CPSC 441: Computer Graphics Hidden Surface Removal Cont'

1
CPSC 441 Computer Graphics Hidden Surface
Removal (Cont.)

• Dr. Jinxiang Chai

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Outline

• Backface Culling
• Painters algorithm
• BSP
• Z-buffer
• Scan line
• Ray casting
• Reading section 9-1 to 9-11, 9-14,9-15

3
Review Backface Culling
, draw polygon
view direction
4
Review Painters Example
Sort by depth Green rect Red circle Blue tri
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Review Painters Algorithm

• Sort all objects zmin and zmax
• If an object is uninterrupted (its zmin and zmax
  are adjacent in the sorted list), it is fine
• If 2 objects DO overlap
• 3.1 Check if they overlap in x
• - If not, they are fine
• 3.2 Check if they overlap in y
• - If not, they are fine
• - If yes, need to split one

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Review Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
b
b
f
4
6
2
b
f
5-2
5-1
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Review Rendering with a BSP Tree

• If eye is in front of plane
• Draw back polygons
• Draw on polygons
• Draw front polygons
• If eye is behind plane
• Draw front polygons
• Draw on polygons
• Draw back polygons
• Else eye is on plane
• Draw front polygons
• Draw back polygons

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Outline

• Backface Culling
• Painters algorithm
• BSP
• Z-buffer
• Scan line
• Ray casting
• Reading section 9-1 to 9-11, 9-14,9-15

9
Depth (Z) Buffer

• Simple modification to scan-conversion
• Maintain a separate buffer storing the closest
  z value for each pixeldepth buffer
• Only draw pixel if depth value is closer than
  stored z value
• Update buffer with closest depth value

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Z-Buffering Example
NOTE Can draw these shapes in any order
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Depth (Z) Buffer

• Advantages
• Always works. The nearest object always
  determines the color of a pixel
• Polygon drawn in any order
• Commonly in hardware
• Disadvantages
• Needs a whole extra buffer
• Requires extra storage space (How big?)
• Still lots of overdraw

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Depth (Z) Buffer

• Advantages
• Always works. The nearest object always
  determines the color of a pixel
• Polygon drawn in any order
• Commonly in hardware
• Disadvantages
• Needs a whole extra buffer
• Requires extra storage space (How big?)
  (1k1k24bits)
• Still lots of overdraw

13
Scan Line Algorithm

• Scan line algorithm for polygon drawing
• - how can we modify it for hidden surface
  removals?

Scan line
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Scan Line Algorithm

• Assume for each line of screen, we have
  scan-lines for all polygons intersecting that
  line
• For each polygon, keep track of extents of scan
  line
• Whenever the x-extents of two scan lines overlap,
  determine ordering of two polygons

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Scan Line Algorithm

• Scan line algorithm with depth information

Scan line
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Scan Line Algorithm

• Scan line algorithm with depth information

Scan line
Z0.18
Z0.38
Scan line spans
Z0.5
Z0.5
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Scan Line Algorithm
Scan line
Z0.18
Z0.38
Scan line spans
Z0.5
Z0.5
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Scan Line Algorithm
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Scan Line Algorithm
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Scan Line Algorithm
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Scan Line Algorithm

• Advantages
• Takes advantage of coherence resulting in fast
  algorithm
• Does not require as much storage as depth buffer
• Only draw visible pixels
• Commonly in software
• Disadvantages
• More complex algorithm
• Requires all polygons sent to renderer before
  drawing

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Ray Casting

• For each pixel enter Pij
• - Send a ray from eye point, c, through pij
  into scene
• - Intersect ray with each object
• - Select nearest intersection

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Ray Casting

• Implementation
• - Might parameterize each ray as
• - Each object Ok returns tkgt0 such that
  first intersection with ok occurs at r(tk)

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Ray Casting

• Implementation
• - Might parameterize each ray as
• - Each object Ok returns tkgt0 such that
  first intersection with ok occurs at r(tk)
• - Q given the set tk, what is the first
  intersection point?

25
Ray Casting

• Implementation
• - Might parameterize each ray as
• - Each object Ok returns tkgt0 such that
  first intersection with ok occurs at r(tk)
• - Q given the set tk, what is the first
  intersection point?

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Ray Casting

• Ray casting properties
• - process pixels one at a time
• - draw each visible pixel once
• - efficient algorithm needed for ray-object
  intersection
• - may (not) use pixel coherence
• - simple but generally not used

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Hidden Surface removal opengl

• Backface culling
• - glEnable(GL_CULL_FACE),
  glDisable(GL_CULL_FACE)
• - glCullFace(GL_BACK)

, cull polygon
view direction
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Z-buffer opengl

• In opengl, depth values are normalized to
  0.0,1.0
• - Specify depth-buffer operations
• glutInitDisplayMode // with argument
  GLUT_DEPTH
• - Specify initial depth-buffer value
• glClear(GL_DEPTH_BUFFER_BIT) //
  initialize depth-buffer values to 1.0
• glClearDepth (depth) // specify an
  initial depth-buffer value
• - Activate depth-testing operations
• glEnable (GL_DEPTH_TEST)

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Summary

• Backface Culling
• Painters algorithm
• BSP
• Z-buffer
• Scan line
• Ray casting
• Reading section 9-1 to 9-11,9-14,9-15