Visibility culling Clipping

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Visibility culling Clipping
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The visibility problem

• What polygons are visible?
• There are few visible polygons.
• Avoid redundant processing
• Three classes of non visible objects
• Outside the volume (view frustum culling)
• Facing away (back-face culling)
• Occluded (occlusion culling)

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Visibility culling
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Visibility culling
View frustum culling
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Visibility culling
Occlusion culling
View frustum culling
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Visibility culling
Occlusion culling
View frustum culling
Back-face culling
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Clipping

• 2D clipping
• Line / polygon clipping by the viewport
• 3D frustum culling
• Occlusion culling
• Lines are used for polygons

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Convex

• Convex polygon line between every two points
  belong to the polygon.
• The intersection of two convex regions convex
  region (single).
• The intersection of convex and concave ?
• Clipping intersection of a polygon with
  rectangle.

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Clipping endpoints
B
Ymax
A
Ymin
Xmin
Xmax
Ax gt Xmin, Ax lt Xmax
Ay gt Ymin, Ay lt Ymax
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Clipping lines

• Both points inside trivially accepted
• Brute force
• Calculate the infinite line-edge intersection
• Check if the intersection is on the edge/line

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Cohen-Sutherland algorithm

• Trivial acceptance
• Trivial rejection
• Subdivision into two trivial parts
• Especially effective in two common cases
• Large viewports
• Small viewports

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Cohen-Sutherland algorithm

• Region coding
• Assign code to endpoints
• Simple calculation
• Sign for bit value
• Zero for acceptance
• And for rejection
• Or for acceptance

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Cohen-Sutherland example

• Line AB
• And(A,B) 0, Or(A,B) ? 0
• Test A with bottom edge
• Create AC (rejected) and CB
• Code(C) 0 ? Choose B
• Test B with the right/top edge

B
E
D
C
A
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Cohen-Sutherland
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Cohen-Sutherland disadvantages

• Random edge choice
• Redundant edge-line cross calculations

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Cyrus-Beck algorithm

• Put line in a parametric form
• P(t) P0 (P1 P0)t
• Calculate 4 line-edge intersections only 1D
• Check if there is intersection

P1
C0
C1
P0
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Cyrus-Beck algorithm

• Denote L(t) P0(P1 ? P0)t, t?0,1 .
• PiD is a point on the edge LiD with normal NiD.
• For every vector V colinear with LiD, V?NiD 0.
• Specifically, for VL(t) ? PiD,
• 0 NiD?(L(t) ? PiD)

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Cyrus-Beck algorithm

• 0 NiD ? (L(t) ? PiD)
• NiD ? (P0 (P1 ? P0)t ? PiD)
• NiD ? (P0 ? PiD) NiD ? ((P1 ? P0)t)
• Solving for t, where ? (P1 ? P0)
• Works especially fast when rectangle is upright

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Cyrus-Beck algorithm

• If ?NiD?? 0, L and LiD are parallel
• The intersections of L and LiD are computed
• If ti?0,1, there might be an intersection
• Based on the sign of ?NiD??, each point is
  classified as PE (potentially entering) or PL
  (potentially leaving)
• PE with the largest t and PL with the smallest t
  define the intersection

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Cohen-Sutherland polygons

• Create a list of vertices v1, , vn
• Clip against a single infinite edge

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Cohen-Sutherland polygons
Inside
Outside
Inside
Outside
Inside
Outside
Inside
Outside
p
s
i
s
p
1st Output
2nd Output
s
p
i
p
s
Output
No Output
Output
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Hierarchical clipping

• Build hierarchical scene representation
• The bounding box of root includes the children
• Test the root node
• If it is outside, stop and discard everything
• If its fully inside, render everything
• Otherwise, test recursively every child

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Example
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6
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4
5
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3
5
6
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