Not for Sale

• #### Conclusion and References 16-16

FIGURE 10 Delaunay triangulation result.

see this, examine Figure 10. If the radius of the circle is one and the distance A to D is one, the angle ACD is 60°, and thus angle ABD is 30°. If the radius of the circle is less than one (it cannot be greater), then angles ACD and ABD are larger. Similarly, if the distance A to D is greater than one (it cannot be less), then angles ACD and ABD are again larger. Therefore, no Delaunay triangulation can have an angle less than 30°. Since the three angles of a triangle sum to 180°, no angle can be greater than 120°. Thus, there is an algorithm for triangulation with a guarantee on the shape of the triangles. More sophisticated versions of the algorithm allow one to vary the size of the triangles to get higher accuracy in regions of interest.

At present there is no known method for partitioning a three-dimensional region into tetrahedra that has provable lower bounds on the size of the dihedral angles. Today this is an important research problem.

## INFORMATION CAPTURE AND ACCESS

In the second portion of this lecture, I explore the science base that needs to be created to support the emerging technology for information capture and access. But first I would like to make a personal observation on contributions to science. I believe that the most fundamental contributions are not the theorems or solutions to known problems but are, rather, the formulations of the correct questions to ask. Once the correct questions are posed, it is usually not too long until answers emerge. It is the formulating of the questions that shapes a new discipline. In the area of information capture and access, we are still grappling with an attempt to formulate the correct questions.

Let me proceed by telling an apocryphal story. I call it the bus stop story. The story is about myself, a faculty member at Cornell University. Cornell is located in a small town called Ithaca, in upstate New York. The temperature in the winter drops below freezing. Although I live within walking distance, on winter evenings I go to the bus stop and ride the bus home. The last bus passes the campus stop at 6 p.m. One evening I arrived at the bus stop at 5:57 and waited 10 minutes. There was no bus. What should I do? Do I assume that the bus is delayed and wait? Or is it possible that the bus was a few minutes early and I had better start walking home? Before answering the question, consider more technology.

Modern computing and communication technology is sufficient to determine the location of a vehicle with sufficient accuracy to record its location on a street map. One such technology is based on an accurate time signal from a satellite. In fact boaters and hikers already use this technology to determine their location. Imagine a time in the not-far-distant future when use of this technology is common practice and taxi, delivery, and emergency services routinely track and dispatch their vehicles with it.

Imagine, also, that personal workstations have shrunk to the size of pocket calculators and that they are equipped with cellular communication. In this situation, I pull out my portable communication workstation and connect to the bus company's database, locate the current position of the bus, and discover that it is currently rounding the bend on Stewart Avenue. If I am patient for a few more minutes, I can ride the bus home. Note that in this transaction, I needed to pull my gloves off to key in a series

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COMPUTING, COMMUNICATION, AND THE INFORMATION AGE FIGURE 10 Delaunay triangulation result. see this, examine Figure 10. If the radius of the circle is one and the distance A to D is one, the angle ACD is 60°, and thus angle ABD is 30°. If the radius of the circle is less than one (it cannot be greater), then angles ACD and ABD are larger. Similarly, if the distance A to D is greater than one (it cannot be less), then angles ACD and ABD are again larger. Therefore, no Delaunay triangulation can have an angle less than 30°. Since the three angles of a triangle sum to 180°, no angle can be greater than 120°. Thus, there is an algorithm for triangulation with a guarantee on the shape of the triangles. More sophisticated versions of the algorithm allow one to vary the size of the triangles to get higher accuracy in regions of interest. At present there is no known method for partitioning a three-dimensional region into tetrahedra that has provable lower bounds on the size of the dihedral angles. Today this is an important research problem. INFORMATION CAPTURE AND ACCESS In the second portion of this lecture, I explore the science base that needs to be created to support the emerging technology for information capture and access. But first I would like to make a personal observation on contributions to science. I believe that the most fundamental contributions are not the theorems or solutions to known problems but are, rather, the formulations of the correct questions to ask. Once the correct questions are posed, it is usually not too long until answers emerge. It is the formulating of the questions that shapes a new discipline. In the area of information capture and access, we are still grappling with an attempt to formulate the correct questions. Let me proceed by telling an apocryphal story. I call it the bus stop story. The story is about myself, a faculty member at Cornell University. Cornell is located in a small town called Ithaca, in upstate New York. The temperature in the winter drops below freezing. Although I live within walking distance, on winter evenings I go to the bus stop and ride the bus home. The last bus passes the campus stop at 6 p.m. One evening I arrived at the bus stop at 5:57 and waited 10 minutes. There was no bus. What should I do? Do I assume that the bus is delayed and wait? Or is it possible that the bus was a few minutes early and I had better start walking home? Before answering the question, consider more technology. Modern computing and communication technology is sufficient to determine the location of a vehicle with sufficient accuracy to record its location on a street map. One such technology is based on an accurate time signal from a satellite. In fact boaters and hikers already use this technology to determine their location. Imagine a time in the not-far-distant future when use of this technology is common practice and taxi, delivery, and emergency services routinely track and dispatch their vehicles with it. Imagine, also, that personal workstations have shrunk to the size of pocket calculators and that they are equipped with cellular communication. In this situation, I pull out my portable communication workstation and connect to the bus company's database, locate the current position of the bus, and discover that it is currently rounding the bend on Stewart Avenue. If I am patient for a few more minutes, I can ride the bus home. Note that in this transaction, I needed to pull my gloves off to key in a series

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