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3D clipping
Shuabhangi Shinde
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Clipping volume
In 3-D we are using clipping volume or view volume.
Common 3-d clipping volumes
Rectangular paralleloiped i.e. box used for parallelprojection
or axmonmetric projection
A truncated pyramidal volume, used for
perspectiveprojection.
These volumes are six sided with sides : left, right,
top,bottom, hither(near) and yon(far)
Objects within the view volume may be seen, thoseoutside are not
displayed.
Objects crossing the boundary are cut, and only theportion with
in the view volume is shown.
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Bit 6 Bit 5 Bit 4 Bit 3 Bit 2 Bit 1
Far Near Top Bottom Right left
The two dimensional concept of region codescan be extended to 3d
by considering 6 sides
and 6-bit code instead of four sides and 4 bit
code.
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Bit 1=1 if the end point is left of the view volume
Bit 2 = 1 if the end point is right of the view volume
Bit 3 = 1 if the end point is below of the view volume
Bit 4 = 1 if the end point is above of the view volume
Bit 5 = 1 if the end point is front of the view volume
Bit 6 = 1 if the end point is behind of the view volume
Otherwise the bit is set to 0
For example region code of 100100 identifies a point asbelow and
behind the view volume and the region code000000 indicates a point
with in the view volume.
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Y axis
+1
-1
-Z-1
BackClippingPlanez=-1
FrontClipping
Plane
y=z
y=-z3-D Extension of 2-D Cohen-Sutherland Algorithm,
Outcode of six bits. A bit is true (1) when theappropriate
condition is satisfied
Bit 1 - Point is above view volume y > -z
Bit 2 - Point is below view volume y < z
Bit 3 - Point is right of view volume x > -z
Bit 4 - Point is left of view volume x < z
Bit 5 - Point is behind view volume z < -1
Bit 6 - Point is in front of view volume z > zmin
3D Cohen-Sutherland Algorithm
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3d midpoint subdivision algorithm
Find the locations of endpoints i.e. endpoint codes of
linesegments with respect to clipping volume.
If codes for both endpoints are zero then the line iscompletely
visible and stop.
If codes for endpoints are not zero and the logical andingof
them is also non zero then line is completely invisibleand stop
If codes for two endpoints do not satisfy the conditions 2and 3
the lines are partially visible.
Divide the partially visible line segments in equal parts
andrepeat steps 2 and 2 for sudivided line segments until weget
completely visible and completely invisible linesegments. Draw the
visible line segment and discard theinvisible one
STop
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Normalized View Volume
1000
00
00
00
KzDz
KyDy
KxDx
DxXWXV minmin
DyYWYV minmin
DzZWZV minmin
Kx=
Ky=
Kz=
minmax
minmax
XWXW
XVXV
minmax
minmax
YWYW
YVYV
minmax
minmax
ZWZWZVZV
Dx=
Dy=
Dz=
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Viewport Clipping
Cohen Sutherland (6 Bit code) Bit 1 =1 x
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