Embed Size (px)
DESCRIPTION
Citation preview
1of30
2D CLIPPING
• Clipping is a procedure that identifies those portions of a picture that are either inside or outside of a specified region of space.
• Clip Window is the region against which an object is to be clipped.• It may be a polygon or curved boundaries. But rectangular clip regions are preferred.
• For viewing transformations, picture parts within window area are displayed. Everything outside window area is discarded.
2of30
CLIPPING (Cont…)
•Clipping algorithm – 2 methods– Clipping applied in world coordinates &
contents of window interior are mapped to device coordinates
– Eliminates processing necessary to transform those primitives outside window to device space
– Map complete world coordinate picture to device coordinate or normalized device coordinate, then clip against view port boundaries.
– Reduce calculations by allowing concatenation of viewing & geometric transformation matrices.
3of30
Types of clipping
Based on different output primitives
– Point clipping
– Curve clipping
– Text clipping
– Exterior clipping
– Line clipping (Straight line segments)
– Area clipping (Polygons)
4of30
1.POINT CLIPPING
•Clip window is a rectangle in standard position.•A point p=(x,y) is saved for display, if the following inequalities are satisfied,
–xwmin < x < xwmax
–ywmin < y < ywmax where xwmin,xwmax ,ywmin & ywmax are edges of clip window (WC window or view port boundaries)
•If any one of these 4 inequalities is not satisfied, the point is clipped i.e, not saved for display.
– Can be applied to scenes involving explosions or sea foam that are modeled with particles (points) distributed in some region of the scene.
5of30
2.Curve clipping
• Curve clipping procedures
will involve non-linear
equations (so requires more
processing than for objects
with linear boundaries)
6of30
Curve clipping (cont)
•Preliminary test (Test for overlapping)– The bounding rectangle for a circle or other curved object
is used to test for overlap with a rectangular clip window.– If the bounding rectangle is completely inside (save
object), completely outside (discard the object)– Both cases- no computation is necessary.– If bounding rectangle test fails, use computation-saving
approaches•Circle – coordinate extents of individual quadrants & then octants are used for preliminary testing before calculating curve–window intersections•Ellipse – coordinate extents of individual quadrants are used.•If 2 regions overlap, solve the simultaneous line-curve equations to obtain the clipping intersection points.
7of30
3.TEXT CLIPPING
•Depends on methods used to generate characters & the requirements of a particular application
•Methods for processing character strings relative to a window boundary,
• All-or-none string clipping strategy• All or none character clipping strategy• Clip the components of individual characters
8of30
TEXT CLIPPING (cont)
• All-or-none string clipping strategy– Simplest method, fastest text clipping– All string - inside clip window, keep it, otherwise discard.– Bounding rectangle considered around the text pattern– If bounding position of rectangle overlap with window
boundaries, string is rejected.• All or none character clipping strategy
– Discard or reject an entire character string that overlaps a window boundary i.e, discard those characters that are not completely inside the window.
– Compare boundary limits of individual characters with the window.
– Any character which is outside or overlapping the window boundary are clipped.
9of30
TEXT CLIPPING (cont)
10of30 TEXT CLIPPING (cont)
• Clip the components of individual characters
– Treat characters same as lines
– If individual char overlaps a clip window boundary, clip off the parts of the character that are outside the window.
TEXT CLIPPING (cont)
11of30
4.EXTERIOR CLIPPING
•Clip a picture to the exterior of a specified region
•The picture parts to be saved are those that are outside the region.
•Eg. Multiple window systems, applications that require overlapping pictures.
12of30
5.Line Clipping
•For the image below consider which lines and points should be kept and which ones should be clipped
wymax
wymin
wxmin wxmax
Window
P1
P2
P3
P6
P5P7
P10
P9
P4
P8
13of30
Line clipping procedure
• A line clipping procedure involves several parts:1. Test a given line segment to determine whether it lies
completely inside the clipping window.2. Determine whether it lies completely outside the
window3. If not 1 & 2, perform intersection calculations with
one or more clipping boundaries.• A line with both endpoints inside all clipping boundaries
is saved• A line with both endpoints outside any one of the clip
boundaries is discarded• Other lines cross one or more clipping boundaries &
require calculation of multiple intersection points
14of30
Point Clipping
A point (x,y) is not clipped if:
wxmin ≤ x ≤ wxmax AND wymin ≤ y ≤ wymax
otherwise it is clipped
wymax
wymin
wxmin wxmax
Window
P1
P2
P5
P7
P10
P9
P4
P8
Clipped
Points Within the Window are Not Clipped
Clipped
Clipped
Clipped
15of30
Line Clipping
Examine the end-points of each line to see if they are in the window or not
Situation Solution Example
Both end-points inside the window
Don’t clip
One end-point inside the window, one outside
Must clip
Both end-points outside the window
Clipping decision should be made appropriately
16of30
Line clipping – parametric test
• Performed if one or both endpoints of line segment are outside the clipping rectangle
• The parametric representation for line segment with endpoints (x1,y1) and (x2,y2) is given by
X=x1+u (x2-x1)Y=y1+u (y2-y1), 0< u <1
• Used to determine values for parameter u for intersections with the clipping boundary
• If u value (for intersection with a rectangle boundary edge) is outside the range 0 to 1, the line does not enter the interior of window boundary.
• If u is within the range o to 1, the line segment does indeed cross into the clipping area.
• This method is applied to each clipping boundary edge in turn to determine whether any part of the line segment is to be displayed.
• Clipping line segments with these parametric tests require a good deal of computation & faster approaches to clipping are possible.
17of30
Cohen-Sutherland Clipping Algorithm
•Oldest, most popular & efficient line clipping algorithm
•It reduces the number of line intersections that must be calculated by performing initial tests & speeds up processing
•Every line endpoint in a picture is assigned a 4-digit binary code called a region code
•Region code identifies the location of a point relative to the boundaries of the clipping rectangle
18of30
Cohen-Sutherland: World Division
World space is divided into regions based on the window boundaries
– Each region has a unique four bit region code– Region codes indicate the position of the
regions with respect to the window
1001 1000 1010
00010000
Window0010
0101 0100 0110
above below right left
3 2 1 0
Region Code
19of30
Cohen-Sutherland: Labelling
Every end-point is labelled with the appropriate region code
wymax
wymin
wxmin wxmax
Window
P3 [0001]P6 [0000]
P5 [0000]
P7 [0001]
P10 [0100]
P9 [0000]
P4 [1000]
P8 [0010]
P12 [0010]
P11 [1010]
P13 [0101] P14 [0110]
20of30
Cohen-Sutherland: Lines In The Window
Lines completely contained within the window boundaries have region code [0000] for both end-points so are not clipped
wymax
wymin
wxmin wxmax
Window
P3 [0001]P6 [0000]
P5 [0000]
P7 [0001]
P10 [0100]
P9 [0000]
P4 [1000]
P8 [0010]
P12 [0010]
P11 [1010]
P13 [0101] P14 [0110]
21of30
Cohen-Sutherland: Lines Outside The Window
Any lines with a common set bit in the region codes of both end-points can be clipped
– The AND operation (result – not 0000) can efficiently check this
wymax
wymin
wxmin wxmax
Window
P3 [0001]P6 [0000]
P5 [0000]
P7 [0001]
P10 [0100]
P9 [0000]
P4 [1000]
P8 [0010]
P12 [0010]
P11 [1010]
P13 [0101] P14 [0110]
22of30
Cohen-Sutherland: Other Lines
Lines that cannot be identified as completely inside or outside the window may or may not cross the window interior
These lines are processed as follows:– Compare an end-point outside the window to a
boundary (choose any order in which to consider boundaries e.g. left, right, bottom, top) and determine how much can be discarded
– If the remainder of the line is entirely inside or outside the window, retain it or clip it respectively
23of30
Cohen-Sutherland: Other Lines (cont…)
– Otherwise, compare the remainder of the line against the other window boundaries
– Continue until the line is either discarded or a segment inside the window is found
We can use the region codes to determine which window boundaries should be considered for intersection
– To check if a line crosses a particular boundary we compare the appropriate bits in the region codes of its end-points
– If one of these is a 1 and the other is a 0 then the line crosses the boundary
24of30
Cohen-Sutherland Examples
Consider the line P9 to P10 below
– Start at P10
– From the region codes of the two end-points we know the line doesn’t cross the left or right boundary
– Calculate the intersection of the line with the bottom boundary to generate point P10’
– The line P9 to P10’ is completely inside the window so is retained
wymax
wymin
wxmin wxmax
Window
P10 [0100]
P9 [0000]
P10’ [0000]
P9 [0000]
25of30
Cohen-Sutherland Examples (cont…)
Consider the line P3 to P4 below
– Start at P4
– From the region codes of the two end-points we know the line crosses the left boundary so calculate the intersection point to generate P4’
– The line P3 to P4’ is completely outside the window so is clipped
wymax
wymin
wxmin wxmax
WindowP4’ [1001]
P3 [0001]
P4 [1000]
P3 [0001]
26of30
Cohen-Sutherland Examples (cont…)
Consider the line P7 to P8 below
– Start at P7
– From the two region codes of the two end-points we know the line crosses the left boundary so calculate the intersection point to generate P7’
wymax
wymin
wxmin wxmax
Window
P7’ [0000]
P7 [0001] P8 [0010]P8’ [0000]
27of30
Cohen-Sutherland Examples (cont…)
Consider the line P7’ to P8
– Start at P8
– Calculate the intersection with the right boundary to generate P8’
– P7’ to P8’ is inside the window so is retained
wymax
wymin
wxmin wxmax
Window
P7’ [0000]
P7 [0001] P8 [0010]P8’ [0000]
28of30
Calculating Line Intersections
Intersection points with the window boundaries are calculated using the line-equation parameters
– Consider a line with the end-points (x1, y1) and (x2, y2)
– The y-coordinate of an intersection with a vertical window boundary can be calculated using:
y = y1 + m (xboundary - x1)
where xboundary can be set to either wxmin or wxmax
29of30
Calculating Line Intersections (cont…)
– The x-coordinate of an intersection with a horizontal window boundary can be calculated using:
x = x1 + (yboundary - y1) / m
where yboundary can be set to either wymin or wymax
– m is the slope of the line in question and can be calculated as m = (y2 - y1) / (x2 - x1)
30of30
Liang-Barsky line clipping
• Faster line clipper
• Based on the analysis of parametric equation of a line segment of the form
x=x1+u Δx
y=y1+u Δy, 0<=u<=1
Δx=x2-x1 & Δy=y2-y1
• More efficient
• Both Cohen-Sutherland and Liang-Barsky algorithm can be extended to 3-D clipping
