A Unified Pythagorean Hodograph Approach to the Medial Axis Transform and Offset Approximation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F11%3A43898294" target="_blank" >RIV/49777513:23520/11:43898294 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.cam.2011.02.001" target="_blank" >http://dx.doi.org/10.1016/j.cam.2011.02.001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cam.2011.02.001" target="_blank" >10.1016/j.cam.2011.02.001</a>
Alternative languages
Result language
angličtina
Original language name
A Unified Pythagorean Hodograph Approach to the Medial Axis Transform and Offset Approximation
Original language description
Algorithms based on Pythagorean hodographs (PH) both in Euclidean plane and 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 Euclidean plane and 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. Based on this approach we design a new, simple interpolation algorithm. The main advantage of the presented unifying method lies in the fact that it uses, only after some simple additional computations, an arbitrary algorithm for interpolation by planar PH curves also for interpolation by spatial MPH curves. We present the functionality of our method on $G^1$ Hermite data, nevertheless one could obtain also higher order algorithms.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Computational and Applied Mathematics
ISSN
0377-0427
e-ISSN
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Volume of the periodical
235
Issue of the periodical within the volume
12
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
12
Pages from-to
3413-3424
UT code for WoS article
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EID of the result in the Scopus database
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