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If a pair of curves are in different positions but have the same curvature and torsion, then they are
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of the tangent field (done numerically, if not analytically) yields the curve.
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Regular 3-D curves are shape and size determined by their curvature and torsion
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for the tangent, normal, and binormal vectors can be derived using the
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Analysis: Differential Forms in Analysis, Geometry, and Physics
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A curve can be described, and thereby defined, by a pair of
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of the curve. From just the curvature and torsion, the
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31:in three-dimensional space, with non-zero
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103:the curve but which can ideally be the
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141:Differential geometry of curves
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27:states that every regular
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72:{\displaystyle \kappa }
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262:Theorems about curves
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92:{\displaystyle \tau }
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256:Categories
152:References
123:Congruence
105:arc length
35:, has its
129:congruent
115:. Then,
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67:κ
33:curvature
233:(1976).
135:See also
45:torsion
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23:, the
41:scale
37:shape
29:curve
239:ISBN
207:ISBN
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51:Use
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