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Nima Kalantari

CSCE 441 - Computer Graphics

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Culling, Clipping, and Viewport

Some slides from Scott Schaefer and Pradeep Sen

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So far

Normalized Device Coordinates (NDC)

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Outline

  • View volume culling
    • Clipping
  • Backface culling
  • Viewport

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View Volume Culling

Normalized Device Coordinates (NDC)

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View Volume Culling

  • Objects have thousands of triangles
    • Time-consuming to check each triangle

Normalized Device Coordinates (NDC)

Thousands of

Triangles

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View Volume Culling

  • Check the bounding sphere against all the six planes

Normalized Device Coordinates (NDC)

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View Volume Culling

  • Check the bounding sphere against all the six planes

Normalized Device Coordinates (NDC)

r

c

z

Z = -1

n

p

outside frustum

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View Volume Culling

  • Worth doing if the scene is big and only a small portion of the it is inside the view volume (frustum)

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View Volume Culling

  • What if only part of the object is inside?
    • Some triangles inside (accept)
    • Some triangles outside (reject)
    • Some triangles intersect the plane (clipping)

Normalized Device Coordinates (NDC)

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Outline

  • View volume culling
    • Clipping
  • Backface culling
  • Viewport

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Clipping

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Triangle Clipping Algorithm

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Clipping Space

  • Should we perform the clipping in NDC?

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Clipping

z

x

y

z

near

far

far (+1)

near (-1)

Camera Coordinate

NDC

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Clipping

x

y

z

near

far

far (+1)

near (-1)

Camera Coordinate

NDC

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Clipping

x

y

z

near

far

far (+1)

near (-1)

Camera Coordinate

NDC

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Clipping

x

y

z

near

far

far (+1)

near (-1)

Camera Coordinate

NDC

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Clipping

  • Done before perspective division (in clip space)
  • Clip triangles against each plane in clip space
    • x = +w
    • x = -w
    • y = +w
    • y = -w
    • z = +w
    • z = -w

​

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Clipping Equation

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Triangle Clipping Algorithm

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Triangle Clipping Algorithm

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Triangle Clipping Algorithm

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Triangle Clipping Algorithm

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Triangle Clipping Algorithm

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Four cases for each plane

  • All vertices outside
    • Cull triangle
  • One vertex outside
    • Break to two
    • Clip against the next plane
  • Two vertices outside
    • Break to one triangle
    • Clip against the next plane
  • All vertices inside
    • Clip against the next plane

​

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Summary

  • At the end of clipping all vertices are
    • -w ≤ x, y, z ≤ w

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Outline

  • View volume culling
    • Clipping
  • Backface culling
  • Viewport

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Backface Culling

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Backface Culling

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Backface Culling

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Backface Culling

view direction

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Backface Culling

view direction

, draw triangle

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Backface Culling

view direction

, cull triangle

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Outline

  • View volume culling
    • Clipping
  • Backface culling
  • Viewport

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Screen

  • Array of pixels [width × height]
  • Index of pixels
    • x-direction: 0 to width – 1
    • y-direction: 0 to height - 1
  • Pixels are located at (x + 0.5, y + 0.5)

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Viewport

  • Transformation from NDC to screen
  • Mapping x values from [-1, +1] to [0, width]
  • Mapping y values from [-1, +1] to [0, height]

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Coordinate spaces

Modelview matrix

Projection matrix

Clipping

Homogenize

Viewport Transform

Rasterization

screen-space coordinates

normalized device coordinates (NDC)

object space coordinates

eye space coordinates

clip-space coordinates

coordinates of the vertices of the objects

eye at origin, facing –z, +x is right, +y is up

vertices are now:

0 < x < screen width

0 < y < screen height

vertices are now (xc, yc, zc, wc)

all vertices are now from -1 to 1