aliasing and anti aliasing1.pdf

7/30/2019 aliasing and anti aliasing1.pdf

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Computer Graphics & Visualization

Lecture 4Anti-Aliasing

Line and Polygon Clipping

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Anti-Aliasing

OverviewSuper SamplingArea Sampling (prefiltering)Weighting (postfiltering)


Antialiasing

Aliasing, jagged edges or staircasingcan be reduced by:

Higherscreenresolution

- Needahugeframebuffer

Antialiasingtechniques

- Varypixelintensitiesalongboundariestosmooththeedge.


Antialiasing Techniques

Super Sampling

Computeintensitiesatsub-pixelgridpositionsandcombinetheresultstoobtainthepixelintensity.

Area Sampling

Findpixelintensitybycalculatingtheareasofoverlapofeachpixelwithintheobjectstobedisplayed.


Supersampling

(zero line width)

Example:astraightlineonagrayscaledisplay

Divideeachpixelintosub-pixels.

Thenumberofintensitiesarethemaxnumberofsub-pixelsselectedonthelinesegmentwithinapixel.


Supersampling

(finite line width)

Theintensitylevelforeachpixelisproportionaltothenumberofsub-pixelsinsidethepolygonrepresentingthelinearea.

Lineintensityisdistributedovermorepixels.


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Postfiltering

Equalareascancontributetounequalintensity.Aweightedavarage.

WeigtingMasks

Predefinedtablevaluesforeachsubpixel

Filtering Techniques

Includesneighbouringpixels


Filter Functions

Optimalfiltersarecomputationallymoreexpensive.

Conefiltersareaveryreasonablecompromisebetweencostandquality.


Anti-Aliasing

Line Intensity Differences:

Thediagonallineappearslessbrightthanthehorizontal.

Totalintensityisproportionaltotheirlength.


Line and PolygonClipping

Overview Cohen-Sutherland line clipping algorithm Liang-Barsky line clipping algorithm

Sutherland-Hogeman polygon clipping


Clipping Algorithms

Line Clipping:

Cohen-Suterland(encoding)

- Oldestandmostcommonlyused

Nicholl-Lee-Nicholl(encoding)(moreefficient)

Liang-Barsky (parametric)(moreefficient)

Polygon Clipping:

Sutherland-Hodgeman

- Divideandconquerstrategy

Weiler-Atherton(modifiedforconcavepolygons)


1001 1000 1010

0101 0100 0110

0001 0000 0010

C0 = Bit code of P0Cend = Bit code of Pend

Cohen-Sutherland Line-Clipping

1. EncodeendpointsBit0=pointisleftofwindowBit1=pointisrightofwindowBit2=pointisbelowwindowBit3=pointisabovewindow

2. IfC0 Cend 0 thenP0Pend istriviallyrejected

3. IfC0 Cend = 0 thenP0Pend istriviallyaccepted

4. Otherwisesubdivideandgotostep1withnewsegment.


3/5

3


1001 1000 1010

0101 0100 0110

0001 0000 0010

Clip order: Left, Right, Bottom, Top

A1

A3

B3

C3

D3

E2

D2

C2

B2

A2

B1

C11) A1C1 1) A2E2

2) B1C1 2) B2E2

3) reject 3) B2D2

4) B2C2

5) accept

1) A3D3

2) A3C3

3) A3B3

4) accept




Willdounnecessaryclipping.

Efficientwhenmostofthelinestobeclippedareeitherrejectedoraccepted(notsomanysubdivisions).

Easytoprogram


Parametric form

Alinesegmentwithendpoints

(x0, y0) and(xend, yend)

wecandescribeintheparametricform

x = x0 + uxy = x

0

+ uy 0 u 1

where

x = xend x0y = yend y0


Liang-Barsky Line-Clipping

MoreefficientthanCohen-Sutherland

Alineisinsidetheclippingregionforvaluesofu suchthat:

xwmin x0 + ux xwmax x = xend x0

ywmin y0 + uy ywmax y = yend y0

Canbedescribedas

u pk qk, k = 1, 2, 3, 4


k

kk

p

qu =

0max44

min033

0max22

min011

yywqyp

ywyqyp

xxwqxp

xwxqxp

==

==

==

==

where

Leftboundary

Rightboundary

Bottomboundary

Topboundary


The infinitely line intersects the clipregion edges when:



Whenpk< 0,asu increases

- linegoesfromoutsidetoinside- entering

Whenpk> 0,

- linegoesfrominsidetooutside- exiting

Whenpk= 0,

- lineisparalleltoanedge

Ifthereisasegmentofthelineinsidetheclipregion,asequenceofinfinitelineintersectionsmustgo:entering,entering,exiting,exiting


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EnterEnter

ExitExit

Enter

Exit

EnterExit

Clipregion



1. Setumin = 0 andumax = 1.

2. Calculatetheu values:

3. Ifu < umin oru > umax ignoreit.Otherwiseclassifytheu valuesasenteringorexiting.

4. Ifumin < umax thendrawalinefrom:

( x0 + x umin, y0 + y umin ) to( x0 + x umax, y0 + y umax )


0,10

0,0 10,0

10,10

P0(-5,3)

Pend(15,9)

6

7

39

310

2

1

)39(

03

4

3

)5(15

)5(10

4

1

))5(15(

05

0max

4

4

min0

3

3

0max

2

2

min0

1

1

=

=

==

=

=

==

=

=

==

=

=

==

y

yyw

p

qu

y

ywy

p

qu

x

xxw

p

qu

x

xwx

p

qu

top

bottom

right

left

u < 0 thenignore

u > 1 thenignore

Entering uenter = 1/4

Exiting uleave = 3/4

ExampleLiang-Barsky



Wehaveuenter= 1/4 anduleave = 3/4

Pend - P0 = (15+5,9-3) = (20,6)

Ifuenter< uleave ,thereisalinesegment

- computeendpointsbysubstitutingu values Drawalinefrom

(-5+(20)(1/4), 3+(6)(1/4))to

(-5+(20)(3/4), 3+(6)(3/4))

x y


0,10

0,0 10,0

10,10

P0(-8,2)

Pend(2,14)

3

2

214

210

6

1

)214(

02

5

9

)8(2

)8(10

5

4

))8(2(

08

0max

4

4

min0

3

3

0max

2

2

min0

1

1

=

=

==

=

=

==

=

=

==

=

=

==

y

yyw

p

qu

y

ywy

p

qu

x

xxw

p

qu

x

xwx

p

qu

top

bottom

right

left

u < 0 thenignore

u > 1 thenignore

Entering uenter= 4/5

Exiting uleave = 2/3

Example

Liang-Barsky



Wehaveuenter= 4/5 anduleave = 2/3

Pend - P0 = (2+8, 14-2) = (10, 12)

uenter> uleave ,thereisnolinesegmentdodraw


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Nicholl-Lee-Nicholl Line Clipping

Avoidsmultipleclippingofanindividuallinebycreatingmoreregions.

Onlythreeregionsneedtobeconsidered.

FindpositionofPend relativetoP0.

P0

P0

P0

inside edgeregion cornerregion



IfP0 insideandPend outside:

IfP0 istotheleft:

B

RL

T

P0

LB

LR

LT

P0L

L

L

LB

TRT

P0

LT

TB

IfP0 istotheleftandabove:



To determine region

compareslopes,and

boundariesoftheNLNregion.


Sutherland-HodgemanPolygon Clipping

Four test cases:1. Firstvertexinsideandthesecondoutside(in-outpair)

2. Bothverticesinsideclipwindow

3. Firstvertexoutsideandthesecondinside(out-inpair)

4. Bothverticesoutsidetheclipwindow

Concavepolygonsmaybedisplayedwithextralines.


Weiler-Atherton

Polygon Clipping

Clipsconcavepolygonscorrectly.

Insteadofalwaysgoingaroundthepolygonedges,wealso,wanttofollowwindowboundaries.

Foranoutside-to-insidepairofvertices,followthepolygonboundary.

Foraninside-to-outsidepairofvertices,followthewindowboundaryinaclockwisedirection.

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