10 an cg polygonclipping

7/29/2019 10 an CG PolygonClipping

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Computer GraphicsPolygon Clipping

By

Asmita Nag


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What is Polygon Clipping Its the process of finding the exact part of a polygon

lying inside the view volume

To maintain consistency, clipping of a polygon shouldresult in a polygon, not a sequence of partially

unconnected lines


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Before Clipping After ClippingBefore Clipping After Clipping

It is not merely Line Clipping...


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Modify line clipping procedures.

After applying line clipper the polygon is displayed

as a series of unconnected line segments.

Before Clipping After Clipping



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For polygon clipping generate algorithm for approp

riate area fill

Before Clipping After Clipping



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Example

Examples...


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Example

Examples...


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Example

Examples...


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Clip the polygon by processing the polygon boundary as a whole against each window.

Process all polygon vertices against each clip recta

ngle boundary in turn.First clip the polygon against the left boundary to pr

oduce a new sequence of vertices.

The new sequence of vertices is then successive passed to right, bottom and top boundary clipper.

At each step a new sequence of output vertices is generated and passed to the next boundary clipper

Sutherland Hodgeman Method


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Original

Polygon

Clip

Bottom

Clip

Top

Clip

Left

Clip

Right

Polygon Clipping


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Initial Condition

Sutherland-Hodgeman Algo.

Clip Against Right Clipping Boundarylip Against Top Clipping Boundaryhe Clipped Polygonlip Against Bottom Clipping Boundarylip Against Left Clipping Boundary


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Case 1

Inside Outside

Polygon

being

clipped

Clip

boundary

s

p:output

4 Cases of Polygon Clipping

Case 2

Inside Outside

s

p

i:output

Case 3

Inside Outside

s

p

(no output)

Case 4

Inside Outside

s

i:first output

p:second output


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Algorithm

Input vertex P

Firs t Point YesNo

F=P

Does SP intersect

E?No

Yes

Compute

Intersection PointI

Output

vertex I

S=P

Is S on left

side of E?

Exit

NO

Yes

Output

vertex S

Close Polygon entry

Does SF

intersect E?

Compute

Intersect ion I

Yes

Output

vertex I

Exit

No


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Sutherland-HodgmanPolygon Clipping

Input each edge (vertex pair) successively.

Output is a new list of vertices.

Each edge goes through 4 clippers.

The rule for each edge for each clipper is:

If first input vertex is outside, and second is inside,output the intersection and the second vertex

If both input vertices are inside, then just outputsecond vertex

If first input vertex is inside, and second is outside,output is the intersection

If both vertices are outside, output is nothing


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Sutherland-Hodgman Polygon Clipping

v2

v1

v3

Right

Clipper

Bottom

Clipper

Top

Clipper

Left

Clipper

v1v2

v2v3

v3v1

v1

v2

v2

v2

v3v1

v2v2

v2v3

v3v1

v1v2

v2

v3

v1

v2 v2v2

v2v3

v3v1

v1v2

v3

Figure 6-27, page 332

v2

v1v2

v2 v2v2

v2v1

v1v2

v2v2

v1

v2

v2

v2

Edges Output Edges Output Edges Output Edges Output

Final


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Problems with Sutherland-Hodgman

What if you clip these?


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Weiler-Atherton Algorithm

When we have non-convex polygons then the

algorithm above might produce polygons with

coincident edges

This is sometimes OK for rendering but is not

for other applications (e.g. shadows)

The Weiler-Atherton algorithm produces

separate polygons for each visible fragment


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Weiler-Atherton Algorithm

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A

B

i j

k

l

clip region

polygon

loop of polygon

vertices

loop of region

vertices


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Find the intersection vertices and connect them

in the two lists

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A

B

i j

k

l

clip region

polygon

i

l

k

j

Add vertex i:


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A

B

i j

k

l

clip region

polygon

i

l

k

j

Add vertex l:

Find the intersection vertices and connect

them in the two lists


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A

B

i j

k

l

clip region

polygon

i

l

k

j

Add vertex k:

Find the intersection vertices and connect

them in the two lists


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a b

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A

B

i j

k

l

clip region

polygon

i

l

k

j

Completed Loop

Add vertex j:


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A

B

i j

k

l

clip region

polygon

i

l

k

j

Entering

Leaving

Classify each intersection vertex as Entering

orLeaving


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a

b

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i

l

k

j

EnteringLeaving

Capture clipped polygons

Start at an entering vertex

If you encounter a leaving

vertex swap to right hand (

clip polygon) loop If you encounter an enterin

g vertex swap to left hand (

polygon) loop

A loop is finished when you arrive back at start

Repeat whilst there are ent

ering vertices


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0

a

b

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i

l

k

j

EnteringLeaving

Capture clipped polygons

Loop 1:

L, 4, 5, K

Loop 2:

J, 9, 0, I


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10 an cg polygonclipping

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