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1.
Construction of G[sup]3 rational motion of degree eight
Marjetka Krajnc, Vito Vitrih, Karla Ferjančič, 2015, original scientific article

Abstract: 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 besedah
Summary of found: ...data up to order three in the geometric sense. Nonlinearity in the spherical part of...
Keywords: motion design, geometric interpolation, rational spline motion, geometric continuity
Published: 15.10.2015; Views: 1014; Downloads: 67
URL Full text (0,00 KB)

2.
Isogeometric analysis with geometrically continuous functions on two-patch geometries
Bert Jüttler, Vito Vitrih, Mario Kapl, Katharina Birner, 2015, original scientific article

Abstract: 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 besedah
Summary of found: ...We study the linear space of Cs-smooth iso geometric functions defined on a multi-patch domain %... ...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 domain
Published: 15.10.2015; Views: 1324; Downloads: 112
URL Full text (0,00 KB)

3.
Hermite interpolation by rational G [sup] k motions of low degree
Bert Jüttler, Marjetka Krajnc, Gašper Jaklič, Emil Žagar, Vito Vitrih, 2013, original scientific article

Abstract: 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 besedah
Summary of found: ...design is described by using techniques of geometric interpolation. This enables us to reduce the...
Keywords: mathematics, numerical analysis, motion design, geometric interpolation, rational spline motion, geometric continuity
Published: 03.04.2017; Views: 749; Downloads: 7
URL Full text (0,00 KB)

4.
Dimension and basis construction for C2-smooth isogeometric spline spaces over bilinear-like G2 two-patch parameterizations
Mario Kapl, Vito Vitrih, 2018, original scientific article

Found in: ključnih besedah
Summary of found: ...iso geometric analysis, geometric continuity, second order continuity, two-patch...
Keywords: isogeometric analysis, geometric continuity, second order continuity, two-patch domain, bilinear-like
Published: 15.01.2018; Views: 645; Downloads: 96
URL Full text (0,00 KB)

5.
Solving the triharmonic equation over multi-patch planar domains using isogeometric analysis
Mario Kapl, Vito Vitrih, 2019, original scientific article

Found in: ključnih besedah
Summary of found: ...iso geometric analysis, triharmonic equation, geometric continuity, multi-patch domain...
Keywords: isogeometric analysis, triharmonic equation, geometric continuity, multi-patch domain
Published: 17.04.2019; Views: 321; Downloads: 102
URL Full text (0,00 KB)

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