A convex curve (black) forms a connected subset of the boundary of a convex set (blue), and has a supporting line (red) through each of its points.A parabola, a convex curve that is the graph of the convex function
In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going back to Archimedes. Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex curves include the closed convex curves (the boundaries of bounded convex sets), the smooth curves that are convex, and the strictly convex curves, which have the additional property that each supporting line passes through a unique point of the curve.
Bounded convex curves have a well-defined length, which can be obtained by approximating them with polygons, or from the average length of their projections onto a line. The maximum number of grid points that can belong to a single curve is controlled by its length. The points at which a convex curve has a unique supporting line are dense within the curve, and the distance of these lines from the origin defines a continuous support function. A smooth simple closed curve is convex if and only if its curvature has a consistent sign, which happens if and only if its total curvature equals its total absolute curvature.
a convexcurve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going...
In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...
triangle is strictly convex. Convexcurve – Type of plane curve Concave polygon – Simple polygon which is not convexConvex polytope – Convex hull of a finite...
is always a convexcurve. The intersection of all the convex sets that contain a given subset A of Euclidean space is called the convex hull of A. It...
nonnegative matrix is a convex function of its diagonal elements. Concave function Convex analysis Convex conjugate ConvexcurveConvex optimization Geodesic...
or by intersecting circles centered on a partial curve. Every body of constant width is a convex set, its boundary crossed at most twice by any line...
a sequence of points is convex, concave, or flat: Differential geometry of curves Directed line segment Orientability Convex hull Signed arc length Abraham...
Since they lie on a parabola, which is a convexcurve, it is easy to see that the vertices of the convex hull, when traversed along the boundary, produce...
life table. There are three generalized types of survivorship curves: Type I or convexcurves are characterized by high age-specific survival probability...
indifference curve, that is the magnitude of the slope is decreasing or becoming less steep, then the preference is convex. The theory of indifference curves was...
The curve of Wilson is the across arch curvature or posterior occlusal plane. Arc of the curve, which is concave for mandibular teeth and convex for maxillary...
A curved mirror is a mirror with a curved reflecting surface. The surface may be either convex (bulging outward) or concave (recessed inward). Most curved...
Entasis is the architectural term for applying a convexcurve to a surface for aesthetic purposes, or increasing strength. Its best-known use is in certain...
but 1/2. Since a convexcurve intersects almost every line either twice or not at all, the unoriented Crofton formula for convexcurves can be stated without...
scimitar (/ˈsɪmɪtər/ or /ˈsɪmɪtɑːr/) is a single-edged sword with a convexcurved blade associated with Middle Eastern, South Asian, or North African...
needed] curves or arcs that, as a result of a point of inflection from concave to convex or vice versa,: 218 have ends of the overall curve that point...
similarity transformations of the curve, and that can be used to measure how far the curve is from being a convexcurve. If the curve is parameterized by its arc...
smooth, convexcurve the angle of the tangent line changes monotonically, and the resulting dual curve is also smooth and convex. Further, both curves above...
It is a form of back for an automobile body consisting of a single convexcurve from the top to the rear bumper. This automotive design element "relates...
are sometimes illustrated graphically with a Beveridge curve, a downward-sloping, convexcurve that shows a fixed relationship between the unemployment...
of each of its supporting lines. The interior of a closed convexcurve is a convex set. Convex function - a function in which the line segment between any...
the curve, and can be computed as the total curvature divided by 2π. In polygons, the turning number is referred to as the polygon density. For convex polygons...
continuously down at the back. The design features a single unbroken convexcurve from the roof to the rear. Flower car In the US used in the funeral industry...
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