Today
Research overview
Introduction
Course details
Announcements
Transforms
Textbook
Fundamentals of Computer Graphics, 3rd ed.,
Peter Shirley and Steve Marschner.
Chapter 1 Read it for fun (some interesting bits)
Chapter 2 Misc Math (should all be revie
COMP 557
3: View transformations, GL MODELVIEW
Jan. 13, 2015
Lecture 3
View/eye/camera coordinates
In order to dene an image of a scene, we need to specify the 3D position of the viewer and we also
need to specify the orientation of the viewer. The way th
COMP 557
4 Projections
Jan. 15, 2015
Lecture 4
Up to now we have dened points in a 3D world coordinate space and we have considered how to
transform into a 3D camera coordinate space. Our next step is to project the points into an image.
Images are 2D, no
COMP 557
5 Projective Transforms
Jan. 20, 2015
Lecture 5
Projective transformation (from eye to clipping coordinates)
Last lecture we considered how to project 3D points to the 2D projection plane. The problem with
doing this is that we would lose the inf
COMP 557
6 Clipping, windowing, rasterization
Jan. 22, 2015
Lecture 6
Last lecture I introduced the view volume and mentioned how it is used to limit the set of points,
lines, objects, etc that need to be drawn in an image. We might have a very complicate
COMP 557
7 Graphics Pipeline, Hidden Surface Removal
Jan. 27, 2015
Lecture 7
At the begin of this lecture I discuss the standard graphics pipeline. This nishes up Part 1 of the
course, covered in lectures 1-6, and also provides a segue to Part 2 which con
COMP 557
8 Ecient Ray Casting
Jan. 29, 2015
Lecture 8
Last lecture we looked at several methods for solving the hidden surface removal problem. Many
such methods boil down to the problem of nding, for each pixel, what is the closest surface in the
view vo
COMP 557
9: Object hierarchies, fractals, L-systems
Feb. 3, 2015
Lecture 9
It is often natural to model objects as consisting of parts, and the parts themselves as consisting
of subparts, etc. Think of a bicycle. It has 2 wheels, a frame, a seat, handle b
COMP 557
10 Cubic Curves and Bicubic Surfaces
Today I will give an introduction to the topic of smooth curves and surfaces in
Feb. 5, 2015
3
.
Cubic Curves (and splines)
Up to now, we have mostly considered simple linear shapes lines, polygons and second
COMP 557
12 - Lighting, Material, Shading
Feb 12, 2015
We now move to third part of the course where we will be concerned mostly with what intensity
values to put at each pixel in an image. We will begin with a few simple models of lighting and
surface re
COMP 557
11 Meshes
Feb 10, 2015
Meshes
You all know what vertices and edges are in the context of graphs. In computer graphics, a mesh
is a specify type of graph. Vertices are points in Rn where n = 2 or 3. Edges are line segments.
Polygons are cycles in
COMP 557
16-texture mapping
Feb 26, 2015
Texture Mapping
One often wishes to paint a surface with a certain pattern, or a texture. In general this is called
texture mapping. The texture might be dened by a digital photograph T (sp , tp ) where (sp , tp )
COMP 557
17 - texture mapping (cont.), procedural shading
March 10, 2015
In the rst half of todays lecture, I elaborated on the ideas of texture mapping that were introduced
last lecture. In the second half, I discussed the idea of procedural shading, and
COMP 557
2: Model transformations, Homogeneous Coordinates
Jan. 8, 2015
Lecture 2
When dening a scene that we want to draw, we will often need to perform transformations on
the objects we want to draw by rotating, scaling, and translation them. To do so,
COMP 557
1 Preliminaries
Jan. 6, 2015
Lecture 1
Computer graphics, broadly dened, is a set of methods for using computers to create and manipulate images. There are many applications of computer graphics including entertainment (games,
cinema, tv commerci
COMP 557 - Fundamentals of Computer Graphics
1
1
Geometry and Transformations
5
The representation of shapes and objects is an important part of creating images with computers. We
will use a variety of different methods for describing shapes, such as poin
3D Transformations
COMP557
Paul Kry
McGill COMP557 Fall 2010
1
Translation
McGill COMP557 Fall 2010
2
Based on slides by Steve Marschner
Scaling
McGill COMP557 Fall 2010
3
Based on slides by Steve Marschner
Rotation about z axis
McGill COMP557 Fall 2010
4
Scene Graphs
September 12
COMP557
Paul Kry
1
Data structures with transforms
Representing a drawing (scene)
List of objects
Transform for each object
can use minimal primitives: ellipse is transformed circle
transform applies to points of object
COMP
3D Viewing
COMP557
Paul Kry
COMP557 McGill
1
Viewing, backward and forward /
Image order and Object order
Image order: backward approach
start from pixel
ask what part of scene projects to pixel
explicitly construct the ray corresponding to the pixel
Fundamentals of Computer Graphics
COMP 557
5 September 2012
Paul Kry
Today
Research overview
Announcements
Introduction
Course details
Transforms
3
My Research - Animation
Simulating the real world
Challenging because of complexity
Fundamental ideas
E
Lights and Shading
COMP557
Paul Kry
McGill COMP557 Fall 2012
1
McGill COMP557 Fall 2012
2
Shading
Compute light reflected (scattered) toward camera
Inputs:
eye direction
light direction
(for each of many lights)
surface normal
surface parameters
(co
Projection Taxonomy
COMP 557
Paul Kry
McGill COMP577 Fall 2012
1
Review
What goes where on projection?
gluPerspective and glFrustum
Frustum applications
Tiled rendering, anaglyphs, depth of field, shifted perspective
History of projection
Depth Cues
Pipeline and Rasterization
McGill 557 Fall 2011
Basded on slides by Steve Marschner
1
The graphics pipeline
The standard approach to object-order graphics
Many versions exist
software, e.g., Pixars REYES architecture
many options for quality and flexi
Pipeline Operations
McGill COMP557 Fall 2012
Based on slides by Steve Marschner
1
Pipeline
overview
you are here
APPLICATION
COMMAND STREAM
3D transformations; shading
VERTEX PROCESSING
TRANSFORMED GEOMETRY
conversion of primitives to pixels
RASTERIZATION
COMP 557 - Fundamentals of Computer Graphics
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Spline Curves and Surfaces
We have talked about points and lines, and perhaps triangles as primitives that we can transform, project,
and draw. But these do
COMP 557 - Fundamentals of Computer Graphics
1
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Camera coordinates and viewing transformations
In the previous section, we looked at transformation between coordinate systems, and in many respects
the goal of modelling was to bring all quantities into a
COMP 557 - Fundamentals of Computer Graphics
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3.11
Clipping
Section 3.5 introduced the concept of a view volume, and briey mentioned its use, namely to limit the
set of points, lines, objects, etc that need to be considered when making an image
COMP 557
18 - environment mapping
Mar. 12, 2015
Rendering mirror surfaces
The next texture mapping method assumes we have a mirror surface, or at least a reectance
function that contains a mirror component. Examples might be a car window or hood, a puddle