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Equidecomposable quadratic regions. (English) Zbl 1195.68104
Botana, Francisco (ed.) et al., Automated deduction in geometry. 6th international workshop, ADG 2006, Pontevedra, Spain, August 31–September 2, 2006. Revised papers. Berlin: Springer (ISBN 978-3-540-77355-9/pbk). Lecture Notes in Computer Science 4869. Lecture Notes in Artificial Intelligence, 24-38 (2007).
Summary: This article describes an algorithm that decides whether a region in three dimensions, described by quadratic constraints, is equidecomposable with a collection of primitive regions. When a decomposition exists, the algorithm finds the volume of the given region. Applications to the ‘Flyspeck’ project are discussed.
For the entire collection see [Zbl 1132.68006].
MSC:
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
51M20 Polyhedra and polytopes; regular figures, division of spaces
51M25 Length, area and volume in real or complex geometry
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
Software:
Flyspeck; kepler98
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