Bicolored Order Types
Abstract: In their seminal work on Multidimensional Sorting, Goodman and Pollack introduced the so-called order type, which for each ordered triple of a point set in the plane gives its orientation, clockwise or counterclockwise. This information is sufficient to solve many problems from discrete geometry where properties of point sets do not depend on the exact coordinates of the points but only on their relative positions. Goodman and Pollack showed that an efficient way to store an order type in a matrix λ of quadratic size (w.r.t. the number of points) is to count for every oriented line spanned by two points of the set how many of the remaining points lie to the left of this line. We generalize the concept of order types to bicolored point sets (every point has one of two colors). The bicolored order type contains the orientation of each bicolored triple of points, while no information is stored for monochromatic triples. Similar to the uncolored case, we store the number of blue points.... https://www.cgt-journal.org/index.php/cgt/article/view/46
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Erschienen in
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Bicolored Order Types ; volume:3 ; number:2 ; year:2024
Computing in Geometry and Topology ; 3, Heft 2 (2024)
- Urheber
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Aichholzer, Oswin
Brötzner, Anna
- DOI
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10.57717/cgt.v3i2.46
- URN
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urn:nbn:de:101:1-2024030306541463052540
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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14.08.2025, 11:02 MESZ
Datenpartner
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Aichholzer, Oswin
- Brötzner, Anna
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