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1.
Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
Marjetka Krajnc, Vito Vitrih, 2012, izvirni znanstveni članek

Opis: The paper presents an interpolation scheme for ▫$G^{1}$▫ Hermite motion data, i.e., interpolation of data points and rotations at the points, with spatial quintic Pythagorean-hodograph curves so that the Euler-Rodrigues frame of the curve coincides with the rotations at the points. The interpolant is expressed in a closed form with three free parameters, which are computed based on minimizing the rotations of the normal plane vectors around the tangent and on controlling the length of the curve. The proposed choice of parameters is supported with the asymptotic analysis. The approximation error is of order four and the Euler-Rodrigues frame differs from the ideal rotation minimizing frame with the order three. The scheme is used for rigid body motions and swept surface construction.
Najdeno v: osebi
Ključne besede: Pythagorean-hodograph, Euler-Rodrigues frame, rotation minimizing frame, motion design, quaternion, Hermite interpolation
Objavljeno: 15.10.2013; Ogledov: 1161; Prenosov: 58
URL Polno besedilo (0,00 KB)

2.
Geometric interpolation by spatial cubic rational curves
Vito Vitrih, 2012, predavanje na tuji univerzi

Najdeno v: osebi
Objavljeno: 15.10.2013; Ogledov: 1298; Prenosov: 15
URL Polno besedilo (0,00 KB)

3.
Hermite interpolation by rational Gk motions of low degree
Vito Vitrih, 2012, predavanje na tuji univerzi

Najdeno v: osebi
Objavljeno: 15.10.2013; Ogledov: 1342; Prenosov: 10
URL Polno besedilo (0,00 KB)

4.
Lattices on tetrahedral partitions
Vito Vitrih, 2008, objavljeni znanstveni prispevek na konferenci

Opis: In this paper, four-pencil lattices on tetrahedral partitions are studied. Theexplicit representation of a lattice, based upon barycentric coordinates, enables us to extend the lattice from a single tetrahedron to a tetrahedral partition. It is shown that the number of degrees of freedom is equal to the number of vertices of the tetrahedral partition. The proof is based on a lattice split approach.
Najdeno v: osebi
Ključne besede: mreža, tetraeder, interpolacija
Objavljeno: 15.10.2013; Ogledov: 1633; Prenosov: 71
URL Polno besedilo (0,00 KB)

5.
Racionalne Bézierove krivulje
Vesna Volaš, 2013, diplomsko delo

Najdeno v: osebi
Ključne besede: racionalne Bézierove krivulje, polinomske Bézierove krivulje, de Casteljauev algoritem, Octave, magnetni disk
Objavljeno: 10.07.2015; Ogledov: 1756; Prenosov: 9
URL Polno besedilo (0,00 KB)

6.
Baricentrične koordinate nad večkotniki
Kaja Ferjančič, 2014, diplomsko delo

Najdeno v: osebi
Ključne besede: baricentrične koordinate, Wachspressove koordinate, koordinate povprečne vrednosti
Objavljeno: 10.07.2015; Ogledov: 2244; Prenosov: 31
URL Polno besedilo (0,00 KB)

7.
Bézierove in Gordon-Coons krpe
Irena Čavdek, 2014, diplomsko delo

Najdeno v: osebi
Ključne besede: Bézier, Gordon-Coons, krpa, krivulja, CAGD
Objavljeno: 10.07.2015; Ogledov: 2077; Prenosov: 21
URL Polno besedilo (0,00 KB)

8.
Osnove numeričnega računanja
Vito Vitrih, 2015, drugo učno gradivo

Najdeno v: osebi
Ključne besede: numerično računanje, reševanje sistemov linearnih in nelinearnih enačb, interpolacija, numerično odvajanje in integriranje, Bezierove krivulje
Objavljeno: 15.10.2015; Ogledov: 1542; Prenosov: 51
URL Polno besedilo (0,00 KB)
Gradivo ima več datotek! Več...

9.
Construction of G[sup]3 rational motion of degree eight
Marjetka Krajnc, Vito Vitrih, Karla Ferjančič, 2015, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: motion design, geometric interpolation, rational spline motion, geometric continuity
Objavljeno: 15.10.2015; Ogledov: 961; Prenosov: 65
URL Polno besedilo (0,00 KB)

10.
Parametric curves with Pythagorean binormals
Marjetka Krajnc, Vito Vitrih, Jernej Kozak, 2015, izvirni znanstveni članek

Opis: In this paper, a class of rational spatial curves that have a rational binormal is introduced . Such curves (called PB curves) play an important role in the derivation of rational rotation-minimizing osculating frames. The PB curve construction proposed is based upon the dual curve representation and the Euler-Rodrigues frame obtained from quaternion polynomials. The construction significantly simplifies if the curve is a polynomial one. Further, polynomial PB curves of the degree % 7 and rational PB curves of the degree % 6 that possess rational rotation-minimizing osculating frames are derived, and it is shown that no lower degree curves, constructed from quadratic quaternion polynomials, with such a property exist.
Najdeno v: osebi
Ključne besede: pitagorejski hodograf, pitagorejska binormala, racionalna krivulja, dualne koordinate, rotacijsko minimizirajoče ogrodje, pitagorejska binormala, racionalna krivulja, dualne koordinate, rotacijsko minimizirajoče ogrodje, Pythagorean-hodograph, Pythagorean-binormal, rational curve, dual coordinates, rotation-minimizing frame, osculating frame
Objavljeno: 15.10.2015; Ogledov: 1145; Prenosov: 64
URL Polno besedilo (0,00 KB)

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