cg filling polys

8/11/2019 CG Filling Polys

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Polygon Filling


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Filling the Spans

Span-filling is an important step in the whole polygon-fillingalgorithm, and it is implemented by a three-step process:

Find the intersections of the scan line with all edges of the

polygon.

Sort the intersections by increasing x coordinates.

Fill in all pixels between pairs of intersections that lie interior to

the polygon.

Now more questions arise:

How do we find and sort the intersections efficiently?

How do we judge whether a pixel lying inside or outside the polygon?


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Parity (Odd-Even) Rule

Parity starting from even

oddodd

odd

odd

even

even

even


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Filling Rules

Given an intersection with an arbitrary, fractional xvalue, how do we determine which pixel on either side

of that intersection is interior?

A: The strictly

inside rule:


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Filling Rules


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Filling Rules

How do we deal with the special case in which thevertices define a horizontal edge?

Bottom edges are drawn Top edges are not


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Example

A B

C D

E

FG

HI

J


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Edge Coherence Scan fill method

Brute-force technique of testing each polygon edge forintersection with each new scan lineit is inefficient andslow.

Clever Solution: if an edge intersects with a scan line, and the

slope of the edge is m,then successive scan line intersectionscan be found from:

xi+1

= xi+ 1/m

The floating-point arithmetic can be avoided by storing thenumerator, comparing to the denominator, and incrementingxwhen it overflows.


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1/m = 2/5

xmin= 3,

the sequence is:

numerator:

denominator:

Edge Coherence (cont.)

2

5

35

16

m

,...5

14

5

63,

5

43,

5

23

5

23

5

43

5

14

2

5

4 1


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Catch the intersection information in a table Edge Table (ET) with all edges sorted by ymin

Active Edge Table(AET) containing

The edges that intersect the current scan line

Their points of intersection

Sorted byx-coordinate, left to right

Catching Edge/Scan line intersections


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Global edge table (ET): make the

addition of edges to the AET

efficient. It contains all edges

sorted by their smaller y

coordinate.

An Example for the Global Edge Table

ycoordinate

11 13 0 CD

9 2 0 FA

3 7 -5/2 AB

5 7 6/4 BC

9 7 -5/2 EF

11 7 6/4 DE

11

10

9

8

7

6

5

4

3

2

1

0

ymax

xmin

1/m


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An Example of the Active Edge Table

AB

C

F

E

D

2

5

4

611 10

11 13 0

09 2

9 2

AET pointer

FA

EF

DE

CDAs each new scan-liney+1is encounter, update AET:

1). Remove edges not intersected byy+1 (ymax=y)

2). Add edges intersected byy+1 (ymin=y+1)

3). Calculate new xintersections.Y

max

xm

1


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1. Set yto the smallest ycoordinate that has an entry in the ET, that is, yfor

the first nonempty bucket.

2. Initialise the AET to be empty.

3. Repeat until the AET and ET are empty.

3.1 Move from ET bucket yto the AET those edges whose

ymin= y (entering edges).

3.2 Remove from the AET those entries for which y=ymax (edges

not involved in the next scan line), then sort the AET onx

(made easier because ET is pre-sorted).

3.3 Fill in desired pixel values on scan line yby using pairs

ofxcoordinates from the AET.

3.4 Increment yby 1 (to the coordinate of the next scan line).

3.5 For each non-vertical edge remaining in the AET, update

xfor the new y.

Scan-Line Algorithm


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Boundary-Fill

Algorithm


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Polygon Filling:

Boundary-Fill Algorithm

1

2

21


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Polygon Filling:


1

3

31


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Polygon Filling:


1

46

5

41

5 6


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Polygon Filling:


1

4 5

41

5


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Polygon Filling:


1 41

4


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Polygon Filling:


1 71

7


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Polygon Filling:


1 919


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Polygon Filling:


11


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Flood-Fill

Algorithm

Boundar

y-Fill

Algorithm

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