Clipping

1
Clipping

• A fundamental task in graphics is to keep those
  parts of an object that lie outside a selected
  view from being drawn
• Clipping is the removal of all objects or part of
  objects in a modelled scene that are outside the
  real-world window.
• Doing this on a pixel-by-pixel basis would be
  very slow, especially if most objects in the
  scene are outside the window
• More practical techniques are necessary to speed
  up the task

2
Line Clipping

• Lines are defined by their endpoints, so it
  should be possible just to examine these, and not
  every pixel on the line
• We often have windows that are either very large,
  i.e. nearly the whole scene fits inside, or very
  small, i.e. most of the scene lies inside the
  window
• Hence, most lines may be either trivially
  accepted or rejected

3
Cohen-Sutherland

• The Cohen-Sutherland line-clipping algorithm is
  particularly fast for trivial cases, i.e. lines
  completely inside or outside the window.
• Non-trivial lines, I.e. ones that cross a
  boundary of the window, are clipped by computing
  the coordinates of the new boundary endpoint of
  the line where it crosses the edge of the window

4
Outcodes

• The window edges are assumed to be extended so
  that the whole picture is divided into 9 regions
• Each region is assigned a four-bit code, called
  an outcode

5
Cohen Sutherland cont.

• The outcode for each end of the line is computed,
  giving codes c1 and c2.
• One of the following cases will occur
• Both c1 and c2 are 0000. This means that both
  endpoints lie inside the window, so the line may
  be trivially accepted
• If c1 and c2 have one or more bits in common,
  then the line must be wholly outside the window.
  Hence if (c1 AND c2) is not equal to zero, the
  line may be trivially rejected
• If (c1 AND c2) is equal to zero, further
  processing is necessary.

6

• Having decided that a line is non-trivial, it
  must be clipped
• We chop each end-point of the line at the
  nearest window boundary

It may be necessary to repeat this process
several times until the line may be trivially
accepted or rejected.
1
2
3
4
7

• When a line needs to be clipped, an endpoint
  outside the window is chosen (there will always
  be one)
• The algorithm chooses one of the set bits, and
  uses this to determine which window edge to clip
  to.

• In this case, The outcode of point d is 0000, and
  of point a is 1010 (bits for above and right
  are set.)
• Algorithm first works on the above bit, and
  pushes the line to the top edge of the window,
  I.e. point b.

8

• The outcodes of the line are again computed. This
  time, point b has outcode 0010 (I.e. bit for
  right is set), so the line is pushed to the
  right edge of the window (point c)
• The outcodes are computed, both are 0, so line
  accepted

9
Computing intersection points
p2 (x2,y2)
wymax
(Slope)
A
ax wxmax
ay y1 (wxmax-x1) m
p1 (x1,y1)
wymin
NOTE Vertical lines are a special case
wxmin
wxmax
10
Other Clipping algorithms

• The Cohen-Sutherland algorithm requires the
  window to be a rectangle, with edges aligned with
  the co-ordinate axes
• It is sometimes necessary to clip to any convex
  polygonal window, e.g. triangular, hexagonal, or
  rotated.
• The Cyrus-Beck, and Liang-Barsky line clippers
  use the concept of inside/outside half spaces
  generated by edges

11
Polygon Clipping

• A polygon is usually defined by a sequence of
  vertices and edges
• If the polygons are un-filled, line-clipping
  techniques are sufficient
• However, if the polygons are filled, the process
  in more complicated
• A polygon may be fragmented into several polygons
  in the clipping process, and the original colour
  associated with each one

12
Polygon Clipping Algorithms

• The Sutherland-Hodgeman clipping algorithm clips
  any polygon against a convex clip polygon.
• The Weiler-Atherton clipping algorithm will clip
  any polygon against any clip polygon. The
  polygons may even have holes