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

Visible Surface Determination

CS418 Computer Graphics John C. Hart

Painter’s Algorithm

• Display polygons in

back-to-front order

• Sort polygons by z-value

– Which vertex? – O(n log n)

• Problems…
• z

Quadtree Algorithm

• Sort polygons
• Subdivide screen until each region

contains one or zero edges

• Invented by John Warnock in 1969

Quadtree Algorithm

• Sort polygons
• Subdivide screen until each region

contains one or zero edges

• Invented by John Warnock in 1969

Quadtree Algorithm

• Sort polygons
• Subdivide screen until each region

contains one or zero edges

• Invented by John Warnock in 1969

Quadtree Algorithm

• Sort polygons
• Subdivide screen until each region

contains one or zero edges

• Invented by John Warnock in 1969

Quadtree Algorithm

• Sort polygons
• Subdivide screen until each region

contains one or zero edges

• Invented by John Warnock in 1969

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

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

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

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

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)

glFrustum(left,right,bottom,top,near,far)

(-1,1,1) z 1

• 1

x 1

• 1

y

• 1

1

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                                                             

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                                                                         

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                                                                         

• z
•  – /z
• 

1/-z curve z1 z2

•  – /z2
•  – /z1

if z1 > z2 then

•  – /z1 > - – /z2

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

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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