IT 300: Computer Graphics

1. IT 300: Computer Graphics Lecture 4: Areas, text and colors

2. Lecturer Details • Dr. Walid Khedr, Ph.D. • Email: khedrw@yahoo.com • Web: www.staff.zu.edu.eg/wkhedr • Department of Information Technology

3. Course Info • Course Name: Computer Graphics • Course Number: IT300 • Course Group: http://groups.yahoo.com/group/IT300_Computer_Graphics • Programming: JAVA • Prerequisite: JAVA, Linear Algebra • Course Materials: • Text Book • Lectures

4. Main Topics • Introduction • Basic principles of two-dimensional graphics • Scan Conversion: Drawing lines and curves • Areas, text and colors • Basic principles of three-dimensional graphics • Modeling three-dimensional objects • Visible surface determination • Illumination and shading • Special effects and virtual reality

5. Areas, text and colors • Objectives • Filling Areas • Which pixels to fill? • Scan line technique • Seed-fill technique • Scan line seed fill technique • With what value to fill them? • Color Models • RGB Model • CMY Model • HSV Model • Color Interpolation

6. Objectives • Filling areas and polygons is a general technique of computer graphics. • This chapter contains in addition to techniques for filling areas also basic models for colors and a short introduction to handling text in images.

7. Filling Areas • Areas are usually bounded by polygons or closed sequences of curves. • Two fundamental questions: • Which pixels to fill? • With what value to fill them? • In order to fill a polygon, points inside the polygon must be distinguished from exterior ones. • For polygons whose edges do not intersect, it is obvious which points should be considered as inner and outer points. • For polygons with intersecting edges it is not immediately clear what its inner parts are.

8. Which pixels to fill? • In order to fill a polygon, points inside the polygon must be distinguished from exterior ones. • For polygons whose edges do not intersect, it is obvious which points should be considered as inner and outer points. • For polygons with intersecting edges it is not immediately clear what its inner parts are.

9. Filling Areas • Two basic approaches: • Scan line technique: • Take successive scan lines that cross the area and fill in the spans of adjacent pixels that lie inside the area from left to right. • Typically used to fill polygons, circles, and other simple curves. • Seed-fill technique: • Start from a given interior position and paint outward from this position until we encounter the boundary. • Typically used to fill more complex boundaries.

10. Filling Areas

11. The Odd Parity Rule The odd parity rule provides a definition of inner and outer points.

12. The Odd Parity Rule • The odd parity rule is a useful mathematical definition of interior and exterior points of a polygon • but it is not suited for implementation, since the computational costs would be unacceptable if the rule is applied separately to each pixel.

13. Scan-Line Polygon Fill Algorithm • This algorithm handles polygonal regions that are geometrically defined by the coordinates of their vertices (along with the edges that connect the vertices). • Although such regions can be filled by the previous technique, the following is a much more efficient approach.

14. Scan-Line Polygon Fill Algorithm • The algorithm begins with the first scan line the polygon occupies and proceeds line by line towards the last scan line. • For each scan line it finds all intersection points between the current scan line and the edges. • The intersection points are sorted according to their x coordinates and grouped into pairs such as (a, b) and (c, d). • Calculate parity of intersections to determine in/out • A line is drawn from the first point to the second point in each pair.

15. Scan-Line Polygon Fill Algorithm • Special cases to be handled: • Horizontal edges. • Horizontal edges are ignored since the pixels that belong to them are automatically filled during scan conversion. • For vertices lying on scanlines.

16. Scan-Line Polygon Fill Algorithm

17. Scan-Line Polygon Fill Algorithm • When a scan line intersects a vertex. • If the vertex is a local minimum or maximum such as V1 and V7, no special treatment is necessary. • The two edges that join at the vertex will each yield an intersection point with the scan line.

18. Scan-Line Polygon Fill Algorithm • However, in this case we don’t want to count p1 twice (p0,p1,p1,p2,p3), otherwise we will fill pixels between p1 and p2, which is wrong. • To avoid cases where a vertex needs to be counted as one intersection, shorten one of the two intersecting edges by one scan line

19. Scan-Line Polygon Fill Algorithm

20. count twice, once for each edge delete horizontal edges Special cases to be handled chop lowest pixel to only count once

21. Scan-Line Polygon Fill Algorithm • Calculating intersections must be done cleverly. • In particular , we must avoid the brute-force technique of testing each polygon edge for intersection with each new scan line. • Calculations performed in scan-conversion and other graphics algorithms take advantage of various coherence properties • What we mean by coherence is simply that the properties of one part of a scene are related in some way to other parts of the scene so that the relationship can be used to reduce processing.

22. Coherence Method

23. Coherence Method • This allows for integer calculations to be performed.

24. Polygon Fill • Building the sorted edge table • Traverse Edges to construct an Edge Table. • Eliminate horizontal edges • Shorten certain edges (where y changes monotonically) to resolve which intersection points to choose • For each edge, we add it to the scan-line that it begins with (that is, the scan-line equal to its lowest y-value). • For each edge entry, store (1) the x-intercept with the scan-line, (2) the largest y-value of the edge, and (3) the inverse of the slope. • Each scan-line entry thus contains a sorted list of edges. The edges are sorted left to right. (To maintain sorted order, just use insertion based on their x value.)

25. Polygon Data Structure edges xmin ymax 1/m  (9, 6) 1 6 8/4  (1, 2) xmin = x value at lowest y ymax = highest y

26. Polygon Fill

27. Polygon Fill

28. Polygon Fill • Use an active-edge table(AET) to keep track of the edges that the current scanline intersects • The AET contains all edges crossed by the current scan-line. • The edges in the AET are sorted in an increasing order, using the x intersection values.

29. Algorithm (using ET and AET) • Process the scan lines from the bottom of the polygon to its top • Create a list of active edges for the first scan-line • Find intersection points (i.e., xk+1 = xk + 1/m, x0 = xmin), sort them, and fill the spans defined by the pairs • Move to the next scan-line and update AET • Delete edges which are currently in the AET but not intersected by the next scan-line (use ymax to find if next scan-line intersects an edge) • Add new edges from ET which are intersected by the next scanline • If AET is not empty, goto step 2

30. Example

31. Polygon Data Structureafter preprocessing 13 12 11 10  e6 9 8 7  e4 e5 6  e3 e7 e8 5 4 3 2 1  e2 e1 e11 0  e10  e9 11  e6 10 Edge Table (ET) has a list of edges for each scan line. 13 7  e3  e4 e5 6  e7 e8 e6 10 e5 e3 e7 e4 e8 5 e9 e2 e11 e11 e10 0 e1

32. Running the Algorithm ET 13 12 11  e6 10 9 8 7  e3 e4 e5 6  e7 e8 5 4 3 2 1  e2 e11 0  e10  e9 xmin ymax 1/m e2 2 6 -2/5 e3 1/3 12 1/3 e4 4 12 -2/5 e5 4 13 0 e6 6 2/3 13 -4/3 e7 10 10 -1/2 e8 10 8 2 e9 11 8 3/8 e10 11 4 -3/4 e11 6 4 2/3 13 e6 10 e5 e3 e7 e4 e8 5 e9 e2 e11 e10 0 5 0 10 15

33. Running the Algorithm y=0 SLB e10 13 e6 10 1/4 11 4 -3/4  10 e5 e3 e7 e9 e4 e8 11 8 3/8  11 3/8 5 e9 e2 e11 e10 0 5 0 10 15

34. Running the Algorithm y=1 SLB e2 13 e6 1 3/5 2 6 -2/5  10 e5 e3 e7 e11 e4 e8 6 6 2/3 4 2/3  5 e9 e10 e2 e11 9 1/2 10 1/4 4 -3/4  e10 0 e9 5 0 10 15 11 6/8 8 3/8  11 3/8

35. Running the Algorithm y=2 SLB e2 13 e6 1 1/5 1 3/5 6 -2/5  10 e5 e3 e7 e11 e4 e8 6 2/3 7 1/3 4 2/3  5 e9 e10 e2 e11 8 3/4 9 1/2 4 -3/4  e10 0 e9 0 5 10 15 12 1/8 11 6/8 8 3/8 

36. Running the Algorithm y=3 SLB e2 13 e6 1 1/5 4/5 6 -2/5  10 e5 e3 e7 e11 e4 e8 7 1/3 4 2/3  8 5 e9 e10 e2 e11 8 8 3/4 4 -3/4  e10 0 e9 0 5 10 15 12 1/8 8 3/8  12 4/8

37. Running the Algorithm y=4 SLB e2 13 e6 4/5 6 -2/5  10 e5 e3 e7 e11 e4 e8 8 4 2/3  5 e9 e10 e2 e11 8 4 -3/4  e10 0 e9 0 5 10 15 12 4/8 8 3/8  Remove these edges.

38. Running the Algorithm y=4 SLB e2 13 e6 4/5 6 -2/5  2/5 10 e5 e3 e7 e9 e4 e8 12 7/8 12 4/8 8 3/8  5 e9 e2 e11 e11 and e10 are removed. e10 0 0 5 10 15

39. Running the Algorithm y=5 SLB e2 13 e6 2/5 6 -2/5  0 10 e5 e3 e7 e9 e4 e8 12 7/8 8 3/8  13 2/8 5 e9 e2 e11 e10 0 0 5 10 15

40. Running the Algorithm Remove this edge. y=6 SLB e2 13 e6 0 6 -2/5  10 e5 e3 e7 e7 e4 e8 9 1/2 10 10 -1/2  5 e9 e8 e2 e11 12 10 8 2  e10 0 e9 0 5 10 15 13 2/8 8 3/8  13 5/8

41. Running the Algorithm Add these edges. e3 1/3 12 1/3  e4 4 12 -2/5  13 e6 e5 10 e5 e3 e7 4 13 0  e4 e8 y=7 SLB e7 5 9 1/2 10 -1/2  e9 e2 e11 e10 e8 0 12 8 2  0 5 10 15 e9 13 5/8 8 3/8 

42. Seed Fill Algorithm • Polygon filling process start from seed pixel. • As soon as the filling process is initialed, the neighborhood of seed point is checked for its color content. • For neighboring pixels with old or previous color, they are flooded with new color. • The algorithm terminates once encountering a boundary pixel or pixels of new color in all sides. • Disadvantage: considerable stacking is needed

43. The order of pixels that should be added to stack using 4-connected is above, below, left, and right. For 8-connected is above, below, left, right, above-left, above-right, below-left, and below-right.

44. Start Position Boundary Fill Algorithm 4-connected (Example)

45. 1 2 3 Boundary Fill Algorithm 4-connected (Example)

46. 1 4 2 Boundary Fill Algorithm 4-connected (Example)

47. 1 2 Boundary Fill Algorithm 4-connected (Example)

48. 5 1 Boundary Fill Algorithm 4-connected (Example)

49. 1 Boundary Fill Algorithm 4-connected (Example)

50. Boundary Fill Algorithm 4-connected (Example)