New directions in geometric traversal theory

Project Details

Description

Computational geometry is a field of research in which deep mathematical insights from the area of geometry are used to obtain practical solutions to engineering challenges encountered in a wide variety of applications, iii the high—tech industry and in other places.

This proposal centers on finding small sets of straight lines which pass through, or close to, a set of given objects. These kinds of problems arise naturally, say, when one wants to plan a small set of metro lines that will serve several neighborhoods, where construction considerations require the metro lines to be as straight as possible. Various other applications are not hard to imagine. In reality, the ‘objects’ may have very different forms and may be placed in different shapes. Instead of solving each such problem in an ad—hoc manner, we would like to develop a general way to efficiently find such ‘nets of lines’. We shall study also high—dimensional variants of the problem, e.g., where the objects are three—dimensional and we want to find 2—din1ensional flats that pass close to them — a subject which becomes more and more relevant with the development of 3d printing. If successful, the project will provide both new theoretical insights and new practical solutions.

StatusActive
Effective start/end date1/01/22 → …

Funding

  • United States-Israel Binational Science Foundation (BSF)

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