HiddenSurface Removal: Culling and Clipping

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School of Computing Staffordshire University
3D Computer Graphics
Hidden-Surface RemovalCulling and Clipping
Dr. Claude C. Chibelushi
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Outline

• Introduction
• Efficiency considerations
• Back-face culling
• View-volume culling
• Bounding volumes View volume
• Culling
• Polygon clipping
• Summary

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Introduction

• Complexity of graphics worlds is increasing
• need to avoid potential increase in computational
  cost
• accelerate rendering of large environments by
  minimising geometric complexity
• approaches visibility culling, level-of-detail
  representation, image-based rendering
• typically, only small fraction of graphics world
  is visible
• many techniques based on estimation of
  potentially visible portion of world

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Introduction

• Culling / clipping
• identification and removal of segments which are
  
• occluded by other surfaces of same opaque object
• e.g. cull back-facing polygons
• outside field of view
• cull segments that do not project onto view
  window
• clip primitives that are partially inside field
  of view
• 3D volume against which objects are culled /
  clipped is called view volume (or clipping volume)

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Efficiency Considerations

• Reduction of computational cost
• cull invisible segments from graphics pipeline
• as early as possible
• using low cost visibility tests
• to avoid lengthy occlusion tests for trivial
  cases, e.g.
• apply extent testing (e.g. frustum culling)
• apply occlusion culling (e.g. back-face culling)

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Efficiency Considerations

• Extent testing tests based on bounding boxes /
  volumes
• object / frustum culling
• if bounding volume of object is outside field of
  view
• Back-face culling for opaque solid objects
• computational savings
• in general, approximately half of object faces
  are back-facing
• hence, back-face culling approximately halves
  rendering time

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Efficiency Considerations
3D Models
Possible 3D graphics pipeline for scene
comprising single convex object
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Back-Face Culling
visible
invisible
visible
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Back-Face Culling

• Implementation
• Dot product of plane normal with sight vector
  (from any point on polygon to centre of
  projection)
• positive front-facing polygon
• negative back-facing polygon
• zero line of sight flush with polygon surface
• Limitation view direction not taken into account
• viewer could be looking away from object
• requires view-volume culling / clipping

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Back-Face Culling

• Implementation ctd.

Note anticlockwise order of vertices
Front-facing surface n ? s1e ? 0 Back-facing
surface n ? s1e ? 0
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View-Volume Culling

• Objects often enclosed in bounding volume
• to reduce computational costs of e.g.
• frustum culling, collision detection, ray tracing
• Many types of bounding volumes
• bounding box
• parameters object extent
• bounding sphere
• parameters object centre and radius

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View-Volume Culling

• Bounding volumes (2D representation)

• Bounding efficiency may be low
• potential for false positives

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View-Volume Culling

• View volume
• Determines what part of scene projects onto view
  window
• only part of scene within view volume will be
  displayed
• Shape of view volume determined by projection
  method
• parallel projection view volume is
  parallelepiped
• perspective projection view volume is frustum

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View-Volume Culling
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View-Volume Culling
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View-Volume Culling
Scene segment
Core logic for view-volume culling (e.g. segment
is object enclosed in bounding volume)
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View-Volume Culling

• Frustum culling algorithm for bounding box
• cullBoundingBox()
• if any box corner inside frustum
• return IN
• else if all box corners outside same frustum
  plane
• return OUT
• else if any frustum edge intersects box face
• return IN
• else if any box edge intersects frustum face
• return IN
• else if any frustum corner outside any box plane
  
• return OUT
• else return IN

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View-Volume Culling

• Parallel orthographic projection
• Tests for detecting scene point inside view
  volume
• (B and F subscripts refer to back and front
  clipping planes respectively)

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View-Volume Culling

• Perspective projection
• Tests for detecting scene point inside view
  volume
• based on similar-triangles formula

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View-Volume Culling

• Alternative tests for detecting scene point
  inside view volume
• insert point coordinates into plane equation for
  each frustum face result is
• positive for point on higher-coordinate side of
  plane
• negative for point on lower-coordinate side of
  plane
• zero for point inside plane
• e.g. above / below right / left in front /
  behind plane
• test whether combination of signs for all planes
  indicates point is inside view volume

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View-Volume Culling

• Intersection between edge and face
• Computation
• calculate equation of face plane
• calculate intersection between edge and plane
• determine whether intersection contained in face
• project intersection point and face onto nearest
  2D coordinate plane (i.e. x-y, y-z, or x-z)
• determine whether point is to left (or right) of
  all face edges
• if yes, intersection exists

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View-Volume Culling
Intersection between edge and plane

• Intersection

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Polygon Clipping

• Clipping against view volume
• 3D clipping requires intersection calculation
• between polygon edges and view volume faces
• polygon clipping may introduce more vertices

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Polygon Clipping

• Scissoring
• Clipping during scan conversion (i.e. 2D)
• only pixels within viewport will be displayed
• check pixel coordinates against bounds of
  viewport
• simple and general approach
• Simple primitives (e.g. lines, polygons)
• scissoring may be wasteful if large portion of
  primitives lies outside view volume
• Complex primitives (e.g. parametric patches)
• scissoring may be the only practical solution

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Suggested Reading

• Relevant parts of Ch. 12, D. Hearn, M.P. Baker,
  Computer Graphics, 2nd Ed. in C, Prentice-Hall,
  1996.
• Relevant parts of Ch. 10, 14, 15, A. LaMothe,
  Black Art of 3D Game Programming, Waite Group
  Press, 1995.
• Relevant parts of Ch. 9, A. Watt, F. Policarpo,
  3D Games Real-Time Rendering and Software
  Technology, Addison-Wesley, 2001.

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Summary

• Culling / clipping
• identification and removal of segments that are
  outside field of view
• e.g. parallelepiped, frustum
• View-volume / back-face culling, and bounding
  volumes
• improve computational efficiency

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Summary

• View-volume culling
• based on containment and intersection tests
• Back-face culling
• based on orientation test
• Polygon clipping in 3D, or 2D (scissoring)