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Visible Surface Determination

CS418 Computer Graphics

John C. Hart

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Painters Algorithm

Display polygons inback-to-front order

Sort polygons by z-value

Which vertex?

O(nlog n)

Problems

-z

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Quadtree Algorithm

Sort polygons

Subdivide screen until each region

contains one or zero edges

Invented by John Warnock in 1969

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Quadtree Algorithm

Sort polygons

Subdivide screen until each region

contains one or zero edges

Invented by John Warnock in 1969

8/13/2019 z Buffer

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Quadtree Algorithm

Sort polygons

Subdivide screen until each region

contains one or zero edges

Invented by John Warnock in 1969

8/13/2019 z Buffer

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Quadtree Algorithm

Sort polygons

Subdivide screen until each region

contains one or zero edges

Invented by John Warnock in 1969

8/13/2019 z Buffer

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Quadtree Algorithm

Sort polygons

Subdivide screen until each region

contains one or zero edges

Invented by John Warnock in 1969

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Z-Buffer

Key Observation: Each pixel displayscolor of only one triangle, ignores

everything behind it

Dont 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)

Ifz> zbuffer(x,y) then

framebuffer(x,y) = fragment color

zbuffer(x,y) =z

-far

-far

-far

-far-far

-far

-far

-far

-far

-far

-far-far

framebuffer

zbuffer

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Z-Buffer

Key Observation: Each pixel displayscolor of only one triangle, ignores

everything behind it

Dont 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)

Ifz> zbuffer(x,y) then

framebuffer(x,y) = fragment color

zbuffer(x,y) =z

-far

-.1

-.2

-.3-.4

-.5

-.6

-.7

-.8

-far

-far-far

framebuffer

zbuffer

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Z-Buffer

Key Observation: Each pixel displayscolor of only one triangle, ignores

everything behind it

Dont 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)

Ifz> zbuffer(x,y) then

framebuffer(x,y) = fragment color

zbuffer(x,y) =z

-far

-.1

-.2

-.3-.4

-.3

-.1

-.7

-.8

-far

-far-far

framebuffer

zbuffer

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Z-Buffer

Get fragment z-values by interpolatingz-values at vertices during rasterization

Perspective projection destroys

z-values, setting them all tod

Need a perspective distortion that

preserves at least the ordering of

z-values

-far

-.1

-.2

-.3-.4

-.3

-.1

-.7

-.8

-far

-far-far

framebuffer

zbuffer

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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

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Perspective Projection

screen

-z

y

zview

yview

d

yclip

clip view

view

viewclip

view/

y y

d z

yy

z d

view

viewviewview

viewview view

viewviewview

view

/1

1

/1

/1/ 0 1

1

x

z dxx

yy y

z dzz

dz dd

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Perspective Distortion

screen

-z

y

zview

yview

1

yclip

viewclip

view

yy

z

view

viewviewview

viewviewview

viewviewview

viewview

1

1

1 0 1

1

x

zxx

yyyz

zz

zz

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Distorted z-Values

viewclip

view

yy

z

view

viewviewview

viewviewview

viewviewview

viewview

1

1

1 0 1

1

x

zxx

yyyz

zz

zz

-z

-/z

-

1/-zcurve

z1 z2

-/z2

-/z1

ifz1>z2then

-/z1> -/z2

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Normalized Perspective Distortion

2 near right left

right left right left2 near top bottom

top bottom top bottom

far near 2 far near

far near far near

1 0

x

y

z

x

y

z(0,0,-far)

(-1,1,1)

z1 -1

x

1

-1

y

-1

1

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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

-.2

-.3

-.4

-.5

-.6

-.7

-.8

-far

framebuffe

r

hierarchical zbuffer

-.3

-.5

-.7

-far

-.5

-far

-far