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Author |
Fougerolle, Y.; Truchetet, F.; Gielis, J. |
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Title |
Potential fields of self intersecting Gielis curves for modeling and generalized blending techniques |
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P1 Proceeding |
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Year  |
2017 |
Publication |
Modeling In Mathematics |
Abbreviated Journal |
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Volume |
2 |
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Pages |
67-81
T2 - |
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Keywords |
P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
The definition of Gielis curves allows for the representation of self intersecting curves. The analysis and the understanding of these representations is of major interest for the analytical representation of sectors bounded by multiple subsets of curves (or surfaces), as this occurs for instance in many natural objects. We present a construction scheme based on R-functions to build signed potential fields with guaranteed differential properties, such that their zero-set corresponds to the outer, the inner envelop, or combined subparts of the curve. Our framework is designed to allow for the definition of composed domains built upon Boolean operations between several distinct objects or some subpart of self-intersecting curves, but also provides a representation for soft blending techniques in which the traditional Boolean union and intersection become special cases of linear combinations between the objects' potential fields. Finally, by establishing a connection between R-functions and Lame curves, we can extend the domain of the p parameter within the R-p-function from the set of the even positive numbers to the real numbers strictly greater than 1, i.e. p is an element of]1, +infinity[. |
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Wos |
000442076400006 |
Publication Date |
2017-04-20 |
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ISSN |
978-94-6239-261-8; 978-94-6239-260-1; 978-94-6239-260-1 |
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UA library record; WoS full record; WoS citing articles |
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Open Access |
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no |
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Call Number |
UA @ admin @ c:irua:153801 |
Serial |
8395 |
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Author |
Fougerolle, Y.D.; Truchetet, F.; Demonceaux, C.; Gielis, J. |
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Title |
A robust evolutionary algorithm for the recovery of rational Gielis curves |
Type |
A1 Journal article |
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Year |
2013 |
Publication |
Pattern recognition |
Abbreviated Journal |
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Volume |
46 |
Issue |
8 |
Pages |
2078-2091 |
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Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
Gielis curves (GC) can represent a wide range of shapes and patterns ranging from star shapes to symmetric and asymmetric polygons, and even self intersecting curves. Such patterns appear in natural objects or phenomena, such as flowers, crystals, pollen structures, animals, or even wave propagation. Gielis curves and surfaces are an extension of Lamé curves and surfaces (superquadrics) which have benefited in the last two decades of extensive researches to retrieve their parameters from various data types, such as range images, 2D and 3D point clouds, etc. Unfortunately, the most efficient techniques for superquadrics recovery, based on deterministic methods, cannot directly be adapted to Gielis curves. Indeed, the different nature of their parameters forbids the use of a unified gradient descent approach, which requires initial pre-processings, such as the symmetry detection, and a reliable pose and scale estimation. Furthermore, even the most recent algorithms in the literature remain extremely sensitive to initialization and often fall into local minima in the presence of large missing data. We present a simple evolutionary algorithm which overcomes most of these issues and unifies all of the required operations into a single though efficient approach. The key ideas in this paper are the replacement of the potential fields used for the cost function (closed form) by the shortest Euclidean distance (SED, iterative approach), the construction of cost functions which minimize the shortest distance as well as the curve length using R-functions, and slight modifications of the evolutionary operators. We show that the proposed cost function based on SED and R-function offers the best compromise in terms of accuracy, robustness to noise, and missing data. |
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000317944800002 |
Publication Date |
2013-01-29 |
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Edition |
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ISSN |
0031-3203 |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
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Times cited |
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Open Access |
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Call Number |
UA @ admin @ c:irua:107181 |
Serial |
8485 |
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