Polygon clipping

Polygon Clipping
Collection of connected lines is considered as
Polygon. A polygon clipper takes as input the
vertices of a polygon and returns one(or
more)
polygons. A closed Polygon when clipped
C
then we may get one or more open c
d
polygon or
D
lines. a
A
b
B

When we want clipping of a solid polygon
area(closed polygon), then after clipping the
resulting polygon should be closed. It requires
that lines ab & cd be added to make it closed
polygon. Hence it is difficult to find out
which
pieces of sections should be joined to make
the clipped polygon closed.

A polygon is called convex if the line joining
any two interior points of the polygon lies
completely inside the polygon. A non-
convex polygon is said to be concave.

B B

A
A

Another problem occurs when clipping a
closed polygon into several distinct smaller
polygons as shown:

Clipping
Window

Concave
Polygon

By convention, a polygon with vertices p1..pn
is said to be positively oriented if it produces
a anticlockwise direction. And if produces
clockwise it will be negative oriented.
C D
D C
L R
E
L R
E B B
A
A

SUTHERLAND-HODGMAN ALGORITHM
Each edge of the polygon must be tested
against each edge of the clip rectangle; new
edges must be added, and existing edges must
be discarded, retained, or divided. Multiple
polygons may result from clipping a single
polygon. We need an organized way to deal
with all these cases.

Steps of Sutherland-Hodgman's polygon
clipping algorithm
 Polygons can be clipped against each edge
of the window one at a time.

 Vertices which are kept after clipping
against one window edge are saved for
clipping against the remaining edges.
 Note that the number of vertices usually
changes and will often increases.

The original polygon
and the clip
rectangle.

After clipped by the
right clip boundary.

right and bottom
clip boundaries.

right, bottom, and
left clip boundaries.

After clipped by
all four
boundaries.

Four Cases of polygon clipping against one
Edge:
The clip boundary determines a visible and
Invisible region. The edges from vertex can
be
one of four types:
 Case 1 : Wholly inside visible region - save
endpoint
 Case 2 : Exit visible region - save the
intersection

 Case 3 : Wholly outside visible region -
save nothing
 Case 4 : Enter visible region - save
intersection and endpoint
V1
V2 V1
V1’

V2

Out  in in  in
Save V1’,V2 Save V2

V2

V1
V2 V1’ V1

in  out out  out
Save V1’ Save none

Polygon clipping

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