Jinxiang Chai

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Computer Graphics CPSC 441

• Jinxiang Chai

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Final exam

• Time 100pm-300, 5/12
• Location HRBB 113

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Scan Line Conversion

• How to draw a line?
• - Digital Differential Analyzer (DDA)
• - Midpoint algorithm
• - Understand both algorithms
• - Strengths and limitations

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Scan Conversion of Polygons

• How to draw a polygons?
• - Active edge list
• - Boundary fill
• - Flood fill
• - Understand three algorithms
• - Limitations and strengths

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Clipping Lines
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Clipping Lines
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Clipping Lines

• Given a line with end-points (x0, y0), (x1, y1)
• and clipping window (xmin, ymin), (xmax, ymax),
• determine if line should be drawn and clipped
  end-points of line to draw.

(xmax,ymax)
(x1, y1)
(x0, y0)
(xmin,ymin)
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Line Clipping

• How to clip a line?
• - Simple line clipping algorithm
• - Cohen--Sutherland
• - Liang-Barsky

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Clipping Polygons

• Clipping polygons is more complex than clipping
  the individual lines
• - Input polygon

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Clipping Polygons

• Clipping polygons is more complex than clipping
  the individual lines
• - Input polygon
• - Output original polygon, new polygon, or
  nothing

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Polygon Clipping

• How to clip a polygon?
• - Sutherland-Hodgman Clipping (convex
  polygons)
• - Weiler-Atherton Algorithm (general
  polygons)

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2D/3D Transformation

• Various transform matrices
• - 2D/3D rotation
• - 2D/3D translation
• - 2D/3D scaling
• - 2D affine transform

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2D/3D Coordinate Transformation

• Various transform matrix
• - 2D/3D rotation
• - 2D/3D translation
• - 2D/3D scaling
• - 2D affine transform
• How to do 2D/3D matrix composition

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2D Coordinate Transformation

• Transform object description from to

p
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2D Coordinate Transformation

• 2D translation

p
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2D Coordinate Transformation

• 2D translation

0
1
p
0
1
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2D Coordinate Transformation

• 2D translationrotation

p
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2D Coordinate Transformation

• 2D translation scaling

p
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Composite 2D/3D Transformation

• A 2D lamp character

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Composite 2D/3D Transformation

• A 2D lamp character

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Composite 2D/3D Transformation

• A 2D lamp character

?
Given , , how to compute the
global position of the point p?
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2D/3D Hierarchical Models

• Hierarchical model can be composed of instances
  using trees or directed acyclic graphs (DAGs)
• - edges contains geometric transformations
• - nodes contains geometry

world
base
Upper arm
lower arm
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A More Complex Example Human Figure
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Motion Capture Data

• .asf file
• .amc file

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3D-gt2D Geometry Pipeline
Rotate and translate the camera
View space
World space
Object space
Focal length
Aspect ratio resolution
Normalized project space
Image space
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3D Geometry Pipeline

• Before being turned into pixels by graphics
  hardware, a piece of geometry goes through a
  number of transformations...

Model space (Object space)
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3D Geometry Pipeline

• Before being turned into pixels by graphics
  hardware, a piece of geometry goes through a
  number of transformations...

World space (Object space)
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3D Geometry Pipeline

• Before being turned into pixels by graphics
  hardware, a piece of geometry goes through a
  number of transformations...

Eye space (View space)
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3D Geometry Pipeline

• Before being turned into pixels by graphics
  hardware, a piece of geometry goes through a
  number of transformations...

Normalized projection space
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Projections

• Parallel projection
• - definition
• - properties
• Perspective projection
• - definition
• - homogeneous coordinates
• - vanishing point
• - properties

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3D Geometry Pipeline

• Before being turned into pixels by graphics
  hardware, a piece of geometry goes through a
  number of transformations...

Image space, window space, raster space, screen
space, device space
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3D Rendering pipeline
Modeling transformation
Transform into 3D world system
Illuminate according to lighting and reflectance
lighting
Transform into 3D camera coordinate system
Viewing transformation
Transform into 2D camera system
Project transformation
Clip primitives outside cameras view
Clipping
Draw pixels (includes texturing, hidden surface,
etc.)
Scan conversion
Image
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Hidden Surface Removals

• Backface Culling
• Painters algorithm
• BSP
• Z-buffer
• Scan line
• Ray casting

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Color

• Human visual system
• Tristimulus of Color Theory
• Chromaticity
• Different colors models

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Tristimulus of Color Theory

• Spectral-response functions of each of the three
  types of cones
• Color matching function based on RGB
• - any spectral color can be represented as a
  linear combination of these primary colors

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Chromaticity Diagram

• Determining purity and dominant wave length for a
  given color
• Identify complementary colors
• Compare color gamuts for different primaries

Image taken from http//fourier.eng.hmc.edu/e180/h
andouts/color1/node27.html
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Lighting

• Ambient lighting
• Diffuse lighting
• Specular lighting
• Spot lights and light attenuation

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Shading Algorithms

• Flat Shading
• Gouraud Shading
• Phong Shading

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Texture mapping others

• Texture mapping, environment mapping, bump/normal
  mapping, displacement mapping,

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Rendering

• Local illumination
• Global illumination
• - ray tracing
• - radiosity
• - photon mapping

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Rotation representation

• Rotation matrix
• Fixed angle and Euler angle
• Axis angle
• Quaternion

Understand their properties in terms of matrix
composition, compactness, and rotation
interpolation
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Mocap

• Various mocap techniques
• Advantages and disadvantages

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Keyframe interpolation

• Basic concept
• Various curve representation
• Various spline representation

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Forward Kinematcs and Inverse Kinematics

• Basic concepts
• IK approaches
• Jacobian matrix
• Problems in IK and how to address them