CGMB 314 Intro to Computer Graphics

1. CGMB 314Intro to Computer Graphics Fill Area Primitives

2. Filling 2D Shapes • How do we fill shapes? Texture Fill Pattern Fill Solid Fill

3. Filling 2D Shapes (cont…) • Some requirements • A digital representation of the shape • The shape must be closed • It must have a well defines inside and outside • A test for determining if a point is inside or outside of the shape • A rule or procedure for determining the colors of points inside the shape

4. Representing Filled Shapes • Digital images • Inside determined by a color or range of colors Original Image Pink pixels have been filled with yellow

5. Representing Filled Shapes (cont…) • A digital outline and a seed point indicating the interior Digital outline and seed points Filled outlines

6. Representing Filled Shapes (cont…) • An implicit function representing a shape’s interior The inside of a circle of radius R The inside of a unit square

7. Representing Filled Shapes (cont…) • An equation or list of edges representing a shape’s boundary and a rule for determining its interior • E.g. • Edge list • Line from (0,0) to (1,0) • Line from (1,0) to (1,1) • Line from (1,1) to (0,1) • Line from (0,1) to (1,1) • Rule for interior points • All points to the right of all of the (ordered) edges

8. Representing Filled Shapes (cont…) • Edge list • Line from (0,0) to (1,0) • Line from (1,0) to (1,1) • Line from (1,1) to (0,1) • Line from (0,1) to (1,1) • Rule for interior points • All points to the right of all of the (ordered) edges Ordered edges

9. Representing Filled Shapes (cont…) • Edge list • Line from (0,0) to (1,0) • Line from (1,0) to (1,1) • Line from (1,1) to (0,1) • Line from (0,1) to (1,1) • Rule for interior points • All points to the right of all of the (ordered) edges Filled shape

10. Fill Options • How to set pixel colors for points inside the shape? Texture Fill Pattern Fill Solid Fill

11. Seed Fill • Approach • Select a seed point inside a region • Move outwards from the seed point, setting neighboring pixels until the region is filled Seed point Move outwards to neighbors Stop when the region is filled

12. Selecting the Seed Point • Difficult to place the seed point automatically • Seed fill works best in an interactive application where the user sets the seed point What is the inside of this shape? * It depends on the user’s intent

13. Seed Fill • Basic algorithm select seed pixelinitialize a fill list to contain seed pixelwhile (fill list not empty) { pixel  get next pixel from fill list setPixel(pixel) for (each of the pixel’s neighbors) { if (neighbor is inside region AND neighbor not set) add neighbor to fill list } }

14. Which neighbors should be tested? • There are two types of 2D regions • 4-connected region (test 4 neighbors) • Two pixels are 4-connected if they are vertical or horizontal neighbors • 8-connected region (test 8 neighbors) • Two pixels are 8-connected if they are vertical, horizontal, or diagonal neighbors

15. Which neighbors should be tested? • Using 4-connected and 8-connected neighbors gives different results Magnified area Fill using 4-connected neighbors Original boundary Fill using 8-connected neighbors

16. When is a Neighbor Inside the Region? • There are two types of tests, resulting in two filling approaches • Boundary fill • Flood fill

17. Boundary Fill • Fill condition • The region is defined by a set of boundary pixels • A neighbor of an inside pixel is also inside if it is not a boundary pixel Seed pixel Boundary pixel Original image and seed point Image after 4-connected boundary fill

18. Flood Fill • Fill condition • The region is defined by a patch of like-colored pixels • A neighbor of an inside pixel is also inside if its color is within a range of the seed pixel’s original color • The range of inside colors can be specified in the application Seed pixel Original image and seed point Image after 4-connected flood fill

19. Improving Performance • Problems with the basic algorithm • We don’t know how big the fill list should be • Worst case, all the image pixels • Slow • Pixels may be checked many times to see if they have already been set (especially for 8-connected regions)

20. Improving Performance (cont…) • Use coherence (logical connection) to improve performance and reduce memory requirements • Neighbor coherence • Neighboring pixels tend to be in the same region • Span coherence • Neighboring pixels along a given scan line tend to be in the same region • Scan-line coherence • The filling patterns of adjacent scan lines tends to be similar

21. Improving Performance (cont…) • Span-based seed fill algorithm Seed point

22. Improving Performance (cont…) • Span-based seed fill algorithm • Start from the seed point • Fill the entire horizontal span of pixels inside the region Seed point

23. Improving Performance (cont…) • Span-based seed fill algorithm • Determine spans of pixels in the rows above and below the current row that are connected to the current span • Add the left-most pixel of these spans to the fill list

24. Improving Performance (cont…) • Span-based seed fill algorithm • Repeat until the fill list is empty

25. Improving Performance (cont…) • Span-based seed fill algorithm • Repeat until the fill list is empty

26. Improving Performance (cont…) • Span-based seed fill algorithm • Repeat until the fill list is empty

27. Improving Performance (cont…) • Span-based seed fill algorithm • Repeat until the fill list is empty

28. Filling Axis-Aligned Rectangles • An axis-aligned rectangle is defined by its corner points (Xmin, Ymin) and (Xmax, Ymax) (Xmax, Ymax) (Xmin, Ymin)

29. Filling Axis-Aligned Rectangles • Filling can be done in a nested loop for (j = Ymin, j < Ymax, j++) { for (i = Xmin, i < Xmax, i++) { setPixel(i, j, fillColor) } } (Xmax, Ymax) (Xmin, Ymin)

30. Filling General Polygons • Representing general polygons • Defined by a list of connected line segments • The line segments must form a closed shape (i.e. the boundary must connected) • General polygons • Can be self intersecting • Can have interior holes

31. Filling General Polygons • Specifying the interior • Must be able to determine which points are inside the polygon • Need a fill rule

32. Filling General Polygons • Specifying the interior • There are two commonly used fill rules • Even-odd parity rule • Non-zero winding rule Filled using even-odd parity rule Filled using none-zero winding rule

33. Even-odd Parity Rule • To determine if a point P is inside or outside • Draw a line from P to infinity • Count the number of times the line crosses an edge • If the number of crossing is odd, the point is inside • If the number of crossing is even, the point is outside

34. Non-zero Winding Number Rule • The outline of the shape must be directed • The line segments must have a consistent direction so that they formed a continuous, closed path

35. Non-zero Winding Number Rule • To determine if a points is inside or outside • Determine the winding number (i.e. the number of times the edge winds around the point in either a clockwise or counterclockwise direction) • Points are outside if the winding number is zero • Point are inside if the winding number is not zero

36. Non-zero Winding Number Rule • To determine the winding number at a point P • Initialize the winding number to zero and draw a line (e.g. horizontal) from P to infinity • If the line crosses an edge directed bottom to up • Add 1 to the winding number • If the line crosses an edge directed top to bottom • Subtract 1 from the winding number

37. Inside-Outside Tests • The non-zero winding number rule and the even-odd parity rule can give different results for general polygons • When polygons self intersect • When polygons have interior holes Even-odd parity Non-zero winding

38. Inside-Outside Tests • Standard polygons • Standard polygons (e.g. triangles, rectangles, octagons) do not self intersect and do not contain holes • The non-zero winding number rule and the even-odd parity rule give the same results for standard polygons

39. Shared Vertices • Edges share vertices • If the line drawn for the fill rule intersects a vertex, the edge crossing would be counted twice • This yields incorrect and inconsistent even-odd parity checks and winding numbers Line pierces the outline- Should count as one crossing Line grazes the outline- Should count as no crossings

40. Dealing with Shared Vertices • Check the vertex type (piercing or grazing) • If the vertex is between two upwards or two downwards edges, the line pierces the edge • Process a single edge crossing • If the vertex is between an upwards and a downwards edge, the line grazes the vertex • Don’t process any edge crossings Vertex between two upwards edges- Process a single crossing Vertex between upwards and downwards edges- Process no crossings

41. Dealing with Shared Vertices • Ensure that the line does not intersect a vertex • Use a different line if the first line intersects a vertex • Could be costly if you have to try several lines • If using horizontal scan line for the inside-outside test • Preprocess edge vertices to make sure that none of them fall on a scan line • Add a small floating point value to each vertex y-position

42. Filling Polygons via Boundary Fill • Polygons are defined by their edges

43. Filling Polygons via Boundary Fill • Polygons are defined by their edges • Use a line drawing algorithm to draw edges of the polygon with a boundary color

44. Filling Polygons via Boundary Fill • Polygons are defined by their edges • Fill the inside of the polygon using a boundary fill

45. Filling Polygons via Boundary Fill • Problems • Pixels are drawn on both sides of the line • The polygon contains pixels outside of the outline • Polygons with shared edges will have overlapping pixels • Efficiency • Drawing outlines and then filling can be less efficient that combining the edge drawing and filling in one step

46. Raster-Based Filling • Fill polygons in raster-scan order • Fill spans of pixels inside the polygon along each horizontal scan line • More efficient addressing by accessing spans of pixels • Only test pixels at the span endpoints

47. Raster-Based Filling • For each scan line • Determine points where the scan line intersects the polygon

48. Raster-Based Filling • For each scan line • Set pixels between intersection points (using a fill rule) • Even-odd parity rule: set pixels between pairs of intersections • Non-zero winding rule: set pixels according to the winding number

49. Raster-Based Filling • Basic algorithm (with even-odd parity rule) for (each scan line, j) {find the x-intersections between the scan line and each edgesort the x-intersections by increasing x-valuefor (each pair of intersection points, x1 and x2) { while (x1 < i < x2) setPixel(i, j, fillColor) } }

50. Conventions for Setting Edge Pixels • Adjacent polygons share edges • When rendered, some pixels along the edges are shared • Need to know what color to use for shared edge pixels