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Flashcards in CSCE4230 - Final Deck (46):
1

Construct a scaling matrix
S = (S1, S2, S3)

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

2

Construct a clockwise Rotation by X matrix

1 0 0
0 C -S
0 S C

3

Construct a clockwise Rotation by Y matrix

C 0 S
0 1 0
-S 0 C

4

Construct a clockwise Rotation by Z matrix

C -S 0
S C 0
0 0 1

5

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

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

6

Matrix multiplication

(AB)ij = Σ AikBkj

7

Matrix Transpose

(A^T)ij = Aji

8

Scalar Product

= Σ Ui Vi

9

Vector Cross Product

p2p3 - p3p2
p3p1 - p1p3
p1p2 - p2p1

10

Vector Length

||V|| = √v1^2 + v2^2 + v3^2

11

Orthogonal Vectors

U1V1 + U2V2 + U3V3 = 0

12

Matrix inverse

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

13

Orthogonal Matrix

U^T = U^-1

14

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

Counterclockwise

15

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

Clockwise

16

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

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

17

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

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

18

rotate counter clockwise about y-axis

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

19

Rotate counter clockwise through angle Theta about the pole

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

20

Formula for lagrangian polynomial interpolation

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) ]

21

What is the Cohen Sutherland Line Clipping Test

C0 | C1 = 0 -> ACCEPT
C0 & C1 != 0 -> REJECT

22

In Phong Illumination what is: Ij

Reflective Intensity

23

In Phong Illumination what is: Iaj

ambient light intensity

24

In Phong Illumination what is: Ipj

point light intensity

25

In Phong Illumination what is: Kdj

diffuse reflectivity - delivers surface color

26

In Phong Illumination what is: φ

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

27

In Phong Illumination what is: d

distance to point source

28

In Phong Illumination what is: Ksj

specular reflectivity

29

In Phong Illumination what is: θ

V^T R for unit vectors V, R

30

In Phong Illumination what is: n

shininess

31

What is Lambert Shading

rendering each polygonal face with a single set of RGB intensities

32

What is Gouraud Shading

applying an illumination model only at the vertices

33

What is Phong Shading

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

34

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

Gouraud Shading

35

Uses normals obtained by linear interpolation of the vertex unit normals

Phong Shading

36

This shading suffers from poor highlights

Gouraud Shading

37

What is the OpenGL pipeline?

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

38

What is the first property of a Bezier Curve

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

39

What is the second property of a Bezier Curve

Continuity
C ∈ (C^∞[0, 1])^3

40

What is the third property of a Bezier Curve

The curve is globally controlled by datapoints

41

What is the fourth property of a Bezier Curve

C is coordinate-free

42

What is the firth property of a Bezier Curve

C has the convex hull property

43

What is the sixth property of a Bezier Curve

C has the variation diminishing property

44

construct a counter clockwise rotation about x

1 0 0
0 C S
0 -S C

45

construct a counter clockwise rotation about y

C 0 -S
0 1 0
S 0 C

46

construct a counter clockwise rotation about z

C S 0
-S C 0
0 0 1