CSCE4230 - Final

Question 1

Construct a scaling matrix

S = (S1, S2, S3)

Answer 1

S1 0 0 0
0 S2 0 0
0 0 S3 0
0 0 0 1

Question 2

Construct a clockwise Rotation by X matrix

Answer 2

1 0 0
0 C -S
0 S C

Question 3

Construct a clockwise Rotation by Y matrix

Answer 3

C 0 S
0 1 0
-S 0 C

Question 4

Construct a clockwise Rotation by Z matrix

Answer 4

C -S 0
S C 0
0 0 1

Question 5

Scalar multiplication
[4][ a11 a12 a13
a21 a22 a23
a31 a32 a33]

Answer 5

4(aij) (i,j = 1, 2, 3)

Question 6

Matrix multiplication

Answer 6

(AB)ij = Σ AikBkj

Question 7

Matrix Transpose

Answer 7

(A^T)ij = Aji

Question 8

Scalar Product

Answer 8

<u> = Σ Ui Vi</u>

Question 9

Vector Cross Product

Answer 9

p2p3 - p3p2
p3p1 - p1p3
p1p2 - p2p1

Question 10

Vector Length

Answer 10

||V|| = √v1^2 + v2^2 + v3^2

Question 11

Orthogonal Vectors

Answer 11

U1V1 + U2V2 + U3V3 = 0

Question 12

Matrix inverse

Answer 12

AA^-1 = A^-1 A = I

Question 13

Orthogonal Matrix

Answer 13

U^T = U^-1

Question 14

Clockwise or Counter-clockwise
1 0 0
0 C S
0 -S C

Answer 14

Counterclockwise

Question 15

Clockwise or Counter-clockwise
1 0 0
0 C -S
0 S C

Answer 15

Clockwise

Question 16

point of intersection of the line defined by points p0 = (x0,y0) and p1 = (x1,y1) with the bottom boundary y = Ymin

Answer 16

( (x1 - x0) / (y1 - y0) ) (ymin - y0) + x0 , ymin)

Question 17

point of intersection of the line defined by points p0 = (x0,y0) and p1 = (x1,y1) with the bottom boundary x = Xmax

Answer 17

(xMax , ( (y1-y0) / (x1-x0) ) (xmax - x0) + y0 ) )

Question 18

rotate counter clockwise about y-axis

Answer 18

R = 
C  0  S  0
0   1  0  0
-S  0 C  0
0   0  0  1

R( X, Y, Z, 1 ) = Cx + Sz
y
-Sx + Cz
1

Question 19

Rotate counter clockwise through angle Theta about the pole

Answer 19

1) Rotate 45 degrees CW about Z
2) Rotate CCW through theta about X
3) Rotate 45 degrees CCW about Z

Question 20

Formula for lagrangian polynomial interpolation

Answer 20

y0[ (x−x1)(x−x2) / (x0−x1)(x0−x2)] + y1[ (x−x0)(x−x2) / (x1−x0)(x1−x2) ]+y2[ (x−x0)(x−x1)/ (x2−x0)(x2−x1) ]

Question 21

What is the Cohen Sutherland Line Clipping Test

Answer 21

C0 | C1 = 0 -> ACCEPT

C0 & C1 != 0 -> REJECT

Question 22

In Phong Illumination what is: Ij

Answer 22

Reflective Intensity

Question 23

In Phong Illumination what is: Iaj

Answer 23

ambient light intensity

Question 24

In Phong Illumination what is: Ipj

Answer 24

point light intensity

Question 25

In Phong Illumination what is: Kdj

Answer 25

diffuse reflectivity - delivers surface color

Question 26

In Phong Illumination what is: φ

Answer 26

angle of incidence L^T N for unit vectors L, N

Question 27

In Phong Illumination what is: d

Answer 27

distance to point source

Question 28

In Phong Illumination what is: Ksj

Answer 28

specular reflectivity

Question 29

In Phong Illumination what is: θ

Answer 29

V^T R for unit vectors V, R

Question 30

In Phong Illumination what is: n

Answer 30

shininess

Question 31

What is Lambert Shading

Answer 31

rendering each polygonal face with a single set of RGB intensities

Question 32

What is Gouraud Shading

Answer 32

applying an illumination model only at the vertices

Question 33

What is Phong Shading

Answer 33

applying the illumination model at every surface point associated with a pixel

Question 34

Computes colors for pixels not associated with vertices by linear interpolation of the vertex value

Answer 34

Gouraud Shading

Question 35

Uses normals obtained by linear interpolation of the vertex unit normals

Answer 35

Phong Shading

Question 36

This shading suffers from poor highlights

Answer 36

Gouraud Shading

Question 37

What is the OpenGL pipeline?

Answer 37

``` OMEPCPNVW Object Coordinates | Model View Eye Coordinates | Projection Clip Coordinates | Perspective Division Normalized Device Coordinates | Viewport Mapping Window Coordinates and Depth ```

Question 38

What is the first property of a Bezier Curve

Answer 38

Only the endpoints are interpolated | C(0) = P0 C(1) = Pn

Question 39

What is the second property of a Bezier Curve

Answer 39

Continuity | C ∈ (C^∞[0, 1])^3

Question 40

What is the third property of a Bezier Curve

Answer 40

The curve is globally controlled by datapoints

Question 41

What is the fourth property of a Bezier Curve

Answer 41

C is coordinate-free

Question 42

What is the firth property of a Bezier Curve

Answer 42

C has the convex hull property

Question 43

What is the sixth property of a Bezier Curve

Answer 43

C has the variation diminishing property

Question 44

construct a counter clockwise rotation about x

Answer 44

1 0 0 0 C S 0 -S C

Question 45

construct a counter clockwise rotation about y

Answer 45

C 0 -S 0 1 0 S 0 C

Question 46

construct a counter clockwise rotation about z

Answer 46

C S 0 -S C 0 0 0 1