Computer Graphics

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Computer Graphics

• Panos Trahanias
• e-mail trahania_at_csd.uoc.gr

??358 Spring 2009
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Architecture of a Vector Display
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Architecture of a Raster Display
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Random scan versus raster scan
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Conceptual Framework of CG
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Line Drawing Midpoint Algorithm
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Line Drawing Midpoint Algorithm
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Line Drawing Midpoint Algorithm
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Line Drawing Midpoint Algorithm
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Line Drawing Midpoint Algorithm
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Line Drawing Midpoint Algorithm
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Line Drawing Midpoint Algorithm
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Circle Drawing Midpoint Algorithm
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Circle Drawing Midpoint Algorithm
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Circle Drawing Midpoint Algorithm
Eight-way symmetry
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Circle Drawing Midpoint Algorithm
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Circle Drawing Midpoint Algorithm
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Circle Drawing Midpoint Algorithm
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Circle Drawing Midpoint Algorithm
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Circle Drawing Midpoint Algorithm
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Ellipse Drawing Midpoint Algorithm
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Ellipse Drawing Midpoint Algorithm
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Ellipse Drawing Midpoint Algorithm
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Antialiasing Midpoint Line Algorithm
Increasing Resolution
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Antialiasing Midpoint Line Algorithm
Unweighted Area Sampling
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Antialiasing Midpoint Line Algorithm

• Properties of Unweighted Area Sampling
• Intensity of a pixel intersected by a line
  decreases as the distance between the pixel
  center and the edge increases.
• A primitive (e.g. line) does not influence a
  pixel at all if they are not intersected.
• Equal areas contribute equal intensity,
  regardless of the distance between the pixels
  center and the area.

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Antialiasing Midpoint Line Algorithm
Unweighted Area Sampling Box Filter
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Antialiasing Midpoint Line Algorithm
Weighted Area Sampling Cone Filter
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Antialiasing Midpoint Line Algorithm
Dramatic Effects of the cone filter.
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Antialiasing Midpoint Line Algorithm
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Antialiasing Midpoint Line Algorithm
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Antialiasing Midpoint Line Algorithm
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Antialiasing Midpoint Line Algorithm
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Polygon Filling
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Polygon Filling
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Polygon Filling
Calculation of Span Extrema
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Polygon Filling
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Polygon Filling
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Polygon Filling
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Polygon Filling
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Polygon Filling
Polygon Filling Algorithm
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Polygon Filling
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Filling Ellipse Arcs
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Clipping Lines
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Clipping Lines
Cohen-Sutherland Line-Clipping Algorithm
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Clipping Lines
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Clipping Lines
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Clipping Lines
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Clipping Lines
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Clipping Lines
Parametric Line-Clipping Algorithm
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Clipping Lines
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Clipping Lines
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Clipping Lines
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Geometrical Transformations
2D Transformations - Translation
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Geometrical Transformations
2D Transformations - Scaling
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Geometrical Transformations
2D Transformations - Rotation
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Geometrical Transformations
Homogeneous Coordinates
The XYW homogeneous coordinate space, with the
W1 plane and point P(X,Y,W) projected onto the
W1 plane.
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Geometrical Transformations
2D Transformations Affine Transformations
45o rotation and then nonuniform scaling of the
unit cube. The result is an affine transformation.
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Geometrical Transformations
2D Transformations Shear Transformations
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Geometrical Transformations
Composition of 2D Transformations
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Geometrical Transformations
2D Transformations the Window-to-Viewport
Transformation
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Geometrical Transformations
2D Transformations the Window-to-Viewport
Transformation
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Geometrical Transformations
2D Transformations the Window-to-Viewport
Transformation
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Geometrical Transformations
3D Transformations Coordinate Systems
Left-handed Coordinate System
Right-handed Coordinate System
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Geometrical Transformations
Composition of 3D Transformations
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Geometrical Transformations
Composition of 3D Transformations 1st Approach
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Geometrical Transformations
Composition of 3D Transformations 2nd Approach
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Geometrical Transformations
Composition of 3D Transformations
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Viewing in 3D
Conceptual model of 3D viewing
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Viewing in 3D
Projections - Projectors
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Viewing in 3D
Perspective Projections 1-point PP
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Viewing in 3D
Perspective Projections 2-point PP
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Viewing in 3D
Parallel Projections
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Viewing in 3D
Parallel Projections Isometric Projection
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Viewing in 3D
Parallel Projections Oblique Projection
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Viewing in 3D
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Viewing in 3D
Specifying an Arbitrary 3D View
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Viewing in 3D
Specifying an Arbitrary 3D View
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Viewing in 3D
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Viewing in 3D
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Viewing in 3D
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Viewing in 3D
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Viewing in 3D
The Mathematics of Planar Geometric Projections
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Viewing in 3D
Alternative Perspective Projection
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Viewing in 3D
Alternative Perspective Projection
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Viewing in 3D
Implementation of Planar Geometric Projections
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Viewing in 3D
Implementation of 3D Viewing
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Viewing in 3D
Parallel Projection
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Viewing in 3D
Parallel Projection
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Viewing in 3D
Parallel Projection
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Viewing in 3D
Parallel Projection
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Viewing in 3D
Shearing Matrix
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Viewing in 3D
Final Translation / Scaling Step
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Viewing in 3D
Perspective Projection
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Viewing in 3D
Perspective Projection
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Viewing in 3D
Perspective Projection
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Viewing in 3D
Perspective Projection
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Viewing in 3D
Perspective Projection
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Viewing in 3D
Perspective Projection Step 4 - Shear
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Viewing in 3D
Perspective Projection
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Viewing in 3D
Perspective Projection
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Viewing in 3D
Perspective Projection
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Viewing in 3D
Implementation Summary
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Visible Surface Determination
Image Precision Approaches
Object Precision Approaches
for (each pixel in the image) determine the
object closest to the viewer that is pierced by
the projector through the pixel draw the pixel
in the appropriate color
for (each object in the world) determine those
parts of the object whose view is unobstructed by
other parts of it or any other object draw
those parts in the appropriate color
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Techniques for Efficient Visible-surface
Algorithms
Extents and Bounding Volumes
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Techniques for Efficient Visible-surface
Algorithms
Back-face Culling
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Z-Buffer Algorithm
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Z-Buffer Algorithm
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Z-Buffer Algorithm
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Scan-Line Algorithms
Much like polygon scan-conversion
algorithms Each ET entry contains
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Scan-Line Algorithms
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Scan-Line Algorithms
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Scan-Line Algorithms
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Scan-Line Algorithms
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Scan-Line Algorithms
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Scan-Line Algorithms
Pseudocode for a general scan-line algorithm
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Visible-Surface Ray Tracing
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Visible-Surface Ray Tracing
Pseudocode for a simple ray tracer
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Visible-Surface Ray Tracing
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Visible-Surface Ray Tracing
Anti-alised ray tracing
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List-Priority Algorithms
The Depth-Sort Algorithm
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List-Priority Algorithms
Depth Comparisons
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List-Priority Algorithms
The Depth-Sort Algorithm Tests to resolve
ambiguities
The Depth-Sort Algorithm Tests with polygons
reversed
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List-Priority Algorithms
The Depth-Sort Algorithm Results of Tests
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List-Priority Algorithms
The Depth-Sort Algorithm Unnecessary polygon
split
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Illumination and Shading
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Illumination and Shading
Diffuse Reflection
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Illumination and Shading
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Illumination and Shading
Atmospheric Attenuation
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Illumination and Shading
Depth Cueing
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Illumination and Shading
Specular Reflection
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Illumination and Shading
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Illumination and Shading
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Illumination and Shading
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Illumination and Shading
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Illumination and Shading
Surface Normals
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Illumination and Shading
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Illumination and Shading
Normal Vector Interpolation
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Illumination and Shading
Gouraud Shading Phong Shading
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Illumination and Shading
Texture Mapping
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Illumination and Shading
Scan-line Shadow Algorithm
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Illumination and Shading
Two-Pass Object Precision Shadow Algorithm
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Illumination and Shading
Transparency
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Illumination and Shading
Calculating the refraction vector