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loxodromic curve - translation to russian
WIKIMEDIA DISAMBIGUATION PAGE
Loxodromic (disambiguation)
loxodromic curve
общая лексика
локсодромия
loxodromic curve
локсодромия
loxodromic
общая лексика
локсодромический
локсодромный
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
Loxodromic
Loxodromic may refer to:
- a loxodrome, see rhumb line
- a loxodromic transform, see Möbius transformation#Loxodromic transforms
- Loxodromic navigation, a method of navigation by following a rhumb line
