A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames
نویسندگان
چکیده
منابع مشابه
Quintic space curves with rational rotation-minimizing frames
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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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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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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This article is devoted to the rotation minimizing frames that are associated with spatial curves. Firstly we summarize some results concerning the differential geometry of the sweeping surfaces which are generated by these frames (the so–called profile or moulding surfaces). In the second part of the article we describe a rational approximation scheme. This scheme is based on the use of spatia...
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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 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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ژورنال
عنوان ژورنال: Advances in Computational Mathematics
سال: 2016
ISSN: 1019-7168,1572-9044
DOI: 10.1007/s10444-016-9473-0