Economic Models for Turbulent Times Part I

Crust is an algorithm for reconstructing surfaces of any topology. In other words, it is a computational method for digitally rendering any 2-D shape, using data in three-dimensional space as input.

CSAIL buildings at MIT

Strange topology at MIT

Such methods garner a lot of attention these days. Here are a few reasons why: Graphical simulation models are increasingly needed for visualization and testing purposes in the field of particle physics. World of Warcraft and Second Life rely heavily on computationally intensive computer graphics, and scalable distributed systems. The U.S. economy is a highly complex system, partly guided by the results of mathematical models.

Crust was developed as a collaborative effort between two staff scientists at Xerox PARC and a researcher at MIT.

None of this happened recently. In fact, Crust hasn’t been semantically linked with the word “new” since its debut at the 1998 ACM SIGGRAPH Conference.

What is so special about Crust?

The Crust algorithm is special because it has certain features uncommon in most quantitative models, yet highly sought after.

First, Crust offers results with “provable” guarantees. Given a good sample from a smooth surface, Crust’s results are guaranteed. That is, Crust guarantees that its output is topologically correct, converging to the original surface with increasing faithfulness depending on the input data density.

Voronoi pig

Graphical computation with Crust: Voronoi Piggy

The third member of the Crust project team was Manolis Kamvysellis, a Ph.D. student at MIT. Manolis did much of the implementation and testing work—he wrote a short-form version, A New Voronoi Based Reconstruction Algorithm [PDF], of the original ACM journal publication. Happily, he had the good sense to demonstrate Crust with this fine pink pig! Let’s do the same.

Highly efficient porcine reconstruction in three dimensions

Recall that Crust’s criteria for acceptable sample size is determined dynamically . A single topological surface, such as Piggy, may have very detailed surfaces, with high data density. Observe this near Piggy’s ears and snout. Other areas like the hindquarters are quite featureless.

Crust dynamically adjusts its smallest acceptable sample size accordingly. Even minimally detailed surfaces such as Piggy’s lower hind quarters above the hooves can be reconstructed accurately.

To be continued…

Published in: on December 5, 2010 at 7:58 am  Comments (5)  
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5 CommentsLeave a comment

  1. Yes about Crust, I am following this:
    http://bettereconomics.blogspot.com/2010/12/crust.html

    Economists will be all over this. Watch Zero Hedge and their fans jump on this, Hedge Funds will be there, will quick I bet.

  2. What guarantees does Crust offer that other algorithms do not? And how does Crust work with economic data?

    • I haven’t figured out exactly how Crust works with economic data. I had something in mind at the time. Since then, I rather hoped this post would vanish into the ether. However, I am so enamored of Crust piggy, I can’t bear to remove him though. Matt gave me some hope I was on to something…

      Regarding any guarantees Crust offers that other algorithms do not: I had the same question when writing this post. I looked into the matter, read source materials, satisfied myself that the statement was valid, and have since completely forgotten the answer. I will dig up my findings, as your inquiry certainly deserves a reply. Thank you for visiting, and for taking the time to make multiple comments! I do appreciate it, and hope to see you again soon.

  3. @Matt From the link it looks like Crust is 14 years old. I get that voronoi decomposition was newer then … is the application to economics new or something? I can see how you would use it with volatility surface modelling or fixed income surfaces. But surely you’d be far behind the times now.

    • Actually, I am not so certain that would be the case, @human mathematics. Crust is elderly but Voroni decomposition remains useful.

      Maybe Matt was ahead of the curve after all.


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