Titlebook: General Theory of Irregular Curves; A. D. Alexandrov,Yu. G. Reshetnyak Book 1989 Kluwer Academic Publishers 1989 convergence.differentiabl

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Shinji Doi,Junko Inoue,Kunichika Tsumoto deal with regular curves. For instance, a plane curve . = . is regular, and analytical, too. At the same time, viewing it as a spatial curve, we see that the differential-geometrical theory of spatial curves cannot be applied to the curve in question, since at the point . = 0 the first two derivates of the radius-vector of the curve turn to zero.

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,Ergänzende numerische Verfahren,to the arc length will be stated below. There is another possible way of constructing the theory of a curve turn, when the notion of a turn is defined by way of approximating an arbitrary curve by regular curves.

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Introduction, deal with regular curves. For instance, a plane curve . = . is regular, and analytical, too. At the same time, viewing it as a spatial curve, we see that the differential-geometrical theory of spatial curves cannot be applied to the curve in question, since at the point . = 0 the first two derivates of the radius-vector of the curve turn to zero.

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Turn or Integral Curvature of a Curve,to the arc length will be stated below. There is another possible way of constructing the theory of a curve turn, when the notion of a turn is defined by way of approximating an arbitrary curve by regular curves.

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Frenet Formulas and Theorems on Natural Parametrization,dicatrix of the curve ., regular if in any segment [α, .] of the values of the parameter . which correspond to an angular point of the curve, к.(.) is as follow: к.(.) = λ(. − .) + к.(α). It is obvious that a complete one-dimensional indicatrix allows a regular parametrization.

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