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College of Computer and Information Science, Northeastern UniversityApril 17, 20151 CS U540 Computer Graphics Prof. Harriet Fell Spring 2009 Lecture 9.

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Presentation on theme: "College of Computer and Information Science, Northeastern UniversityApril 17, 20151 CS U540 Computer Graphics Prof. Harriet Fell Spring 2009 Lecture 9."— Presentation transcript:

1 College of Computer and Information Science, Northeastern UniversityApril 17, CS U540 Computer Graphics Prof. Harriet Fell Spring 2009 Lecture 9 – January 26, 2009

2 College of Computer and Information Science, Northeastern UniversityApril 17, Today’s Topics Fill: Boundary Fill vs. Polygon Fill 2D Polygon Fill

3 College of Computer and Information Science, Northeastern UniversityApril 17, Scan Line Polygon Fill

4 College of Computer and Information Science, Northeastern UniversityApril 17, Parity Check Draw a horizontal half-line from P to the right. Count the number of times the half-line crosses an edge. 1in 4out 7in

5 College of Computer and Information Science, Northeastern UniversityApril 17, Polygon Data Structure edges xminymax1/m  168/4  (1, 2) (9, 6) xmin = x value at lowest y ymax = highest y Why 1/m? If y = mx + b, x = (y-b)/m. x at y+1 = (y+1-b)/m = (y-b)/m + 1/m.

6 Polygon Data Structure Edge Table (ET) has a list of edges for each scan line. e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e  e  e4  e5 6  e3  e7  e  e2  e1  e11 0  e10  e9

7 College of Computer and Information Science, Northeastern UniversityApril 17, Preprocessing the edges count twice, once for each edge chop lowest pixel to only count once delete horizontal edges For a closed polygon, there should be an even number of crossings at each scan line. We fill between each successive pair.

8 Polygon Data Structure after preprocessing Edge Table (ET) has a list of edges for each scan line. e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e  e  e4  e5 6  e3  e7  e  e2  e1  e11 0  e10  e9 e11 7  e3  e4  e5 6  e7  e8 11  e6 10

9 College of Computer and Information Science, Northeastern UniversityApril 17, The Algorithm 1.Start with smallest nonempty y value in ET. 2.Initialize SLB (Scan Line Bucket) to nil. 3.While current y  top y value: a.Merge y bucket from ET into SLB; sort on xmin. b.Fill pixels between rounded pairs of x values in SLB. c.Remove edges from SLB whose ytop = current y. d.Increment xmin by 1/m for edges in SLB. e.Increment y by 1.

10 Running the Algorithm e2 e3 e4 e5 e6 e7 e8 e9 e10 e ET  e  e3  e4  e5 6  e7  e  e2  e11 0  e10  e9 xminymax1/m e226-2/5 e31/3 121/3 e4412-2/5 e54130 e66 2/313-4/3 e /2 e81082 e91183/8 e /4 e11642/

11 College of Computer and Information Science, Northeastern UniversityApril 17, Running the Algorithm e2 e3 e4 e5 e6 e7 e8 e9 e10 e y=0 SCB  114-3/4  1183/8  e9 e /4 11 3/8

12 College of Computer and Information Science, Northeastern UniversityApril 17, Running the Algorithm e2 e3 e4 e5 e6 e7 e8 e9 e10 e y=1 SLB  26-2/5  642/3  e11 e2 1 3/5 10 1/44-3/4  11 3/8 83/8  e9 e10 6 2/3 9 1/2 11 6/8

13 College of Computer and Information Science, Northeastern UniversityApril 17, Running the Algorithm e2 e3 e4 e5 e6 e7 e8 e9 e10 e y=2 SLB  1 3/56-2/5  6 2/342/3  e11 e2 9 1/24-3/4  11 6/883/8  e9 e /8 8 3/4 7 1/3 1 1/5

14 College of Computer and Information Science, Northeastern UniversityApril 17, Running the Algorithm e3 e4 e5 e6 e7 e8 e9 e y=3 SLB  1 1/56-2/5  7 1/342/3  e11 e2 8 3/44-3/4  12 1/883/8  e9 e / /5 e11e2

15 College of Computer and Information Science, Northeastern UniversityApril 17, Running the Algorithm e3 e4 e5 e6 e7 e8 e y=4 SLB  4/56-2/5  842/3  e11 e2 84-3/4  12 4/883/8  e9 e10 e11e2 e9 Remove these edges.

16 College of Computer and Information Science, Northeastern UniversityApril 17, Running the Algorithm e3 e4 e5 e6 e7 e y=4 SLB  4/56-2/5  e2 12 4/883/8  e9 12 7/8 2/5 e2e11 e10 e9 e11 and e10 are removed.

17 College of Computer and Information Science, Northeastern UniversityApril 17, Running the Algorithm e3 e4 e5 e6 e7 e y=5 SLB  2/56-2/5  e2 12 7/883/8  e9 13 2/8 0 e2e11 e10 e9

18 College of Computer and Information Science, Northeastern UniversityApril 17, Running the Algorithm e3 e4 e5 e6 e7 e y=6 SLB  06-2/5  e /2  e7 e2e11 e10 e9 Remove this edge  e8 13 2/883/8  e9 9 1/ /8

19 Running the Algorithm e3 e4 e5 e6 e7 e y=7 SLB  4130  e5 9 1/210-1/2  e7 e2e11 e10 e  e8 13 5/883/8  e9 Add these edges /5  e4 1/3121/3  e3


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