation:
T<0.2, 0.2> * H<0.02, 0.08>
| 0.02, 0, 0.2 |
| 0, 0.08, 0.2 |
| 0, 0, 1 |
Vertex 0 :
Object Coords = (2, 0)
Text Coords = (0.24, 0.2)
, Vertex 1 :
Object Coords =
(4, 6)
Text Coords =
(0.28, 0.68)
Recall that the standard square is the axis-aligned rectangle centered at the origin with sides of length 2.
Let R be the rectangle with width 10 and height 20, centered at the point (25, -15), and rotated by the
angle θ with respect to the horizontal, where θ is such that cos θ = 4/5 and sin θ = 3/5.
a) Find the 3x3 homogeneous coordinate matrix that maps the standard square to rectangle R.
b) Let R' be the rectangle obtained by scaling rectangle R by 3 with respect to the point (8, -7). Find the
3x3 homogeneous coordinate matrix that maps the standard square to R'. - correct answer ✔✔a) T<25, -
15> * R<θ = cos^-1(4/5)> * H<5, 10>
| 4, -6, 25 |
| 3, 8, -15 |
| 0, 0, 1 |
b) M1 = u * M0
u = T<8, -7> * H<3> * T<-8, 7>
| 3, 0, -16 |
| 0, 3, 14 |
| 0, 0, 1 |
M1 =
| 12, -18, 59 |
| 9, 24, -31 |
