Rendering Pipeline

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Rendering Pipeline

• Aaron Bloomfield
• CS 445 Introduction to Graphics
• Fall 2006
• (Slide set originally by Greg Humphreys)

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3D Polygon Rendering

• Many applications use rendering of 3D
  polygonswith direct illumination

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3D Polygon Rendering

• Many applications use rendering of 3D
  polygonswith direct illumination

Quake II (Id Software)
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3D Polygon Rendering

• Many applications use rendering of 3D
  polygonswith direct illumination

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3D Rendering Pipeline
3D Geometric Primitives
Modeling Transformation
Lighting
This is a pipelined sequence of operations to
draw a 3D primitive into a 2D image (this
pipeline applies only for direct illumination)
Viewing Transformation
Projection Transformation
Clipping
Scan Conversion
Image
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Example OpenGL
Modeling Transformation
glBegin(GL_POLYGON) glVertex3f(0.0, 0.0,
0.0) glVertex3f(1.0, 0.0, 0.0) glVertex3f(1.0,
1.0, 1.0) glVertex3f(0.0, 1.0, 1.0) glEnd()
Viewing Transformation
Lighting Texturing
Projection Transformation
OpenGL executes steps of 3D rendering
pipeline for each polygon
Clipping
Scan Conversion
Image
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3D Rendering Pipeline
3D Geometric Primitives
Modeling Transformation
Transform into 3D world coordinate system
Viewing Transformation
Lighting Texturing
Projection Transformation
Clipping
Scan Conversion
Image
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3D Rendering Pipeline
3D Geometric Primitives
Modeling Transformation
Transform into 3D world coordinate system
Transform into 3D camera coordinate system Done
with modeling transformation
Viewing Transformation
Lighting Texturing
Projection Transformation
Clipping
Scan Conversion
Image
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3D Rendering Pipeline
3D Geometric Primitives
Modeling Transformation
Transform into 3D world coordinate system
Transform into 3D camera coordinate system Done
with modeling transformation
Viewing Transformation
Illuminate according to lighting and
reflectance Apply texture maps
Lighting Texturing
Projection Transformation
Clipping
Scan Conversion
Image
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3D Rendering Pipeline
3D Geometric Primitives
Modeling Transformation
Transform into 3D world coordinate system
Transform into 3D camera coordinate system Done
with modeling transformation
Viewing Transformation
Illuminate according to lighting and
reflectance Apply texture maps
Lighting Texturing
Projection Transformation
Transform into 2D screen coordinate system
Clipping
Scan Conversion
Image
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3D Rendering Pipeline
3D Geometric Primitives
Modeling Transformation
Transform into 3D world coordinate system
Transform into 3D camera coordinate system Done
with modeling transformation
Viewing Transformation
Illuminate according to lighting and
reflectance Apply texture maps
Lighting Texturing
Projection Transformation
Transform into 2D screen coordinate system
Clipping
Clip primitives outside cameras view
Scan Conversion
Image
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3D Rendering Pipeline
3D Geometric Primitives
Modeling Transformation
Transform into 3D world coordinate system
Transform into 3D camera coordinate system Done
with modeling transformation
Viewing Transformation
Illuminate according to lighting and
reflectance Apply texture maps
Lighting Texturing
Projection Transformation
Transform into 2D screen coordinate system
Clipping
Clip primitives outside cameras view
Scan Conversion
Draw pixels (includes texturing, hidden surface,
...)
Image
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Camera Coordinates

• Canonical coordinate system
• Convention is right-handed (looking down -z axis)
• Convenient for projection, clipping, etc.

Camera up vector maps to Y axis
y
Camera right vector maps to X axis
Camera back vector maps to Z axis (pointing out
of screen)
z
x
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Viewing Transformation

• Mapping from world to camera coordinates
• Eye position maps to origin
• Right vector maps to X axis
• Up vector maps to Y axis
• Back vector maps to Z axis

back
up
right
View plane
Camera
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Viewing Transformations
p(x,y,z)
3D Object Coordinates
Modeling Transformation
3D World Coordinates
Viewing Transformation
Viewing Transformations
3D Camera Coordinates
Projection Transformation
2D Screen Coordinates
Window-to-Viewport Transformation
2D Image Coordinates
p(x,y)
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Projection

• General definition
• Transform points in n-space to m-space (mltn)
• In computer graphics
• Map 3D camera coordinates to 2D screen
  coordinates
• For perspective transformations, no two rays
  are parallel to each other

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Taxonomy of Projections
FVFHP Figure 6.10
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Parallel Projection

• Center of projection is at infinity
• Direction of projection (DOP) same for all points

DOP
View Plane
Angel Figure 5.4
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Orthographic Projections

• DOP perpendicular to view plane

Front
Top
Side
Angel Figure 5.5
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Oblique Projections

• DOP not perpendicular to view plane

Cavalier (DOP ? 45o)
Cabinet (DOP ? 63.4o)
HB Figure 12.24
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Parallel Projection View Volume
HB Figure 12.30
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Parallel Projection Matrix

• General parallel projection transformation

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Taxonomy of Projections
FVFHP Figure 6.10
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Perspective Projection

• Map points onto view plane along projectors
  emanating from center of projection (COP)

Projectors
Center of Projection
View Plane
Angel Figure 5.9
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Perspective Projection

• How many vanishing points?
• The difference is how many of the three principle
  directions are parallel/orthogonal to the
  projection plane

Angel Figure 5.10
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Perspective Projection View Volume
View Plane
HB Figure 12.30
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Camera to Screen

• Remember Object ? Camera ? Screen
• Just like raytracer
• screen is the zd plane for some constant d
• Origin of screen coordinates is (0,0,d)
• Its x and y axes are parallel to the x and y axes
  of the eye coordinate system
• All these coordinates are in camera space now

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Overhead View of Our Screen
Yeah, similar triangles!
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The Perspective Matrix

• This division by z can be accomplished by a 4x4
  matrix too!
• What happens to the point (x,y,z,1)?
• What point is this in non-homogeneous
  coordinates?

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Taxonomy of Projections
FVFHP Figure 6.10
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Perspective vs. Parallel

• Perspective projection
• Size varies inversely with distance - looks
  realistic
• Distance and angles are not (in general)
  preserved
• Parallel lines do not (in general) remain
  parallel
• Parallel projection
• Good for exact measurements
• Parallel lines remain parallel
• Angles are not (in general) preserved
• Less realistic looking

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Classical Projections
Angel Figure 5.3
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Viewing in OpenGL

• OpenGL has multiple matrix stacks
  trans-formation functions right-multiply the top
  of the stack
• Two most important stacks GL_MODELVIEW and
  GL_PROJECTION
• Points get multiplied by the modelview matrix
  first, and then the projection matrix
• GL_MODELVIEW Object-gtCamera
• GL_PROJECTION Camera-gtScreen
• glViewport(0,0,w,h) Screen-gtDevice

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Summary

• Camera transformation
• Map 3D world coordinates to 3D camera coordinates
• Matrix has camera vectors as columns
• Projection transformation
• Map 3D camera coordinates to 2D screen
  coordinates
• Two types of projections
• Parallel
• Perspective