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