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rectifiable curve - translation to russian

PROPERTY OF A CURVE

Rectifiable curve; Rectifiable path; Arclength; Length of a curve; Curve length; ArcLen; Length of an arc; Length of arc; Chord distance; Length of a function; Non-rectifiable curve; Curvilinear length; Infinite length; Chordal distance; Circular arc length; Length (mathematics); Curve rectification; Signed arc length; Signed length

rectifiable curve

математика

спрямляемая кривая

infinite length

математика

бесконечная длина

rectifiable path

математика

спрямляемая траектория

Definition

Bezier curve

<graphics> A type of curve defined by mathematical formulae, used in computer graphics. A curve with coordinates P(u), where u varies from 0 at one end of the curve to 1 at the other, is defined by a set of n+1 "control points" (X(i), Y(i), Z(i)) for i = 0 to n. P(u) = Sum i=0..n [(X(i), Y(i), Z(i)) * B(i, n, u)] B(i, n, u) = C(n, i) * u^i * (1-u)^(n-i) C(n, i) = n!/i!/(n-i)! A Bezier curve (or surface) is defined by its control points, which makes it invariant under any affine mapping (translation, rotation, parallel projection), and thus even under a change in the axis system. You need only to transform the control points and then compute the new curve. The control polygon defined by the points is itself affine invariant. Bezier curves also have the variation-diminishing property. This makes them easier to split compared to other types of curve such as Hermite or B-spline. Other important properties are multiple values, global and local control, versatility, and order of continuity. [What do these properties mean?] (1996-06-12)

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Wikipedia

Arc length

Arc length is the distance between two points along a section of a curve.

Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification. A rectifiable curve has a finite number of segments in its rectification (so the curve has a finite length).

If a curve can be parameterized as an injective and continuously differentiable function (i.e., the derivative is a continuous function) $f\colon [a,b]\to \mathbb {R} ^{n}$ , then the curve is rectifiable (i.e., it has a finite length).

The advent of infinitesimal calculus led to a general formula that provides closed-form solutions in some cases.

https://en.wikipedia.org/wiki/Arc length

What is the Russian for rectifiable curve? Translation of &#39rectifiable curve&#39 to Russian