clipping

1

Clipping

3

Culling and Clipping

• What can’t we see?

- anything occluded by another object (HSR)

- anything outside view volume

• Today: clipping

11

Clipping Against a Rectangular RegionMultiple Cases

A

B

C

D

E

F

Clip Rectangle

G

H

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Division of Space

ymin

ymax

xmin xmax

Clip Region

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Cohen-Sutherland Clipping:“Outcodes”

1 1 00

minyy

y ymax

minxx

x xmax

min

min1

max

max0

0

1

0

1

:Example

yy

yyb

yy

yyb

0b 1b 2b 3b

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Cohen-Sutherland Clipping:Region Outcodes

ymin

ymax

xminxmax

1001 1000 1010

0001

0101 0100 0110

00100000

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Cohen-Sutherland Clipping:Trivial Acceptance: O(P0) = O(P1) = 0

ymin

ymax

xmin xmax

1001 1000 1010

0001

0101 0100 0110

00100000

P0

P1

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Cohen-Sutherland Clipping:Trivial Rejection: O(P0) & O(P1) 0

ymin

ymax

xmin xmax

1001 1000 1010

0001

0101 0100 0110

00100000

P0

P1

P1P1

P0

P0

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Cohen-Sutherland Clipping: O(P0) =0 , O(P1) 0

ymin

ymax

xmin xmax

1001 1000 1010

0001

0101 0100 0110

00100000

P0

P1

P1

P1 P0

P0

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Cohen-Sutherland Clipping: The Algorithm

• Compute the outcodes for the two vertices

• Test for trivial acceptance or rejection

• Select a vertex for which outcode is not zero- There will always be one

• Select the first nonzero bit in the outcode to define the boundary against which the line segment will be clipped

• Compute the intersection and replace the vertex with the intersection point

• Compute the outcode for the new point and iterate

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Cohen-Sutherland Clipping:Example 1

ymin

ymax

xmin xmax

1001 1000 1010

0001

0101 0100 0110

00100000

A

B

C

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ymin

ymax

xmin xmax

1001 1000 1010

0001

0101 0100 0110

00100000

B

C

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Chopping at each boundary

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ymin

ymax

xmin xmax

1001 1000 1010

0001

0101 0100 0110

00100000

B

C

A

D

E

23


ymin

ymax

xmin xmax

1001 1000 1010

0001

0101 0100 0110

00100000

B

C

D

E

24


ymin

ymax

xmin xmax

1001 1000 1010

0001

0101 0100 0110

00100000

B

C

D

25


ymin

ymax

xmin xmax

1001 1000 1010

0001

0101 0100 0110

00100000

B

C

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Cohen-Sutherland Clipping:Advantages/Extension

• Easily extended to 3 dimensions by adding two bits to the outcode for the z axis.

• Calculations then reduce to intersection of line with plane

• Algorithm most efficient when most segments can either be trivially accepted or trivially rejected

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Cohen Sutherland in 3D

• Use 6-bit outcodes

• When needed, clip line segment against planes

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Other Clipping Algorithm

• Cyrus–Beck, Liang–Barsky

- generally, these try to be more clever about intersections

- represent lines parametrically, solve for intersection t values

P(t) = P0 + t(P1-P0)

- can clip in fewer steps than Cohen–Sutherland

- try to increase number of trivial rejection cases

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Parametric Representation of Lines

)0(0 pp

)1(1 pp

)(p

10)1()( ppp

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Liang-Barsky Clipping

• Consider the parametric form of a line segment

• We can distinguish between the cases by looking at the ordering of the values of where

the line determined by the line segment crosses the lines that determine the window

p() = (1-)p1+ p2 1 0

p1

p2

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Liang-Barsky Parametric Clipping

)()( 010 pppp

0)( iEi ppN

0)( iEi ppN

Edge Ei

0p

1piE

p

N i

InsideOutside

0)( iEi ppN

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Potentially Entering (PE) and Potentially Leaving (PL) Points

001 ppN i

Edge Ei

0p

1p

N i

InsideOutside

Edge Ei

N i

Inside Outside

001 ppN i

Potentially Entering(PE) Point

Potentially Leaving(PL) Point

0p

1p

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Liang-Barsky Clipping:Computing the Intersection

0)( iEi ppN

)()( 010 pppp

0010 ppNppN iEi i

:for solve and )(Let 01 ppD

DN

ppN

i

Ei i0=

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Liang-Barsky Clipping:Potentially Leaving vs. Potentially Entering

ymin

ymax

xmin xmax

= “Inside”

0p

1pPE

PE

PE

PE

PL

PL

PL

PL

0p

0p

1p1p

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Liang-Barsky Clipping:Algorithm Strategy

• Find the largest PE greater than zero.• Find the smallest PL less than one.• Reject the segment if PE > PL.

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Liang-Barsky Clipping:Pseudocode of Algorithm

for (each line segment to be clipped)

alpha_E=0; alpha_L=1;

for (each candidate intersection with a clip edge) {

if (Ni•D!=0) { /*edges not parallel to line*/

calculate alpha;

use sign of Ni•D to class alpha as PE or PL;

if (PE) alpha_E = max(alpha_E,alpha);

if (PL) alpha_L = min(alpha_L,alpha);

}

}

if (alpha_E > alpha_L)

return NULL;

else

return P(alpha_E) and P(alpha_L) as clip intersections

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Polygon Clipping:Convex Polygons

Line segment clipping is done in order. New verticesare generated at clip point. External vertices areeliminated.

1

2

3

45

1

2

3

4’5’

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Polygon Clipping:The Convexity Problem

Single object becomes multiple objects.

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Sutherland-Hodgeman Polygon Clipping

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clipping

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