Title




Potential fields of self intersecting Gielis curves for modeling and generalized blending techniques


Author






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 Rfunctions to build signed potential fields with guaranteed differential properties, such that their zeroset 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 selfintersecting 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 Rfunctions and Lame curves, we can extend the domain of the p parameter within the Rpfunction 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[. 


Language




English


Source (journal)




MODELING IN MATHEMATICS


Source (book)




2nd TbilisiSalerno Workshop on Modeling in Mathematics, MAR 1618, 2015, Tbilisi, GEORGIA


Publication




Paris
:
Atlantis press
,
2017


ISBN




9789462392601






9789462392618
9789462392601


DOI




10.2991/9789462392618_6


Volume/pages




2
(2017)
, p. 6781


ISI




000442076400006


Full text (Publisher's DOI)






Full text (publisher's version  intranet only)





