Visible Surface Determination CS418 Computer Graphics John C. Hart - - PowerPoint PPT Presentation

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Visible Surface Determination CS418 Computer Graphics John C. Hart - - PowerPoint PPT Presentation

Apr 24, 2023 496 likes •742 views

Visible Surface Determination CS418 Computer Graphics John C. Hart Painters Algorithm Painters Algorithm Painters Algorithm Painters Algorithm Painters Algorithm Painters Algorithm Backface Culling Q: How does Bob

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SLIDE 1

Visible Surface Determination

CS418 Computer Graphics John C. Hart

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SLIDE 2

Painter’s Algorithm

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SLIDE 3

Painter’s Algorithm

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SLIDE 4

Painter’s Algorithm

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SLIDE 5

Painter’s Algorithm

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SLIDE 6

Painter’s Algorithm

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SLIDE 7

Painter’s Algorithm

Backface Culling

  • Q: How does Bob Ross paint the trees so

fast?

  • A: He doesn’t paint the back sides of the

trees.

  • Cull triangles that face away from the

viewer v ⋅ n(view) ≤ 0 v

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SLIDE 8

Painter’s Algorithm

  • Display polygons in

back-to-front order

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SLIDE 9

Painter’s Algorithm

  • Display polygons in

back-to-front order

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SLIDE 10

Painter’s Algorithm

  • Display polygons in

back-to-front order

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SLIDE 11

Painter’s Algorithm

  • Display polygons in

back-to-front order

  • Sort polygons by z-value

– O(n log n) – Which vertex?

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SLIDE 12

Painter’s Algorithm

  • Display polygons in

back-to-front order

  • Sort polygons by z-value

– O(n log n) – Which vertex?

  • Problems…
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SLIDE 13

Quadtree Algorithm

  • Subdivide screen until each region is

simple (e.g. one polygon) or is a pixel

  • Invented by

John Warnock in 1969

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SLIDE 14

Z-Buffer

Key Observation: Each pixel displays color of only one triangle, ignores everything behind it

  • Don’t need to sort triangles, just find for each pixel

the closest triangle

  • Z-buffer: one fixed or floating point value per pixel
  • Algorithm:

For each rasterized fragment (x,y) If z > zbuffer(x,y) then framebuffer(x,y) = fragment color zbuffer(x,y) = z

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framebuffer zbuffer

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SLIDE 15

Z-Buffer

Key Observation: Each pixel displays color of only one triangle, ignores everything behind it

  • Don’t need to sort triangles, just find for each pixel

the closest triangle

  • Z-buffer: one fixed or floating point value per pixel
  • Algorithm:

For each rasterized fragment (x,y) If z > zbuffer(x,y) then framebuffer(x,y) = fragment color zbuffer(x,y) = z

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framebuffer zbuffer

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SLIDE 16

Z-Buffer

Key Observation: Each pixel displays color of only one triangle, ignores everything behind it

  • Don’t need to sort triangles, just find for each pixel

the closest triangle

  • Z-buffer: one fixed or floating point value per pixel
  • Algorithm:

For each rasterized fragment (x,y) If z > zbuffer(x,y) then framebuffer(x,y) = fragment color zbuffer(x,y) = z

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framebuffer zbuffer

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SLIDE 17

Z-Buffer

  • Get fragment z-values by interpolating z-values at

vertices during rasterization

  • Perspective projection destroys

z-values, setting them all to –d

  • Need a perspective distortion that preserves at least

the ordering of z-values

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framebuffer zbuffer

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SLIDE 18

Normalized View Volume

x y z x y z

W2V           Model           View           Persp          

Model Coords World Coords Viewing Coords Clip Coords Screen Coords

(0,0,-far) (-1,1,1) z 1

  • 1

x 1

  • 1

y

  • 1

1

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Perspective Projection

screen

  • z

y zview yview d yclip

clip view view view clip view /

y y d z y y z d = − = −

view view view view view view view view view view view

/ 1 1 / 1 / 1/ 1 1 x z d x x y y y z d z z d z d d     −                       = ≡   −               − − −            

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SLIDE 20

Perspective Distortion

screen

  • z

y zview yview 1 yclip

view clip view

y y z = −

view view view view view view view view view view view view

1 1 1 1 1 x z x x y y y z z z z z α β α β β α     −                         − = ≡   +               − − − −              

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SLIDE 21

Distorted z-Values

view clip view

y y z = −

view view view view view view view view view view view view

1 1 1 1 1 x z x x y y y z z z z z α β α β β α     −                         − = ≡   +               − − − −              

  • z
  • α – β/z
  • α

1/-z curve z1 z2

  • α – β/z2
  • α – β/z1

if z1 > z2 then

  • α – β/z1 > -α – β/z2
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SLIDE 22

Normalized Perspective Distortion

2 near right left right left right left 2 near top bottom top bottom top bottom far near 2 far near far near far near 1 − × +     − −   − × +     − −   + × ×   −   − −   −  

x y z x y z

(0,0,-far) (-1,1,1) z 1

  • 1

x 1

  • 1

y

  • 1

1

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SLIDE 23

Hierarchical Z-Buffer

  • Invented by Ned Green in 1994
  • Creates a MIP-map of the z-buffer

– z-value equal to farthest z-value of its four children

  • Before rasterizing a triangle…

– Check z-value of its nearest vertex against z-value of the smallest quadtree cell containing the triangle – If z-test fails, then the entire triangle is hidden and need not be rasterized

  • Works best when displaying

front-to-back

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framebuffer hierarchical zbuffer

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