Paper Info
Title
As-Perpendicular-as-possible surfaces for flow visualization
Abstract
We define APAP surfaces, surfaces that are as perpendicular as possible to steady 3D vector fields, and present a method to construct discrete representations of them. Since, in general, a perfectly perpendicular surface to a vector field does not exist, we propose and minimize an error metric to enforce perpendicularity as much as possible. Our algorithm constructs an APAP surface by deforming a seed surface anchored in a domain point. In the discrete setting this minimization results in iteratively solving linear least-squares problems and integrating a locally scaled version of the vector field. The definition of the error metric and its numerical minimization guarantee that the minimum zero is attained for the perfectly perpendicular surface if it exists. Otherwise, the minimization converges to the same local minimum independent of the seed configuration, and the resulting surface is - in a least-squares sense - as perpendicular as possible to the flow. We apply these APAP surfaces as an interactive flow visualization tool which we demonstrate on a number of synthetic and real flow data sets.
Year
DOI
Venue
2012
10.1109/PacificVis.2012.6183586
PacificVis
Keywords
Field
DocType
numerical minimization guarantee,resulting surface,seed surface,real flow data set,as-perpendicular-as-possible surface,perpendicular surface,minimization result,interactive flow visualization tool,apap surface,minimization converges,vector field,flow visualization,least square,data visualisation,minimisation,iterative methods
Euclidean vector,Perpendicular,Vector field,Mathematical analysis,Iterative method,Flow (psychology),Minimisation (psychology),Minification,Geometry,Flow visualization,Mathematics
Conference
ISSN
Citations 
PageRank 
2165-8765
2
0.37
References 
Authors
27
4
Name
Order
Citations
PageRank
Maik Schulze1443.84
Christian Rossl2523.13
Tobias Germer31478.02
Holger Theisel4147999.18