Computer Graphics

1. Assistant Professor Dr. Sana’a Wafa Al-Sayegh 2nd Semester 2008-2009 Computer Graphics University of Palestine ITGD3107

2. ITGD3107Computer Graphics Chapter 6 Two Dimensional Viewing

3. Two Dimensional Viewing • The Viewing Pipeline • Viewing Effects • Viewing Coordinate Reference Frame • Workstation transformation • Clipping Operations • Line Clipping • Polygon Clipping

4. The Viewing Pipeline • Window • A world-coordinate area selected for display. defines what is to be viewed • Viewport • An area on a display device to which a window is mapped. defines where it is to be displayed • Viewing transformation • The mapping of a part of a world-coordinate scene to device coordinates. • A window could be a rectangle to have any orientation.

5. Two-Dimensional Viewing

6. The Viewing Pipeline

7. The Viewing Pipeline

8. Viewing Effects • Zooming effects • Successively mapping different-sized windows on a fixed-sized viewports. • Panning effects • Moving a fixed-sized window across the various objects in a scene. • Device independent • Viewports are typically defined within the unit square (normalized coordinates)

9. Viewing Coordinate Reference Frame • The reference frame for specifying the world-coordinate window. • Viewing-coordinate origin: P0 = (x0, y0) • View up vector V: Define the viewing yv direction

10. Window-to-Viewport Coordinate Transformation

11. Workstation transformation

12. Clipping Operations • Clipping • Identify those portions of a picture that are either inside or outside of a specified region of space. • Clip window • The region against which an object is to be clipped. • The shape of clip window • Applications of clipping • World-coordinate clipping

13. Clipping Operations • Viewport clipping • It can reduce calculations by allowing concatenation of viewing and geometric transformation matrices. • Types of clipping • Point clipping • Line clipping • Area (Polygon) clipping • Curve clipping • Text clipping • Point clipping (Rectangular clip window)

14. Line Clipping • Possible relationships between line positions and a standard rectangular clipping region Before clipping after clipping

15. Line Clipping • Possible relationships • Completely inside the clipping window • Completely outside the window • Partially inside the window • Parametric representation of a line x = x1 + u(x2 - x1) y = y1 + u(y2 - y1) • The value of u for an intersection with a rectangle boundary edge • Outside the range 0 to 1 • Within the range from 0 to 1

16. Cohen-Sutherland Line Clipping • Region code • A four-digit binary code assigned to every line endpoint in a picture. • Numbering the bit positions in the region code as 1 through 4 from right to left.

17. Cohen-Sutherland Line Clipping • Bit values in the region code • Determined by comparing endpoint coordinates to the clip boundaries • A value of 1 in any bit position: The point is in that relative position. • Determined by the following steps: • Calculate differences between endpoint coordinates and clipping boundaries. • Use the resultant sign bit of each difference calculation to set the corresponding bit value.

18. Cohen-Sutherland Line Clipping • The possible relationships: • Completely contained within the window • 0000 for both endpoints. • Completely outside the window • Logical and the region codes of both endpoints, its result is not 0000. • Partially

19. Splitting Concave Polygons • Identify a concave polygon • Calculating the cross product of successive edge vectors. • If the z component of some cross product is positive while others have a negative, it is concave.

20. Splitting Concave Polygons • Vector method • Calculate the edge-vector cross product in a counterclockwise order. • If any z component turns out to be negative • The polygon is concave. • Split it along the line of the first edge vector in the cross-product pair.

21. Splitting Concave Polygons

22. Polygon Clipping

23. Sutherland-Hodgeman Polygon Clipping • Processing the polygon boundary as a whole against each window edge • Processing all polygon vertices against each clip rectangle boundary in turn

24. Sutherland-Hodgeman Polygon Clipping • Pass each pair of adjacent polygon vertices to a window boundary clipper • There are four cases:

25. Sutherland-Hodgeman Polygon Clipping • Intermediate output vertex list • Once all vertices have been processed for one clip window boundary, it is generated. • The output list of vertices is clipped against the next window boundary. • It can be eliminated by a pipeline of clipping routine. • Convex polygons are correctly clipped. • If the clipped polygon is concave • Split the concave polygon

26. Sutherland-Hodgeman Polygon Clipping v3 v2 v1

27. Weiler-Atherton Polygon Clipping • Developed as a method for identifying visible surfaces • It can be applied with arbitrary polygon-clipping region. • Not always proceeding around polygon edges • Sometimes follows the window boundaries • For clockwise processing of polygon vertices • For an outside-to-inside pair of vertices, follow the polygon boundary. • For an inside-to-outside pair of vertices, follow the window boundary in clockwise direction.

28. Weiler-Atherton Polygon Clipping

29. Other Clipping • Curve clipping • Use bounding rectangle to test for overlap with a rectangular clip window. • Text clipping • All-or-none string-clipping • All-or-none character-clipping • Clip the components of individual characters

30. Exterior Clipping • Save the outside region • Applications • Multiple window systems • The design of page layouts in advertising or publishing • Adding labels or design patterns to a picture • Procedures for clipping objects to the interior of concave polygon windows

31. Exterior Clipping