Surfaces of revolution
Surfaces of Revolution
Brian Curless
CSEP 557
Winter 2013
Idea: rotate a 2D profile curve around an axis.
What kinds of shapes can you model this way?
1
Constructing surfaces of revolution
2
Constructing surfaces of revolution
We no
Reading
Required:
Angel readings for Parametric Curves lecture,
with emphasis on 10.1.2, 10.1.3, 10.1.5, 10.6.2,
10.7.3, 10.9.4.
Optional
Parametric surfaces
Bartels, Beatty, and Barsky. An Introduction to
Splines for use in Computer Graphics and
Geomet
Reading
Required:
Shirley, section 10.11
Further reading:
Watt, sections 10.4-10.5
A. Glassner. An Introduction to Ray Tracing.
Academic Press, 1989. [In the lab.]
Robert L. Cook, Thomas Porter, Loren Carpenter.
Distributed Ray Tracing. Computer Graph
Reading
Jain, Kasturi, Schunck, Machine Vision. McGraw-Hill,
1995. Sections 4.2-4.4, 4.5(intro), 4.5.5, 4.5.6, 5.1-5.4.
[online handut]
Image processing
Brian Curless
CSEP 557
Winter 2013
1
What is an image?
2
Images as functions
We can think of an image
Reading
Required:
Shirley 10.9, 10.11.1
Further reading:
A. Glassner. An Introduction to Ray Tracing.
Academic Press, 1989.
Anti-aliased and accelerated
ray tracing
Brian Curless
CSEP 557
Winter 2013
1
2
Aliasing
Aliasing (cont)
Ray tracing is a form of
Reading
Required:
Witkin, Particle System Dynamics, SIGGRAPH 01
course notes on Physically Based Modeling.
Witkin and Baraff, Differential Equation Basics,
SIGGRAPH 01 course notes on Physically Based
Modeling.
Particle Systems
Optional
Hockney and Eas
Reading
Required:
Angel 10.1-10.3, 10.5.2, 10.6-10.7, 10.9
Optional
Bartels, Beatty, and Barsky. An Introduction to
Splines for use in Computer Graphics and
Geometric Modeling, 1987.
Farin. Curves and Surfaces for CAGD: A Practical
Guide, 4th ed., 1997
Reading
Required:
Shirley, section 10.1-10.7 (online handout)
Triangle intersection (online handout)
Further reading:
Shirley errata on syllabus page, needed if you
work from his book instead of the handout,
which has already been corrected.
T. Whitte
Reading
Required
Angel, sections 1.2, 2.1-2.7, 2.11.5
Displays and framebuffers
Optional
OpenGL Programming Guide (the red book
available online):
Brian Curless
CSEP 557
Winter 2013
First four sections of chapter 2
First section of chapter 6
Foley e
Reading
Required:
Angel, 5.1-5.6
Further reading:
Foley, et al, Chapter 5.6 and Chapter 6
David F. Rogers and J. Alan Adams,
Mathematical Elements for Computer Graphics,
2nd Ed., McGraw-Hill, New York, 1990, Chapter 2.
I. E. Sutherland, R. F. Sproull,
Reading
Required:
Angel chapter 5.
Optional:
OpenGL red book, chapter 5.
Shading
(Part 1)
Brian Curless
CSEP 557
Winter 2013
1
2
Introduction
Our problem
So far, weve talked exclusively about geometry.
Modeling the flow of light in a scene is very compl
Reading
Required:
Angel, sections 8.1 8.6, 8.8
Optional:
OpenGL Programming Guide, chapter 3
Hierarchical Modeling
Brian Curless
CSEP 557
Winter 2013
1
2
Symbols and instances
3D Example: A robot arm
Most graphics APIs support a few geometric
primitives
Reading
Required:
Angel 3.1, 3.7-3.11
Further reading:
Affine transformations
Brian Curless
CSEP 557
Winter 2013
Angel, the rest of Chapter 3
Foley, et al, Chapter 5.1-5.5.
David F. Rogers and J. Alan Adams,
Mathematical Elements for Computer Graphics
Reading
Required:
Angel chapter 5.
Optional:
OpenGL red book, chapter 5.
Shading
(Part 2)
Brian Curless
CSEP 557
Winter 2013
1
2
Gouraud vs. Phong interpolation
Faceted shading
Now we know how to compute the color at a point
on a surface using the Blinn