1. A.Aruna/Assistant Professor/SNSCE
2D Viewing & Clipping
4/27/2017
A.Aruna/Assistant Professor/SNSCE

2. A.Aruna/Assistant Professor/SNSCE
Contents
The viewing pipeline
Viewing coordinate reference frame
Window-to-viewport coordinate transformation
Clipping operations
Point clipping
Line clipping
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

11. A.Aruna/Assistant Professor/SNSCE
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 & painting1111 operations that allow parts of a picture to be selected for copying,moving,erasing, or duplicating
4/27/2017
A.Aruna/Assistant Professor/SNSCE

12. A.Aruna/Assistant Professor/SNSCE
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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

13. A.Aruna/Assistant Professor/SNSCE
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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

14. A.Aruna/Assistant Professor/SNSCE\\
EXAMPLE: apply to scenes involving explosions or sea foam
4/27/2017
A.Aruna/Assistant Professor/SNSCE

15. A.Aruna/Assistant Professor/SNSCE
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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

16. A.Aruna/Assistant Professor/SNSCE
Line clipping
Checking the line endpoints ⇒ inside-outside test
Line clipping
Cohen-Sutherland line clipping
Liang-Barsky line clipping
Nicholl – Lee- Nicholl Line Clipping
4/27/2017
A.Aruna/Assistant Professor/SNSCE

17. A.Aruna/Assistant Professor/SNSCE
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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

18. A.Aruna/Assistant Professor/SNSCE
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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

19. A.Aruna/Assistant Professor/SNSCE
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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

20. A.Aruna/Assistant Professor/SNSCE
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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

21. A.Aruna/Assistant Professor/SNSCE
Polygon Clipping
Modify the line clipping Algorithm
Processed with line segments- unconnected line segments
Depends on the orientation of polygon
4/27/2017
A.Aruna/Assistant Professor/SNSCE

22. A.Aruna/Assistant Professor/SNSCE
Polygon Clipping
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

24. Sutherland-Hodgeman Polygon Clipping
Pass each pair of adjacent polygon vertices to a window boundary clipper
There are four cases:
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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
4/27/2017
A.Aruna/Assistant Professor/SNSCE

26. Sutherland-Hodgeman Polygon Clippingv3 v2 v1
4/27/2017
A.Aruna/Assistant Professor/SNSCE

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.
4/27/2017
A.Aruna/Assistant Professor/SNSCE

28. Weiler-Atherton Polygon Clipping
4/27/2017
A.Aruna/Assistant Professor/SNSCE

29. A.Aruna/Assistant Professor/SNSCE
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
4/27/2017
A.Aruna/Assistant Professor/SNSCE