Paper Info
Title
A unified Pythagorean hodograph approach to the medial axis transform and offset approximation
Abstract
Algorithms based on Pythagorean hodographs (PH) in the Euclidean plane and in Minkowski space share common goals, the main one being rationality of offsets of planar domains. However, only separate interpolation techniques based on these curves can be found in the literature. It was recently revealed that rational PH curves in the Euclidean plane and in Minkowski space are very closely related. In this paper, we continue the discussion of the interplay between spatial MPH curves and their associated planar PH curves from the point of view of Hermite interpolation. On the basis of this approach we design a new, simple interpolation algorithm. The main advantage of the unifying method presented lies in the fact that it uses, after only some simple additional computations, an arbitrary algorithm for interpolation using planar PH curves also for interpolation using spatial MPH curves. We present the functionality of our method for G^1 Hermite data; however, one could also obtain higher order algorithms.
Year
DOI
Venue
2011
10.1016/j.cam.2011.02.001
J. Computational Applied Mathematics
Keywords
Field
DocType
planar ph,rational ph curve,medial axis,hermite data,associated planar ph curve,hermite interpolation,euclidean plane,simple interpolation algorithm,planar domain,spatial mph curve,separate interpolation technique,unified pythagorean hodograph approach,higher order,minkowski space
Nearest-neighbor interpolation,Mathematical optimization,Mathematical analysis,Interpolation,Medial axis,Euclidean space,Minkowski space,Euclidean geometry,Numerical analysis,Hermite interpolation,Mathematics
Journal
Volume
Issue
ISSN
235
12
0377-0427
Citations 
PageRank 
References 
5
0.42
34
Authors
2
Name
Order
Citations
PageRank
Jiří Kosinka1916.53
Miroslav LáVičKa215811.36