Rotation minimizing frames and quaternionic rectifying curves
نویسندگان
چکیده
منابع مشابه
Rotation-minimizing osculating frames
An orthonormal frame (f1, f2, f3) is rotation–minimizing with respect to fi if its angular velocity ω satisfies ω · fi ≡ 0 — or, equivalently, the derivatives of fj and fk are both parallel to fi. The Frenet frame (t,p,b) along a space curve is rotation–minimizing with respect to the principal normal p, and in recent years adapted frames that are rotation–minimizing with respect to the tangent ...
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An adapted orthonormal frame (f1, f2, f3) on a space curve r(t), where f1 = r ′/|r′| is the curve tangent, is rotation–minimizing if its angular velocity satisfies ω · f1 ≡ 0, i.e., the normal–plane vectors f2, f3 exhibit no instantaneous rotation about f1. The simplest space curves with rational rotation–minimizing frames (RRMF curves) form a subset of the quintic spatial Pythagorean–hodograph...
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An orthonormal frame (f1, f2, f3) is rotation–minimizing with respect to fi if its angular velocity ω satisfies ω · fi ≡ 0 or, equivalently, the derivatives of fj , fk are both parallel to fi. The Frenet frame (t,p,b) is rotation–minimizing with respect to the principal normal p, and in recent years adapted frames that are rotation–minimizing with respect to the tangent t have attracted much in...
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The existence of rational rotation–minimizing frames on polynomial space curves is characterized by the satisfaction of a certain identity among rational functions. Part 2 of Remark 5.1 in the original paper states an inequality among the degrees of the denominators of these rational functions, but the proof given therein was incomplete. A formal proof of this inequality, which is essential to ...
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We show that Möbius transformations preserve the rotationminimizing frames which are associated with space curves. In addition, these transformations are known to preserve the class of rational Pythagorean-hodograph curves and also rational frames. Based on these observations we derive an algorithm for G Hermite interpolation by rational Pythagorean-hodograph curves with rational rotation-minim...
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ژورنال
عنوان ژورنال: Annals of the Alexandru Ioan Cuza University - Mathematics
سال: 2021
ISSN: 2344-4967,1221-8421
DOI: 10.47743/anstim.2021.00003