TY - GEN
T1 - Geometry-preserving topological landscapes
AU - Beketayev, Kenes
AU - Weber, Gunther H.
AU - Morozov, Dmitriy
AU - Abzhanov, Aidos
AU - Hamann, Bernd
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2012
Y1 - 2012
N2 - We propose a novel technique for building geometry-preserving topological landscapes. Our technique creates a direct correlation between a scalar function and its topological landscape. This correlation is accomplished by introducing the notion of geometric proximity into the topological landscapes, reflecting the distance of topological features within the function domain. Furthermore, this technique enables direct comparative analysis between scalar functions, as long as they are defined on the same domain. We describe a construction technique that consists of three stages: contour tree computation, contour tree layout, and landscape construction. We provide a detailed description for the latter two steps. For the contour tree layout stage, we discuss dimension reduction and edge routing techniques that produce a drawing of the contour tree on the plane that preserves the geometric proximity. For the landscape construction stage, we develop a contour construction algorithm that takes the contour tree layout as an input, adds contours at heights that correspond to saddles of the contour tree, and produces a contour map. After an additional triangulation step, this construction method results in the landscape that has the same contour tree as the original function.
AB - We propose a novel technique for building geometry-preserving topological landscapes. Our technique creates a direct correlation between a scalar function and its topological landscape. This correlation is accomplished by introducing the notion of geometric proximity into the topological landscapes, reflecting the distance of topological features within the function domain. Furthermore, this technique enables direct comparative analysis between scalar functions, as long as they are defined on the same domain. We describe a construction technique that consists of three stages: contour tree computation, contour tree layout, and landscape construction. We provide a detailed description for the latter two steps. For the contour tree layout stage, we discuss dimension reduction and edge routing techniques that produce a drawing of the contour tree on the plane that preserves the geometric proximity. For the landscape construction stage, we develop a contour construction algorithm that takes the contour tree layout as an input, adds contours at heights that correspond to saddles of the contour tree, and produces a contour map. After an additional triangulation step, this construction method results in the landscape that has the same contour tree as the original function.
KW - multidimensional scaling
KW - scalar field topology
KW - topological landscapes
KW - visual metaphor
UR - http://www.scopus.com/inward/record.url?scp=84872843356&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84872843356&partnerID=8YFLogxK
U2 - 10.1145/2425296.2425324
DO - 10.1145/2425296.2425324
M3 - Conference contribution
AN - SCOPUS:84872843356
SN - 9781450318358
T3 - Proceedings - WASA 2012: Workshop at SIGGRAPH Asia 2012
SP - 155
EP - 160
BT - Proceedings - WASA 2012
T2 - Workshop at SIGGRAPH Asia 2012, WASA 2012
Y2 - 26 November 2012 through 27 November 2012
ER -