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====Rational curves==== Rational curves are subdivided according to the [[Degree of a polynomial|degree]] of the po ...

...tudied cases are smooth plane curves (including [[piecewise]] smooth plane curves), and [[algebraic plane curve]]s. Plane curves also include the [[Jordan curve]]s (curves that enclose a region of the plane but need not be smooth) and the [[Graph ...

...C²]] function, smooth except for the existence of discontinuity curves.<ref name="s150">{{cite journal | last1=Kutyniok | first1=Gitta | last2=Lim ...

...he [[convex hull]] of its arc endpoints. However, it is possible for other curves of constant width to be made of an even number of arcs with varying radii.{ The Reuleaux polygons based on regular polygons are the only curves of constant width whose boundaries are formed by finitely many circular arc ...

[[Image:Dual curve.svg|thumb|right|300px|Curves, dual to each other; see below for [[#Properties of dual curve|properties]] ...metry: projective duality preserves symmetries a projective space, so dual curves have the same symmetry group. In this case both symmetries are realized as ...

[[Category:Piecewise-circular curves]] ...

...e [[plane (mathematics)|2-dimensional plane]] are sometimes called ''Peano curves'', but that phrase also refers to the [[Peano curve]], the specific example ...s''' (approximately space-Filling, self-Avoiding, Simple, and Self-similar curves) ...

...f>{{Cite journal |last=Hofer |first=H. |date=1993 |title=Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimens ...urnal |jstor=2032372 |last1=Seifert |first1=Herbert |title=Closed Integral Curves in 3-Space and Isotopic Two-Dimensional Deformations |journal=Proceedings o ...

...algorithm can also be used to split a single Bézier curve into two Bézier curves at an arbitrary parameter value. ...le=A comprehensive comparison of algorithms for evaluating rational Bézier curves |url=https://drna.padovauniversitypress.it/2024/3/9 |journal=Dolomites Rese ...

...crossings of an [[arrangement of lines]], as the [[involute]]s of certain curves, or by intersecting circles centered on a partial curve. ...of constant width can always be approximated arbitrarily closely by smooth curves of the same constant width. ...

File:Hilbert curve 2.svg|Hilbert curves, first and second orders File:Hilbert curve 3.svg|Hilbert curves, first to third orders ...

...bly more involved than the definition of [[arc length]] of one-dimensional curves, or of the surface area for [[polyhedra]] (i.e., objects with flat polygona ....]]One of the subtleties of surface area, as compared to [[arc length]] of curves, is that surface area cannot be defined simply as the limit of areas of pol ...

[[Category:Piecewise-circular curves]] ...

...s, it has the advantage of easy visualization. By plotting the ''I''-''V'' curves, it is possible to obtain an approximate solution to any arbitrary degree o ...rent-voltage equations on a graph and the point of intersection of the two curves satisfies both equations, giving the value of the current flowing through t ...

...nomial ([[Parametric equation|parametric]]) [[curve]]. Splines are popular curves in these subfields because of the simplicity of their construction, their e ...obachevsky]] at [[Kazan University]] in Russia.<ref>Farin, G. E. (2002). ''Curves and surfaces for CAGD: a practical guide''. Morgan Kaufmann. p. 119.</ref> ...

...ing number of a curve may be any [[integer]]. The following pictures show curves with winding numbers between &minus;2 and 3: ...ite book |first=Manfredo P. |last=Do Carmo |title=Differential Geometry of Curves and Surfaces |year=1976 |publisher=Prentice-Hall |isbn=0-13-212589-7 |chapt ...

...imilar ideas at [[Kazan University]] in Russia,<ref>Farin, G. E. (2002). ''Curves and surfaces for CAGD: a practical guide''. Morgan Kaufmann. p. 119.</ref> ...sum of B-splines with control points/control polygon, and marked component curves]] ...

{{Short description|Method of representing curves and surfaces in computer graphics}} ...ng]], as opposed to [[polygonal modeling]] or [[digital sculpting]]. NURBS curves are commonly used in [[computer-aided design]] (CAD), [[Computer-aided manu ...

A Heegaard splitting is '''stabilized''' if there are essential simple closed curves <math>\alpha</math> and <math>\beta</math> on ''H'' where <math>\alpha</mat ...ng is '''weakly reducible''' if there are disjoint essential simple closed curves <math>\alpha</math> and <math>\beta</math> on ''H'' where <math>\alpha</mat ...