Title: Triangular PN patches subject to surface-area constraints
Authors: Bizzarri, Michal
Lávička, Miroslav
Citation: BIZZARRI, M., LÁVIČKA, M. Triangular PN patches subject to surface-area constraints. Proceedings of the 17th International Conference on Mathematical Methods in Science and Engineering. Costa Ballena, Rota, Cádiz (Spain): CMMSE, 2017. s. 333-341. ISBN 978-84-617-8694-7.
Issue Date: 2017
Publisher: CMMSE
Document type: konferenční příspěvek
conferenceObject
URI: http://hdl.handle.net/11025/29273
ISBN: 978-84-617-8694-7
Keywords: $G^1$ Hermiteova interpolace;PN povrchy;prvek polynomiální oblasti
Keywords in different language: $G^1$ Hermite interpolation;PN surfaces;polynomial area element
Abstract in different language: This paper is devoted to the construction of polynomial surfaces with Pythagorean normals (PN surfaces) interpolating given data subject to prescribed constraints on the surface area of the patch. This is a problem analogous to the interpolation with Pythagorean hodograph (PH) curves satisfying the condition on the arc length. The special structure of PN surfaces allows the surface-area condition to be expressed as algebraic constraints on the surfaces coefficients. We employ these shapes for solving the $G^1$ Hermite interpolation problem by triangular PN patches with prescribed surface area. The presented technique is based on interpolating points on the unit sphere and consequently on solving a system of several linear and one quadratic equations. We show that for generic input data there exist at most two quartic PN patches depending on the particular value of the prescribed surface area.
Rights: Plný text není přístupný.
© CMMSE
Appears in Collections:OBD
Konferenční příspěvky / Conference Papers (KMA)

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