Clipping
When?
2D clipping
2D clipping
„
„
? Part of the primitive is inside the window
defined in WCS
Remark: clipping is done to avoid the cost of
future transformations on those parts of the
primitives that are not visible in the image
Methods
1.
2.
3.
Analytic
During the scan conversion
Copy pixels from one memory region to
another memory region
Remark: Met 1 for lines and polygons, Met 2 for
other primitives
Point clipping
„
Suppose a rectangular window with the
corners (xmin,ymin) and (xmax,ymax)
P(x,y) is visible Ù xmin<= x<=xmax,
ymin<=y <=ymax
Simple alg. for line segments
Suppose F=rectangular window; ? PQ/F
Acceptance / rejection tests
Accept if both ends of the segment are visible
„ Reject if both ends of the segment are un the
same part of the window (left, right, top,
bottom)
Simple alg + tests = efficient alg when the no.
of interior or exterior segments is big
„
Acceptance/rejection tests and coding
Examples
Cohen-Sutherland alg.
Example
Examples
Examples
Examples
Bisection algorithm
„
„
„
Principle: if the tests for acceptance or
rejection fail on PQ then PQ is divided in two
segments, PR, RQ, R=(P+Q)/2
? PR, PQ accepted/rejected …
Remark: segments are accepted or rejected
at most after log2 N steps, where N is the
dimension in pixels of the discretized version
of the segment PQ
Parametric line clipping algorithm
(Cyrus-Beck algorithm)
„
Suppose:
‰
‰
‰
trigonometric sense
An edge of the window is inside the window
The normal N to an edge E is oriented towards
window exterior
The support line for a given segment P1P0 is
P(t)=P0+(P1-P0)t, t in R.
„
‰
Suppose x0<x1
Cyrus-Beck algorithm
CB alg - computations
Simplifying the computations
Nicholl-Lee-Nicholl algorithm
Code of NLN algorithm
Code of NLN algorithm
Code of NLN algorithm
Weiler-Atherton alg.
Polygon clipping
Polygon clipping
Polygon clipping
„
„
Tests for acceptance/rejection: method of
bounded aria by finding the smallest rectagle
that surrounds the polygon
Sutherland-Hodgman algorithm:
‰
‰
‰
‰
Divide-et-impera strategy
No. stages = no. edges of the clipping polygon
I: list of initial vertex
O: list of final vertex
Bounded aria method
SH algorithm
SH Algorithm
SH Algorithm
SH algorithm
SH algorithm
SH algorithm
Liang Barsky algorithm
„
„
„
„
„
Suppose F=rectangle, vertex {P1,P2,…Pn}
numbered in trigonometric order
? {P’1,P’2,…P’n} defining the clipped polygon
Interior region 2 = corner region
Interior region 3 = edge region
Remark: an edge is entering in a corner
region => the corner is added to the output
list
LB alg
LB alg: passing through a corner region
LB alg
LB alg
3d Clipping
3d clipping
3d clipping
„
„
„
With respect to the viewing volume
Methods: generalization from 2d->3d: CohenSutherland, bisection, Cyrus-Beck
Cohen-Sutherlang alg: using the canonic volume
3d clipping, perspective
CS Alg - codes
Bit
Canonic vol./
parallel proj.
Canonic vol./
perspective proj.
3d clipping
CS alg - computations
Cyrus-Beck alg.
CB alg - code