CSCE4230 - Final Flashcards
Construct a scaling matrix
S = (S1, S2, S3)
S1 0 0 0
0 S2 0 0
0 0 S3 0
0 0 0 1
Construct a clockwise Rotation by X matrix
1 0 0
0 C -S
0 S C
Construct a clockwise Rotation by Y matrix
C 0 S
0 1 0
-S 0 C
Construct a clockwise Rotation by Z matrix
C -S 0
S C 0
0 0 1
Scalar multiplication
[4][ a11 a12 a13
a21 a22 a23
a31 a32 a33]
4(aij) (i,j = 1, 2, 3)
Matrix multiplication
(AB)ij = Σ AikBkj
Matrix Transpose
(A^T)ij = Aji
Scalar Product
<u> = Σ Ui Vi</u>
Vector Cross Product
p2p3 - p3p2
p3p1 - p1p3
p1p2 - p2p1
Vector Length
||V|| = √v1^2 + v2^2 + v3^2
Orthogonal Vectors
U1V1 + U2V2 + U3V3 = 0
Matrix inverse
AA^-1 = A^-1 A = I
Orthogonal Matrix
U^T = U^-1
Clockwise or Counter-clockwise
1 0 0
0 C S
0 -S C
Counterclockwise
Clockwise or Counter-clockwise
1 0 0
0 C -S
0 S C
Clockwise
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)
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 ) )
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
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
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) ]
What is the Cohen Sutherland Line Clipping Test
C0 | C1 = 0 -> ACCEPT
C0 & C1 != 0 -> REJECT
In Phong Illumination what is: Ij
Reflective Intensity
In Phong Illumination what is: Iaj
ambient light intensity
In Phong Illumination what is: Ipj
point light intensity
In Phong Illumination what is: Kdj
diffuse reflectivity - delivers surface color
In Phong Illumination what is: φ
angle of incidence L^T N for unit vectors L, N
In Phong Illumination what is: d
distance to point source
In Phong Illumination what is: Ksj
specular reflectivity
In Phong Illumination what is: θ
V^T R for unit vectors V, R
In Phong Illumination what is: n
shininess
What is Lambert Shading
rendering each polygonal face with a single set of RGB intensities
What is Gouraud Shading
applying an illumination model only at the vertices
What is Phong Shading
applying the illumination model at every surface point associated with a pixel
Computes colors for pixels not associated with vertices by linear interpolation of the vertex value
Gouraud Shading
Uses normals obtained by linear interpolation of the vertex unit normals
Phong Shading
This shading suffers from poor highlights
Gouraud Shading
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
What is the first property of a Bezier Curve
Only the endpoints are interpolated
C(0) = P0 C(1) = Pn
What is the second property of a Bezier Curve
Continuity
C ∈ (C^∞[0, 1])^3
What is the third property of a Bezier Curve
The curve is globally controlled by datapoints
What is the fourth property of a Bezier Curve
C is coordinate-free
What is the firth property of a Bezier Curve
C has the convex hull property
What is the sixth property of a Bezier Curve
C has the variation diminishing property
construct a counter clockwise rotation about x
1 0 0
0 C S
0 -S C
construct a counter clockwise rotation about y
C 0 -S
0 1 0
S 0 C
construct a counter clockwise rotation about z
C S 0
-S C 0
0 0 1
