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hyperelliptic curve - translation to russian
ALGEBRAIC CURVE THAT IS A RAMIFIED DOUBLE COVER OF THE PROJECTIVE LINE
Hyper-elliptic curve; Hyperelliptic function
hyperelliptic curve
математика
гиперэллиптическая кривая
hyperelliptic function
математика
гиперэллиптическая функция
epidemic curve
A STATISTICAL CHART USED IN EPIDEMIOLOGY TO VISUALISE THE ONSET OF A DISEASE OUTBREAK.
Epi curve; Epidemiological curve
статистика
эпидемическая кривая
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)
Wikipedia
Hyperelliptic curve
In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the form
where f(x) is a polynomial of degree n = 2g + 1 > 4 or n = 2g + 2 > 4 with n distinct roots, and h(x) is a polynomial of degree < g + 2 (if the characteristic of the ground field is not 2, one can take h(x) = 0).A hyperelliptic function is an element of the function field of such a curve, or of the Jacobian variety on the curve; these two concepts are identical for elliptic functions, but different for hyperelliptic functions.
