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How many degrees of freedom are associated with:
-- all planar quadrilaterals in 3-space?
-- with the mechanical 2D linkage below? |
Which point maps into the origin (0,0,0)in the complete perspective transform into the full (±1) canonical view cube? |

How to find the solutions: Transform some key sample points by the given matrix and see what happens; then solve the resulting equation.

In the middle portion we see the three options for doing the necessary

In the last few stages of the pipeline the most advances have occured in the last decade.

The are due to the availability of ever more powerful (and more general)

and the introduction of ever more sophisticated

A brief review of the development of computer graphics hardware.

as an invited keynote speaker at the Interactive 3D Graphics and Games conference, San Francisco, Feb. 19, 2011.

David Luebke graciously allowed me to use some of his material,

but he did not want me to put it on the web in the public domain -- so pay attention! )

Let's briefly recap the surface decoration effects that you had an opportunity to explore with Assignment #8:

This typically occurs through special graphics hardware:

using special

Example of a typical processing pipeline (as seen by DirectX)

Another schematic view of the same pipeline segment

On 4/7/2011 I received a copy of a brand new textbook that has just been published:

E. Angel and D Shreiner: "Interactive Computer Graphics: A top-down apporach with shader-based OpenGL" 6th Edition, Addison Wesley, 2011.

(If I could turn back the clock by 6 months, I would use this as the textbook for CS 184.)

It does a good job guiding you to these newer developments in the rendering pipeline.

(And it would have made assignment #8 somewhat less confusing).

ABET requirements specify, that such courses:

-- have a

-- teach and test

But it is tedious to assemble many of them into a smooth surface.

A B-spline surface is just the external product of two B-spline curves.

It is difficult to make closed surfaces of higher genus with multiple tunnels or handles.

Here is a generalization to arbitrary topologies:

"Interactive Curves and Surfaces," (with Multimedia Tutorial on CAGD), A. Rockwood and P. Chambers, Morgan Kaufman Publishers, Inc.

[ This was used in recent offerings of CS 284. ]

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