Post on 11-Jan-2016
Computer GraphicsPanos Trahanias
e-mail: trahania@csd.uoc.gr
ΗΥ358
Spring 2009
Panos Trahanias: Computer Graphics
Ιστορική Αναδρομή
Architecture of a Vector Display
Panos Trahanias: Computer Graphics
Ιστορική Αναδρομή
Architecture of a Raster Display
Panos Trahanias: Computer Graphics
Ιστορική Αναδρομή
Random scan versus raster scan
Panos Trahanias: Computer Graphics
Conceptual Framework of CG
Panos Trahanias: Computer Graphics
Line Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Line Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Line Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Line Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Line Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Line Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Line Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Circle Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Circle Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Circle Drawing – Midpoint Algorithm
Eight-way symmetry
Panos Trahanias: Computer Graphics
Circle Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Circle Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Circle Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Circle Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Circle Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Ellipse Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Ellipse Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Ellipse Drawing – Midpoint Algorithm
Panos Trahanias: Computer Graphics
Antialiasing – Midpoint Line Algorithm
Increasing Resolution
Panos Trahanias: Computer Graphics
Antialiasing – Midpoint Line Algorithm
Unweighted Area Sampling
Panos Trahanias: Computer Graphics
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 pixel’s center and the area.
Panos Trahanias: Computer Graphics
Antialiasing – Midpoint Line Algorithm
Unweighted Area Sampling: Box Filter
Panos Trahanias: Computer Graphics
Antialiasing – Midpoint Line Algorithm
Weighted Area Sampling: Cone Filter
Panos Trahanias: Computer Graphics
Antialiasing – Midpoint Line Algorithm
Dramatic Effects of the cone filter.
Panos Trahanias: Computer Graphics
Antialiasing – Midpoint Line Algorithm
Panos Trahanias: Computer Graphics
Antialiasing – Midpoint Line Algorithm
Panos Trahanias: Computer Graphics
Antialiasing – Midpoint Line Algorithm
Panos Trahanias: Computer Graphics
Antialiasing – Midpoint Line Algorithm
Panos Trahanias: Computer Graphics
Polygon Filling
Panos Trahanias: Computer Graphics
Polygon Filling
Panos Trahanias: Computer Graphics
Polygon Filling
Calculation of Span Extrema
Panos Trahanias: Computer Graphics
Polygon Filling
Panos Trahanias: Computer Graphics
Polygon Filling
Panos Trahanias: Computer Graphics
Polygon Filling
Panos Trahanias: Computer Graphics
Polygon Filling
Panos Trahanias: Computer Graphics
Polygon Filling
Polygon Filling Algorithm
Panos Trahanias: Computer Graphics
Polygon Filling
Panos Trahanias: Computer Graphics
Filling Ellipse Arcs
Panos Trahanias: Computer Graphics
Clipping Lines
Panos Trahanias: Computer Graphics
Clipping Lines
Cohen-Sutherland Line-Clipping Algorithm
Panos Trahanias: Computer Graphics
Clipping Lines
Panos Trahanias: Computer Graphics
Clipping Lines
Panos Trahanias: Computer Graphics
Clipping Lines
Panos Trahanias: Computer Graphics
Clipping Lines
Panos Trahanias: Computer Graphics
Clipping Lines
Parametric Line-Clipping Algorithm
Panos Trahanias: Computer Graphics
Clipping Lines
Panos Trahanias: Computer Graphics
Clipping Lines
Panos Trahanias: Computer Graphics
Clipping Lines
Panos Trahanias: Computer Graphics
Geometrical Transformations
2D Transformations - Translation
Panos Trahanias: Computer Graphics
Geometrical Transformations
2D Transformations - Scaling
Panos Trahanias: Computer Graphics
Geometrical Transformations
2D Transformations - Rotation
Panos Trahanias: Computer Graphics
Geometrical Transformations
Homogeneous Coordinates
The XYW homogeneous coordinate space, with the W=1 plane and point P(X,Y,W) projected onto the W=1 plane.
Panos Trahanias: Computer Graphics
Geometrical Transformations
2D Transformations – Affine Transformations
45o rotation and then nonuniform scaling of the unit cube. The result is an affine transformation.
Panos Trahanias: Computer Graphics
Geometrical Transformations
2D Transformations – Shear Transformations
Panos Trahanias: Computer Graphics
Geometrical Transformations
Composition of 2D Transformations
Panos Trahanias: Computer Graphics
Geometrical Transformations
2D Transformations – the Window-to-Viewport Transformation
Panos Trahanias: Computer Graphics
Geometrical Transformations
2D Transformations – the Window-to-Viewport Transformation
Panos Trahanias: Computer Graphics
Geometrical Transformations
2D Transformations – the Window-to-Viewport Transformation
Panos Trahanias: Computer Graphics
Geometrical Transformations
3D Transformations – Coordinate Systems
Right-handed Coordinate System
Left-handed Coordinate System
Panos Trahanias: Computer Graphics
Geometrical Transformations
Composition of 3D Transformations
Panos Trahanias: Computer Graphics
Geometrical Transformations
Composition of 3D Transformations – 1st Approach
Panos Trahanias: Computer Graphics
Geometrical Transformations
Composition of 3D Transformations – 2nd Approach
Panos Trahanias: Computer Graphics
Geometrical Transformations
Composition of 3D Transformations
Panos Trahanias: Computer Graphics
Viewing in 3D
Conceptual model of 3D viewing
Panos Trahanias: Computer Graphics
Viewing in 3D
Projections - Projectors
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projections – 1-point PP
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projections – 2-point PP
Panos Trahanias: Computer Graphics
Viewing in 3D
Parallel Projections
Panos Trahanias: Computer Graphics
Viewing in 3D
Parallel Projections – Isometric Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Parallel Projections – Oblique Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Panos Trahanias: Computer Graphics
Viewing in 3D
Specifying an Arbitrary 3D View
Panos Trahanias: Computer Graphics
Viewing in 3D
Specifying an Arbitrary 3D View
Panos Trahanias: Computer Graphics
Viewing in 3D
Panos Trahanias: Computer Graphics
Viewing in 3D
Panos Trahanias: Computer Graphics
Viewing in 3D
Panos Trahanias: Computer Graphics
Viewing in 3D
Panos Trahanias: Computer Graphics
Viewing in 3D
The Mathematics of Planar Geometric Projections
Panos Trahanias: Computer Graphics
Viewing in 3D
Alternative Perspective Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Alternative Perspective Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Implementation of Planar Geometric Projections
Panos Trahanias: Computer Graphics
Viewing in 3D
Implementation of 3D Viewing
Panos Trahanias: Computer Graphics
Viewing in 3D
Parallel Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Parallel Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Parallel Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Parallel Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Shearing Matrix
Panos Trahanias: Computer Graphics
Viewing in 3D
Final Translation / Scaling Step
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projection
Step 4 - Shear
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Perspective Projection
Panos Trahanias: Computer Graphics
Viewing in 3D
Implementation Summary
Panos Trahanias: Computer Graphics
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;
}
Panos Trahanias: Computer Graphics
Techniques for Efficient Visible-surface Algorithms
Extents and Bounding Volumes
Panos Trahanias: Computer Graphics
Techniques for Efficient Visible-surface Algorithms
Back-face Culling
Panos Trahanias: Computer Graphics
Z-Buffer Algorithm
Panos Trahanias: Computer Graphics
Z-Buffer Algorithm
Panos Trahanias: Computer Graphics
Z-Buffer Algorithm
Panos Trahanias: Computer Graphics
Scan-Line Algorithms
Much like polygon scan-conversion algorithms
Each ET entry contains
Panos Trahanias: Computer Graphics
Scan-Line Algorithms
Panos Trahanias: Computer Graphics
Scan-Line Algorithms
Panos Trahanias: Computer Graphics
Scan-Line Algorithms
Panos Trahanias: Computer Graphics
Scan-Line Algorithms
Panos Trahanias: Computer Graphics
Scan-Line Algorithms
Panos Trahanias: Computer Graphics
Scan-Line Algorithms
Pseudocode for a general scan-line algorithm
Panos Trahanias: Computer Graphics
Visible-Surface Ray Tracing
Panos Trahanias: Computer Graphics
Visible-Surface Ray Tracing
Pseudocode for a simple ray tracer
Panos Trahanias: Computer Graphics
Visible-Surface Ray Tracing
Panos Trahanias: Computer Graphics
Visible-Surface Ray Tracing
Anti-alised ray tracing
Panos Trahanias: Computer Graphics
List-Priority Algorithms
The Depth-Sort Algorithm
Panos Trahanias: Computer Graphics
List-Priority Algorithms
Depth Comparisons
Panos Trahanias: Computer Graphics
List-Priority Algorithms
The Depth-Sort Algorithm – Tests to resolve ambiguities
The Depth-Sort Algorithm – Tests with polygons reversed
Panos Trahanias: Computer Graphics
List-Priority Algorithms
The Depth-Sort Algorithm – Results of Tests
Panos Trahanias: Computer Graphics
List-Priority Algorithms
The Depth-Sort Algorithm – Unnecessary polygon split
Panos Trahanias: Computer Graphics
Illumination and Shading
Panos Trahanias: Computer Graphics
Illumination and ShadingDiffuse Reflection
Panos Trahanias: Computer Graphics
Illumination and Shading
Panos Trahanias: Computer Graphics
Illumination and Shading
Atmospheric Attenuation
Panos Trahanias: Computer Graphics
Illumination and Shading
Depth Cueing
Panos Trahanias: Computer Graphics
Illumination and Shading
Specular Reflection
Panos Trahanias: Computer Graphics
Illumination and Shading
Panos Trahanias: Computer Graphics
Illumination and Shading
Panos Trahanias: Computer Graphics
Illumination and Shading
Panos Trahanias: Computer Graphics
Illumination and Shading
Panos Trahanias: Computer Graphics
Illumination and Shading
Surface Normals
Panos Trahanias: Computer Graphics
Illumination and Shading
Panos Trahanias: Computer Graphics
Illumination and Shading
Normal Vector Interpolation
Panos Trahanias: Computer Graphics
Illumination and Shading
Gouraud Shading – Phong Shading
Panos Trahanias: Computer Graphics
Illumination and Shading
Texture Mapping
Panos Trahanias: Computer Graphics
Illumination and Shading
Scan-line Shadow Algorithm
Panos Trahanias: Computer Graphics
Illumination and Shading
Two-Pass Object Precision Shadow Algorithm
Panos Trahanias: Computer Graphics
Illumination and Shading
Transparency
Panos Trahanias: Computer Graphics
Illumination and Shading
Calculating the refraction vector