2D Viewing & Clipping

1. 2D Viewing & Clipping 한신대 류승택 2005. 6

2. Contents • The viewing pipeline • Viewing coordinate reference frame • Window-to-viewport coordinate transformation • Clipping operations • Point clipping • Line clipping

3. The viewing pipeline [1/5] • window • a world-coordinate area selected for display • define what is to be viewed • view port • an area on a display device to which a window is mapped • define where it is to be displayed • windows & viewport • be rectangles in standard position, with the rectangle edges parallel to the coordinate axes • other geometries : take longer to process

4. The viewing pipeline [2/5] • viewing transformation • the mapping of a part of a world-coordinate scene to device coordinates • 2D viewing transformation = window-to-viewport, windowing transformation

5. The viewing pipeline [3/5] • viewing-transformation in several steps • construct the world-coordinate scene using modeling transformations • transform descriptions in world coordinates to viewing coordinates • map the viewing-coordinate description of the scene to normalized coordinates • transfer to device coordinates

6. The viewing pipeline [4/5] • viewing-transformation • by changing the position of the viewport • can view objects at different positions on the display area of an output device • by varying the size of viewports • can change the size and proportions of displayed objects • zooming effects = panning effects

7. The viewing pipeline [5/5] • viewport • define within the unit square • device-independent ⇒ separating the viewing & other transformations from specific output-device requirements • the unit square is mapped to the display area for the particular output device in use at that time • viewport clipping • perform in normalized coordinates or in device coordinates • to reduce computations by concatenating the various transformation matrices • provide for specifying the world-coordinate window

8. Viewing coordinate reference frame • view up vector • define the viewing yv direction • unit vectors v=(vx, vy) and u=(ux, uy) for the viewing yv and xv axes • The composite 2D transformation to convert world coordinates to viewing coordinates MWC,VC = R • T

9. Window-to-viewport coordinate transformation • transfer to the viewing reference frame • choose the window extents in viewing coordinate • select the viewport limits in normalized coordinate • to maintain the same relative placement in the viewport as in the window

10. Window-to-viewport coordinate transformation • Relative proportions of objects • sx=xvmax-xvmin/xwmax-xwmin, sy=yvmax-yvmin/ywmax-ywmin • sx=sy : maintain • sx≠sy : stretch or contract in either the x or y direction when displayed on the output device • workstation transformation • select a window area in normalized space and a viewport area in the coordinates of the display device

11. Clipping operations • clipping algorithm(simply clipping) • identify those portions of picture that are either inside or outside of a specified region of space • clip window • the region against which an object is to clipped • clipping application • extracting part of a defined scene for viewing • identifying visible surfaces in 3D views • antialiasing line segments or object boundaries • creating objects using solid-modeling procedures • displaying a multiwindow environment • drawing & painting operations that allow parts of a picture to be selected for copying,moving,erasing, or duplicating

12. Clipping operations • world-coordinate clipping • remove those primitives outside the window from further consideration • eliminating the processing necessary to transform those primitives to device space • viewport clipping • reduce calculations by allowing concatenation of viewing and geometric transformation matrices • require that the transformation to device coordinates be performed for all objects, including those outside the window area

13. Point clipping • Assuming that the clip window is a rectangle in standard position P=(x, y) • the edges of the clip window(xwmin, xwmax, ywmin, ywmax) can be either the world-coordinate window boundaries or viewport boundaries • ex. apply to scenes involving explosions or sea foam

14. Line clipping • Line clipping procedure • test a given line segment to determine whether it lies completely inside the clipping window • if it doesn’t, we try to determine whether it lies completely outside the window • if we can’t identify a line as completely inside or completely outside, we must perform intersection calculations with one or more clipping boundaries

15. Line clipping • Checking the line endpoints ⇒ inside-outside test • Line clipping • Cohen-Sutherland line clipping • Liang-Barsky line clipping

16. Line clipping • Cohen-Sutherland line clipping • one of the oldest and most popular line-clipping procedures • speed up the processing of line segments by performing initial tests that reduce the number of intersections that must be calculated • region code : four-digit binary code • ⇒ bit 1:left, bit 2:right, bit 3:below, bit 4:above • for languages in which bit manipulation is possible

17. Line clipping • region-code bit values determined • calculate difference between endpoint coordinates and clipping boundaries • use the resultant sign bit of each difference calculation to set the corresponding value in the region code • bit 1 : the sign bit of x – xwmin • bit 2 : the sign bit of xwmax – x • bit 3 : the sign bit of y – ywmin • bit 4 : the sign bit of ywmax – y

18. Line clipping • Determine which lines are completely inside the clip window and which line are clearly outside • completely inside the clip window • region code of 0000 for both endpoints • trivially accept these lines • clearly outside the clip window • any line that a 1 in the same bit position in region code • trivially reject these lines • by using logical and operation with both region codes

19. Line clipping • check for intersection with the window boundaries • using the slope-intercept form of the line equation • x value Is set either to xwmin or to xwmax • y value Is set either to ywmin or to ywmax