unit 1 notes

1. CS8092-Computer graphics and
Multimedia
Illumination Models and Color
Models

2. Introduction 1
Illumination model:
Given a point on a surface, what is the perceived
color and intensity? Known as Lighting Model,
or Shading Model
Surface rendering:
Apply the Illumination model to color all pixels
of the surface.

3. Introduction 2
Example:
• Illumination model gives color
vertices,
• Surface is displayed via
interpolation of these colors.

4. Introduction 3
Illumination:
• Physics:
– Material properties, light sources, relative
positions, properties medium
• Psychology:
– Perception, what do we see
– Color!
• Often approximating models

5. Light sources 1
Light source: object that radiates energy.
Sun, lamp, globe, sky…
Intensity I = (Ired , Igreen , Iblue)
If Ired = Igreen = Iblue : white light

6. Light sources 2
Simple model: point light source
• position P and intensity I
• Light rays along straight lines
• Good approximation for small
light sources

7. Surface illumination 2
• Suppose, a light source radiates white light,
consisting of red, green and blue light.
reflection
absorption
If only red light is reflected,
then we see a red surface.
transmission

8. Surface illumination 3
• Diffuse reflection: Light is uniformly reflected in
all directions
• Specular reflection: Light is stronger reflected in
one direction.
specular reflection
diffuse reflection

9. Surface illumination 4
• Ambient light: light from the environment. Undirected
light, models reflected light of other objects.

10. Basic illumination model 1
Basic illumination model:
• Ambient light;
• Point light sources;
• Ambient reflection;
• Diffuse reflection;
• Specular reflection.
Ia
Il , Pof V
ka
kd
ks , ns
ka ,kd ,ks :reflection coefficien ts
k p  (kp,red , kp,green,kp,blue)

11. Basic illumination model 2
• Ambient light: environment light. Undirected light,
models reflected light of other objects.
Iamb  ka Ia

12. Color Modols for Computer
Graphics

13. Artist’s Color
Hue
Saturation
Value

14. Value
• Luminance
• Dark to Light
• Value range
– High key
– Middle key
– Low key

15. Hue - Paint Mixing
• Physical mix of
opaque paints
• Primary: RYB
• Secondary: OGV
• Neutral: R + Y + B

16. Hue - Ink Mixing
• Subtractive mix of
transparent inks
• Primary: CMY
• Secondary: RGB
• ~Black: C + M + Y
• Actually use CMYK
to get true black

17. Hue - Ink Mixing
Assumption: ink printed on pure white paper
CMY = White – RGB:
C = 1 – R, M = 1 – G, Y = 1 – B
CMYK from CMY (K is black ink):
K = min(C, M, Y)
C = C – K, M = M – K, Y = Y - K

18. Hue - Light Mixing
• Additive mix of
colored lights
• Primary: RGB
• Secondary: CMY
• White = R + G + B
• Show demonstration
of optical mixing

19. Saturation
• Purity of color

20. Perception of Color
In the end, color is a perceptual phenomenon

21. Color Constancy
Perceived color is
highly context
dependent
Allowing color
recognition with
variable lighting
conditions

22. Color Constancy
Perceived color is
highly context
dependent
Allowing color
recognition with
variable lighting
conditions

23. Simultaneous Contrast

24. Simultaneous Contrast

25. RGB Color Wheel
• Warm/Cool
• Complements
• Split Complement
• Analogous
• Show RGB Cube

26. HSV Color Model
RGB cube HSV top view
HSV is a projection of the RGB space
HSV cone

27. HSV Color Model
Hue, an angular measure (0 … 360)

28. HSV Color Model
Saturation, a fractional measure (0.0 … 1.0)

29. HSV Color Model
Value, a fractional measure (0.0 … 1.0)

30. CIE xyY Color Cone

31. CIE xyY Typical Display
Gamut

32. CIE Lu*v* and Lab
Perceptually Uniform Spaces
Lu*v* rescales xyY Lab color opponents

33. Color Picker

34. End

35. 35
COMPUTER GRAPHICS
OUTPUT PRIMITIVES

36. 36
2D Graphics Algorithms
• Output Primitives
• Line Drawing Algorithms
• DDA Algorithm
• Midpoint Algorithm
• Bersenhem’s Algorithm
• Circle Drawing Algorithms
• Midpoint Circle Algorithm
• Antialising
• Fill-Area Algorithms

37. 37
Output Primitives

38. 38
Output Primitives
• The basic objects out of which a graphics
display is created are called.
• Describes the geometry of objects and –
typically referred to as geometric
primitives.
• Examples: point, line, text, filled region,
images, quadric surfaces, spline curves
• Each of the output primitives has its own
set of attributes.

39. Line Drawing Algorithms
100

40. Line Drawing
• Line drawing is fundamental to computer graphics.
• We must have fast and efficient line drawing functions.
Rasterization Problem: Given only the two end points, how
to compute the intermediate pixels, so that the set of pixels
closely approximate the ideal line.

41. Line Drawing - Analytical Method
 ay
m 
by
bx  ax
c  ay  max
y
x
ax bx
y=mx+c
A(ax,ay)
B(bx,by)

42. Compute one point based on the previous point:
(x0, y0)…….…………..(xk, yk) (xk+1, yk+1) …….
I have got a pixel on the line (Current Pixel).
How do I get the next pixel on the line?
Next pixel on next column
(when slope is small)
Next pixel on next row
(when slope is large)
Incremental Algorithms

43. Current
Pixel
(xk, yk)
To find (xk+1, yk+!):
xk+1 = xk+1
yk+1 = ?
(5,2)
(6,1)
(6,2)
(6,3)
• Assumes that the next pixel to be set is on the next column of
pixels (Incrementing the value of x !)
• Not valid if slope of the line is large.
Incrementing along x

44. Digital DifferentialAnalyzerAlgorithm is an incremental
algorithm.
Assumption: Slope is less than 1 (Increment along x).
Current Pixel = (xk, yk).
(xk, yk) lies on the given line.
Next pixel is on next column.
Next point (xk+1, yk+1) on the line
yk = m.xk + c
xk+1 = xk+1
yk+1 = m.xk+1 + c
= m (xk+1) +c
= yk + m
Given a point (xk, yk) on a line, the next point is given by
xk+1 = xk+1
yk+1 = yk + m
Line Drawing - DDA

45. xk+1 = xk+1
yk+1 = Either yk or yk+1
Midpoint algorithm is an incremental algorithm
Midpoint Algorithm
Assumption:
Slope < 1
Current
Pixel

46. 46
Circle Drawing Algorithms

47. 47
Midpoint Circle Drawing
Algorithm
• To determine the closest pixel position to the
specified circle path at each step.
• For given radius r and screen center position (xc,
yc), calculate pixel positions around a circle path
centered at the coodinate origin (0,0).
• Then, move each calculated position (x, y) to its
proper screen position by adding xc to x andyc
to y.
• Along the circle section from x=0 to x=y in the
first quadrant, the gradient varies from 0 to -1.

48. Midpoint Circle Drawing Algorithm
 8 segments of octants for a circle:
48

49. Midpoint Circle Drawing Algorithm
 Circle function: fcircle (x,y) = x2 + y2 –r2
49
> 0, (x,y) outside the circle
< 0, (x,y) inside the circle
= 0, (x,y) is on the circle
boundary
{
fcircle (x,y) =

50. Midpoint Circle Drawing Algorithm
midpoint
yk-1
Fk < 0
yk+1 = yk
Next pixel = (xk+1, yk)
midpoin
yk-1
yk yk
t
Fk >= 0
yk+1 = yk - 1
Next pixel = (xk+1, yk-1)
50

51. Midpoint Circle Drawing Algorithm
We know xk+1 = xk+1,
Fk = F(xk+1, yk- ½)
Fk = (xk +1)2 + (yk - ½)2 - r2
Fk+1 = F(xk+1, yk- ½)
Fk+1 = (xk +2)2 + (yk+1 - ½)2 - r2
(2) – (1)
-------- (1)
-------- (2)
Fk+1 = Fk + 2(xk+1) + (y2 – y2 ) - (y
k+1 k
51
k+1 k
– y ) + 1
If Fk < 0,
If Fk >= 0,
Fk+1 = Fk + 2xk+1+1
Fk+1 = Fk + 2xk+1+1 – 2yk+1

52. 52
Midpoint Circle Drawing Algorithm
For the initial point, (x0 , y0) = (0, r)
f0 = fcircle (1, r-½ )
= 1 + (r-½ )2 – r2
= 5 – r
4
≈ 1 – r

53. Fill Area Algorithms
• Fill-Area algorithms are used to fill the
interior of a polygonal shape.
• Many algorithms perform fill operations
by first identifying the interior points,
given the polygon boundary.
53

54. Basic Filling Algorithm
The basic filling algorithm is commonly used
in interactive graphics packages, where the
user specifies an interior point of the region to
be filled.
4-connected pixels
54

55. 55
Basic Filling Algorithm
1 Set the user specified point.
2Store the four neighboring pixels in a
stack.
3 Remove a pixel from the stack.
4 If the pixel is not set,
Set the pixel
Push its four neighboring pixels into the stack
5 Go to step 3
6 Repeat till the stack is empty.

56. Basic Filling Algorithm
• Requires an interior point.
• Involves considerable amount of stack
operations.
• The boundary has to be closed.
• Not suitable for self-intersecting
polygons
56

57. 57
Types of Basic Filling Algorithms
• Boundary Fill Algorithm
• For filling a region with a single boundary
color.
• Condition for setting pixels:
• Color is not the same as border color
• Color is not the same as fill color
• Flood Fill Algorithm
• For filling a region with multiple boundary
colors.
• Condition for setting pixels:
• Color is same as the old interior color