A compendium of thirty previously published open problems in computational geometry is presented. [SIGACT News, 32(3) Issue, 120 Sep. 2001, 63–72.] The computational geometry community has made many advances in the relatively short (quarter-century) of the field’s existence. Along the way researchers have engaged with a number of problems that have resisted solution. We gather here a list of op...

Algebraic geometry is a powerful combination of algebra and geometry, with a rich history and many applications, both theoretical and practical. It also has an intimidating reputation. Hence it is important to have a variety of introductory texts at different levels of sophistication. We will see that Schenck's book offers an interesting path into this wonderful subject. 1. What is algebraic ge...

Abstract In the 1993 CCCG at Waterloo the speaker gave a talk on “Teaching Computational Geometry”. Since then textbooks have been published, the field has developed further, and extensive geometric software libraries have become available. How has this impacted teaching computational geometry? Are the issues still the same? Have the topics changed? Can the study of computational geometry be mo...

We promote the concept of object directed computability in computational geometry in order to faithfully generalise the wellestablished theory of computability for real numbers and real functions. In object directed computability, a geometric object is computable if it is the effective limit of a sequence of finitary objects of the same type as the original object, thus allowing a quantitative ...

My research field is Computational Geometry, and I am interested both in theoretical problems and in ‘real life’ applications. This statement includes a summary of my research work to date. The first part covers work involving L1 shortest paths, center point and obnoxious facility location (see [5], [6], [8]) most of this work was done during my Master studies [1999-2001], and is motivated by p...

We will describe an O(n) time reduction from the set-disjointness problem to the farthest pairs problem. This will imply the Ω(n log n) lower bound. Consider an instance of the set-disjointness problem A = {a1, a2, . . . , an} and B = {b1, b2, . . . , bn}. We need to find out whether there exist i and j such that ai = bj. We map the sets A and B to the first and third quadrant of the unit circl...

15 directed towards more application-oriented students. Of course the diier-ent possibilities discussed are not the only ones. Probably each person who teaches a course in computational geometry will choose a diierent set of topics and will treat them in a diierent way. Also computational geometry is still evolving very quickly. New algorithms, approaches, problems and applications are discover...