rectifiable curve - определение. Что такое rectifiable curve
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Что (кто) такое rectifiable curve - определение

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
  • Fermat's method of determining arc length
  • When rectified, the curve gives a straight line segment with the same length as the curve's arc length.
  • Approximation to a curve by multiple linear segments, called rectification of a curve.
  • The Koch curve.
  • Arc length ''s'' of a [[logarithmic spiral]] as a function of its parameter ''θ''.
  • Quarter circle

Epidemic curve         
  • Common source outbreak of Hepatitis A in Nov-Dec 1978
A STATISTICAL CHART USED IN EPIDEMIOLOGY TO VISUALISE THE ONSET OF A DISEASE OUTBREAK.
Epi curve; Epidemiological curve
An epidemic curve, also known as an epi curve or epidemiological curve, is a statistical chart used in epidemiology to visualise the onset of a disease outbreak. It can help with the identification of the mode of transmission of the disease.
Bezier curve         
  • Animation of the construction of a fifth-order Bézier curve
  • cyan: ''y'' {{=}} ''t''<sup>3</sup>}}.
  • Abstract composition of cubic Bézier curves ray-traced in 3D. Ray intersection with swept volumes along curves is calculated with Phantom Ray-Hair Intersector algorithm.<ref>Alexander Reshetov and David Luebke, Phantom Ray-Hair Intersector. In Proceedings of the ACM on Computer Graphics and Interactive Techniques (August 1, 2018). [https://research.nvidia.com/publication/2018-08_Phantom-Ray-Hair-Intersector]</ref>
  • Animation of a linear Bézier curve, ''t'' in [0,1
  • Animation of a quadratic Bézier curve, ''t'' in [0,1
  • Construction of a quadratic Bézier curve
  • Animation of a cubic Bézier curve, ''t'' in [0,1
  • Construction of a cubic Bézier curve
  • Animation of a quartic Bézier curve, ''t'' in [0,1
  • Construction of a quartic Bézier curve
  • Quadratic Béziers in [[string art]]: The end points ('''&bull;''') and control point ('''&times;''') define the quadratic Bézier curve ('''⋯''').
CURVE USED IN COMPUTER GRAPHICS AND RELATED FIELDS
Bezier curve; Bezier curves; Bézier Curve; Bernstein-Bézier curve; Bernstein-Bezier curve; Besier curve; Bezier cubic; Bézier cubic; Bezier splines; Bezier Curve; Cubic bezier; Conic Bezier curve; Conic Bézier curve; Bezier path; Cubic bézier curve; Cubic Bézier 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)
Blancmange curve         
FRACTAL WHICH IS CONSIDERED TO RESEMBLE A BLANCMANGE
Blancmange function; Takagi curve; Takagi-Landsberg curve; Midpoint displacement; Takagi fractal curve; Takagi function; Takagi’s function; Takagi Fractal Curve
In mathematics, the blancmange curve is a self-affine curve constructible by midpoint subdivision. It is also known as the Takagi curve, after Teiji Takagi who described it in 1901, or as the Takagi–Landsberg curve, a generalization of the curve named after Takagi and Georg Landsberg.

Википедия

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 : [ a , b ] R n {\displaystyle 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.