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 1 - 6 / 61 1.Construction of G[sup]3 rational motion of degree eightMarjetka Krajnc, Vito Vitrih, Karla Ferjančič, 2015, original scientific articleAbstract: The paper presents a construction of a rigid body motion with point trajectories being rational spline curves of degree eight joining together with ▫$G^3$▫ smoothness. The motion is determined through interpolation of positions and derivative data up to order three in the geometric sense. Nonlinearity in the spherical part of construction results in a single univariate quartic equation which yields solutions in a closed form. Sufficient conditions on the regions for the curvature data are derived, implying the existence of a real admissible solution. The algorithm how to choose appropriate data is proposed too. The theoretical results are substantiated with numerical examples.Found in: ključnih besedahSummary of found: ...design, geometric interpolation, rational spline motion, geometric continuity... Keywords: motion design, geometric interpolation, rational spline motion, geometric continuityPublished: 15.10.2015; Views: 1015; Downloads: 67 Full text (0,00 KB) 2.Isogeometric analysis with geometrically continuous functions on two-patch geometriesBert Jüttler, Vito Vitrih, Mario Kapl, Katharina Birner, 2015, original scientific articleAbstract: We study the linear space of Cs-smooth isogeometric functions defined on a multi-patch domain % % R2. We show that the construction of these functions is closely related to the concept of geometric continuity of surfaces, which has originated in geometric design. More precisely, the Cs-smoothness of isogeometric functions is found to be equivalent to geometric smoothness of the same order (Gs-smoothness) of their graph surfaces. This motivates us to call them Cs-smooth geometrically continuous isogeometric functions. We present a general framework to construct a basis and explore potential applications in isogeometric analysis. The space of C1-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains is analyzed in more detail. Numerical experiments with bicubic and biquartic functions for performing L2 approximation and for solving Poisson%s equation and the biharmonic equation on two-patch geometries are presented and indicate optimal rates of convergence.Found in: ključnih besedahSummary of found: ...closely related to the concept of geometric continuity of surfaces, which has originated in geometric... Keywords: izogeometrična analiza, geometrijska zveznost, geometrijsko vzezne izogeometrične funkcije, biharmonična enačba, isogeometric analysis, geometric continuity, geometrically continuous isogeometric functions, biharmonic equation, multi-patch domainPublished: 15.10.2015; Views: 1327; Downloads: 112 Full text (0,00 KB) 3.Hermite interpolation by rational G [sup] k motions of low degreeBert Jüttler, Marjetka Krajnc, Gašper Jaklič, Emil Žagar, Vito Vitrih, 2013, original scientific articleAbstract: Interpolation by rational spline motions is an important issue in robotics and related fields. In this paper a new approach to rational spline motion design is described by using techniques of geometric interpolation. This enables us to reduce the discrepancy in the number of degrees of freedom of the trajectory of the origin and of the rotational part of the motion. A general approach to geometric interpolation by rational spline motions is presented and two particularly important cases are analyzed, i.e., geometric continuous quartic rational motions and second order geometrically continuous rational spline motions of degree six. In both cases sufficient conditions on the given Hermite data are found which guarantee the uniqueness of the solution. If the given data do not fulfill the solvability conditions, a method to perturb them slightly is described. Numerical examples are presented which confirm the theoretical results and provide an evidence that the obtained motions have nice shapes.Found in: ključnih besedahSummary of found: ...design, geometric interpolation, rational spline motion, geometric continuity... Keywords: mathematics, numerical analysis, motion design, geometric interpolation, rational spline motion, geometric continuityPublished: 03.04.2017; Views: 749; Downloads: 7 Full text (0,00 KB) 4.Dimension and basis construction for C2-smooth isogeometric spline spaces over bilinear-like G2 two-patch parameterizationsMario Kapl, Vito Vitrih, 2018, original scientific articleFound in: ključnih besedahSummary of found: ...isogeometric analysis, geometric continuity, second order continuity, two-patch domain, bilinear-like... Keywords: isogeometric analysis, geometric continuity, second order continuity, two-patch domain, bilinear-likePublished: 15.01.2018; Views: 647; Downloads: 96 Full text (0,00 KB) 5.Solving the triharmonic equation over multi-patch planar domains using isogeometric analysisMario Kapl, Vito Vitrih, 2019, original scientific articleFound in: ključnih besedahSummary of found: ...isogeometric analysis, triharmonic equation, geometric continuity, multi-patch domain... Keywords: isogeometric analysis, triharmonic equation, geometric continuity, multi-patch domainPublished: 17.04.2019; Views: 321; Downloads: 102 Full text (0,00 KB) 6.Isogeometric collocation on planar multi-patch domainsMario Kapl, Vito Vitrih, 2020, original scientific articleFound in: ključnih besedahSummary of found: ...isogeometric analysis, collocation, superconvergent points, second order continuity, multi-patch domain, Poisson's equation... Keywords: isogeometric analysis, collocation, superconvergent points, second order continuity, multi-patch domain, Poisson's equationPublished: 11.02.2020; Views: 56; Downloads: 14 Full text (0,00 KB)
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