CST 494/598 Computer Graphics Anshuman Razdan [email protected] i3dea.asu.edu/razdan.

CST 494/598Computer Graphics

Anshuman [email protected]

i3dea.asu.edu/razdan

A Razdan and Peter Wonka 2

Disclaimer

These slides can only be used as study material for the class 470 at ASUThe slides cannot be distributed or used for another purposeThe slides may contain errorsThe slides do not contain all the information necessary to succeed in class; additional material from the book must to be studiedThe slides are based on a lecture from Prof. Purgathofer from the Vienna University of Technology


Color and Gray Scale

color information: RGBcolor codes directly in frame buffer

1024 x 1024 x 24 bit/color 3 Mbyte storage

color (lookup) tables

less storage

easy change of color table(e.g., for color coding)

gray scalecalculated from RGB

e.g. intensity = 0.5 [min(r,g,b) + max(r,g,b)]

red green blue Farbe 0 0 0 black 0 0 1 blue 0 1 0 green 0 1 1 cyan 1 0 0 red 1 0 1 magenta 1 1 0 yellowyellow 1 1 1 white


Color Lookup Table

i

j

r i

j

g i

j

b

i

j

xxxx r g b

instead of:

now: selected colors addressed by table index


Line Attributes (1)

type solid, dashed, dotted,…

pixel mask (raster line algorithms)

width Bresenham + additional vertical (horizontal) spans

width dependent on line slope

line caps


Line Attributes (2)width

thick lines as filled rectangles joining two segments: miter round bevel

pen and brush options shape, size, pattern pixel mask simulation of brush strokes

color


Area-Fill Attributes (1)

fill styleshollow with color border

filled with solid color

filled with specific pattern or design (e.g., hatch,…)



fill optionsedge type, width, color

pattern specificationthrough pattern tables

tiling (pattern reference point)

4 00 4

startposition

pixel startposition

4 00 4

4 00 4

4 00 4

4 00 4

4 00 4

4 00 4

4 00 4

4 00 4

4 00 4

4 00 4

4 00 4

4 00 4



combination of fill pattern with background colors

soft fillcombination of colors

antialiasing at object borders

simulation of semitransparent brushes

example: linear soft-fill

pattern background

and

or

xor

replace

F...foreground colorB...background color

BttFP )1(


Scan-Line Polygon-Fill Algorithm

interior pixels along a scan line passing through a polygon area


Scan-L. Fill: Intersecting Vertices

intersection points along scan lines that intersect poly-gon vertices. y: odd number of intersectionsy’: even number of intersections (bad) can be paired for correct interior pixel spans


Scan-L. Fill: Incremental Update

incremental update of intersection point

kk

kk

xxyy

m

1

1

11 kk yy

mxx kk

11

yx

xx kk 1

slope of polygon boundary line: m

(for 2 successive scanlines)


Scan-L. Fill: Sorted Edge Table

sort all edges on smallest y-valueedge entry: [max y-value, x-intercept, inverse slope]

active-edge list for each scan linecontains all edges crossed by that scan lineincremental update

consecutive intersection pairs (spans) filled


Sorted Edge Table: Example

a polygon and its sorted edge table, with edge DC shortened by 1 unit


Scan-Line Fill: Active-Edge List

active-edge list for -DC’ - DE - AE - AB


Inside-Outside Tests


Flood-Fill Algorithm

pixel filling of areaareas with no single color boundary

start from interior point

“flood” internal region

4-connected, 8-connected areas

reduce stack size by eliminating several recursive calls


Flood-Fill: Definition of Boundary

area must be distinguishable from boundaries

example: area definedwithin multiple colorboundaries


Flood-Fill: Connectedness

Definition: 4-connected means, that a connection is only valid in these 4 directions

Definition: 8-connected means, that a connection is only valid in these 8 directions


Example for 4- and 8-connected

a 4-connected area an 8-connected areaa 4-connected area has an 8-connected border

an 8-connected area has a 4-connected border


Simple Flood-Fill Algorithm


Bad Behaviour of Simple Flood-Fill

12

43

recursionsequence


Span Flood-Fill Algorithm

floodFill4 produces too high stacks (recursion!)

solution: incremental horizontal fill (left to right)

recursive vertical fill (first up then down)


Good Behaviour of Span Flood-Fill

1

2

recursionsequence


Span Flood-Fill Example

x



s2

1 2 3

s1



s5 s4

4 5 6 7 8 9 10 11

1 2 3 s2

s1

s3



s5

12 13 14 s4

4 5 6 7 8 9 10 11

s3 1 2 3 s2

s1



12 13 14 s4

4 5 6 7 8 9 10 11

s3 1 2 3 s2

s1

16 17 1815



15 16 17 18

12 13 14 19

4 5 6 7 8 9 10 11

s3 1 2 3 s2

s1



12 13 14

s4 4 5 6 7 8 9 10 11

20 21 22 1 2 3 s2

s3 s1

15 16 17 18

19



12 13 14

23 4 5 6 7 8 9 10 11

20 21 22 1 2 3 s2

s3 s1

15 16 17 18

19



12 13 14

23 4 5 6 7 8 9 10 11

20 21 22 1 2 3 s2

24 25 s1

s3

15 16 17 18

19



12 13 14

23 4 5 6 7 8 9 10 11

20 21 22 1 2 3 s2

24 25 s1=s5

26 27 28 29 30

s4 s3

15 16 17 18

19



12 13 14

23 4 5 6 7 8 9 10 11

20 21 22 1 2 3 s2

24 25 31 32 33

26 27 28 29 30

s4 s3

15 16 17 18

19



12 13 14

23 4 5 6 7 8 9 10 11

20 21 22 1 2 3 s2

24 25 31 32 33

26 27 28 29 30

34 35 s3

15 16 17 18

19



12 13 14

23 4 5 6 7 8 9 10 11

20 21 22 1 2 3 s2

24 25 31 32 33

26 27 28 29 30

34 35 36 37

15 16 17 18

19



12 13 14

23 4 5 6 7 8 9 10 11

20 21 22 1 2 3 38

24 25 31 32 33

26 27 28 29 30

34 35 36 37

15 16 17 18

19


text attributesfont (e.g. Courier, Arial, Times, Roman, …)

styles (regular, bold, italic, underline,…)

size (32 point, 1 point = 1/72 inch)

proportionally sized vs. fixed space fonts

string attributesorientation

alignment (left, center, right, justify)

Character Attributes

vertical

horizontal

slanted

Displayed primitives generated by the raster algorithms discussed in Chapter 3 have a jagged, or stairstep, appearance.

Displayed primitives generated by the raster algorithms

discussed in Chapter 3 have a jagged, or

stairstep, appearance.

Displayed primitives generated by the raster algorithms

discussed in Chapter 3 have a jagged, or

stairstep, appearance.

Displayed primitives generated by the raster algorithms discussed in Chapter 3 have a jagged, or stairstep, appearance.


Antialiasing

what is aliasing?

what is the reason for aliasing?

what can we do against it?


What is Aliasing?

not enough resolution

not enough colors

not enough images / sec

geometric errors

numeric errors

errors that are caused by the discretization of analog data to digital data


Aliasing: Staircase Effect


Various Aliasing Effects


Aliasing from too few Colors

artificial color borders can appear


Aliasing in Animations

jumping images"worming“

backwards rotating wheels

t


Backwards Rotating Wheels


Solutions against Aliasing?

1. improve the deviceshigher resolution

more color levels

faster image sequence

2. improve the imagespostprocessing

antialiasing !

expensiveor

incompatible

software


Shannon Sampling Theorem

a signal can only be reconstructed without information loss if the sampling frequency is at least twice the highest frequency of the signal

this border frequency is called "Nyquist Limit"


Shannon Sampling Theorem

Nyquistsamplinginterval

sampling rate

original signal

reconstructed signal


Antialiasing: Nyquist Sampling Frequency

a signal can only be reconstructed without information loss if the sampling frequency is at least twice the highest frequency of the signal

maxcycle /1x with2

fx

x cycles

i.e. sampling interval one-half cycle interval

max2 ff s Nyquist sampling frequency:


supersampling straight-line segments

subpixel weighting masks

area sampling straight-line segments

filtering techniques

compensating for line-intensity differences

antialiasing area boundaries(adjusting boundary pixel positions)

adjusting boundary pixel intensity

Antialiasing Strategies


Antialiasing: Supersampling Lines

00 00 1100 22 2233 11 00

00 00 4411 66 8888 55 00

3 = max. intensity...0 = min. intensity

9 = max. intensity...0 = min. intensity

thin line line of finite width


Antialiasing


Antialiasing: Area Sampling Lines

calculate the pixel coverage exactly

can be done with incremental schemes

00%% 00%% 4343

1515 7171 8484

9090 5252 33%%


Antialiasing: Pixel Weighting Masks

relative weights for a grid of 3x3 subpixels

more weight for center subpixels

must be divided by sum of weights

subpixel grids can also include some neighboring pixels


Antialiasing: Filtering Techniques

box filter cone filter Gaussian filter

continuous overlapping weighting functions to calculate the antialiased values with integrals


Antialiasing: Compensating for Intensity Differences

unequal line lengths displayed with the same number of pixels in each line/row have different intensities

proper antialiasing compensates for that!


Antialiasing


Antialiasing Area Boundaries (1)

adjusting pixel intensities along an area boundary

alternative 1:supersampling



alternative 2: like midpoint line algorithm

p´ = y ymid = [m(xk + 1) + b] (yk + 0.5)

p´<0 y closer to yk

p´>0 y closer to yk+1

p = p´+ (1m) :p<1m closer to yk

p>1m closer to yk+1

( and p [0,1] )

yymid

Note: We add (1-m) so that the decision parameter p = area covered by polygon!



p = p´+(1-m) = [m(xk + 1) + b] (yk + 0.5) + (1 m)= mxk + b yk + 0.5

=

xk xk+1

yk

yk+ 0.5p for next pixel= overlap areafor current pixel

p´

p = p´-m+1 = p´+(1-m)

mp´-m


Antialiasing Examples


Antialiasing Examples


Summary: Attributes of Primitives

color and greyscale

line attributes

area fill attributes

character attributes

antialiasingaliasing effects

reasons for aliasing

antialiasing strategies

CST 494/598 Computer Graphics Anshuman Razdan [email protected] i3dea.asu.edu/razdan.

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