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A very brief history of computational geometry

A very brief history of computational geometry. Rodrigo Silveira GEOC 2010/11 - Q2. The name “computational geometry”. Initially claimed in different contexts Minsky’s book “ Perceptrons ” (1969) About pattern recognition Forrest paper (1971)

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A very brief history of computational geometry

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  1. A very brief history ofcomputational geometry Rodrigo Silveira GEOC 2010/11 - Q2

  2. The name “computational geometry” • Initially claimed in different contexts • Minsky’s book “Perceptrons” (1969) • About pattern recognition • Forrestpaper (1971) • About curves and surfacesforgeometricmodeling • Shamos’ PhD Thesis “Computational geometry” (1975) • Nowadays widely recognized as a subfield of Algorithm Theory • Within Theoretical Computer Science (TCS) • TCS includes other things like complexity theory, analysis of algorithms, formal semantics, etc.

  3. Computational geometry • Algorithm theory involved in the design and analysis of efficient algorithms for problems with geometric input and output. • Better names are possible • Algorithmic geometry • Geometric algorithms

  4. How it started • Geometry has been around for a while • Euclid constructions in The Elements (300 BC) • Descartes Cartesian geometry (17th century) • Computers brought renewed interest • 50’s first graphics program • For hidden line removal • First CAD (Computer-aided design) programs

  5. How it actually started • Scattered work begin appearing in 60 & 70’s • Béziersplines, combinatorial geometry (Erdös) • As we know it today, started in the 70’s • Geometric problems gain attention from algorithms researchers • Michael Shamos’ PhD thesis (1975) • “Problems in Computational Geometry” • Increasing interest during late 70’s, 80’s • Most “basic algorithms” date from this period

  6. Taking off • Between late 80’s and 90’s it becomes a very active field • 1983: First European workshop on the topic • 1985: First Annual Symposium on Computational Geometry • Also: first textbook (today, more than 4) • 1996: CGAL: first serious implementation of a robust geometric algorithms library • 1997: First handbook on the topic(second in 2000)

  7. Today • Recognized discipline within TCS • “Large” active community • Many research groups in Europe • And Spain! BCN, Madrid, Sevilla, Zaragoza, Girona, Valladolid,… • 4 specialized journals devoted to it • 3 annual specialized conferences • Strong presence in Algorithms conferences But… still with many unanswered questions and open challenges…

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