Computational Geometry

Searching for a meaning to today’s popular design methods and concepts we are all going after. Most of the abstract problems, today described within architectural domains, are very parallel to another field defined by M. Ian Shamos in 1978. Here is the introduction paragraph of his PhD thesis;

Geometry is a subject that has captured the imagination of Man for at least 2500 years. It is at the very foundation of Art, Architecture, and Mathematics, and plays a central role in a host of other areas. Computer Science, by contrast, is a newcomer among such established fields, and it has not yet had the opportunity to benefit from their richness. By the same token, Geometry, developing as it did long before the invention of computers, is laden with ideas, results, and prescriptions that are not easily translated into the modern setting of Analysis of Algorithms. It is now recognized that solving problems on a computer does not merely involve rewriting known formulas in some programming language, but that significant issues arise in problem representation, data structures, algorithm design and computational complexity. It is no surprise that straightforward transcription of classical results does not necessarily produce the best algorithms. And why should it, since until recently the only computations that were feasible were those that could be performed with pencil and paper? The need for fast algorithms is apparent only within the framework of high-speed computers and large quantities of data. What ancient geometer could have imagined problems involving millions of points? The purpose of this thesis is, therefore, to establish a discipline of “Computational” Geometry by recasting classical results into explicit and efficient algorithmic form.

Michael Ian Shamos, 1978

I’m very curiously reading about this conception, thinking about today’s abstract thinking in geometric design. I somehow feel this is closing a theoretical gap of contemporary computational design, which we used to believe is only transferred from engineering methods of naval or aeronautics.