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S curve - translation to English
S curve
WIKIMEDIA DISAMBIGUATION PAGE
‘S’-curve shape; S curve; S-Curve; S-curve; 'S'-curve shape; S Curve (disambiguation); S shape
مُنْحَنَى S,مُنْحَنَى سينِيّ
S-curve
WIKIMEDIA DISAMBIGUATION PAGE
‘S’-curve shape; S curve; S-Curve; S-curve; 'S'-curve shape; S Curve (disambiguation); S shape
مُنْحَنَى S
sigmoid curve
![Plot of the [[error function]]](https://commons.wikimedia.org/wiki/Special:FilePath/Error Function.svg?width=200 "Plot of the [[error function]]")
.svg?width=200 "Some sigmoid functions compared. In the drawing all functions are normalized in such a way that their slope at the origin is 1.")
MATHEMATICAL FUNCTION HAVING A CHARACTERISTIC "S"-SHAPED CURVE OR SIGMOID CURVE
Sigmoid curve; Sigmoidal curve; Double sigmoid; S-shape curve; Double sigmoid curve; Sigmoids; S-shaped curve; Squashing function; S-curve (math); Sigmoid shaped; Sigmoid shape; S-shaped; Sigmoid-shape; Sigmoid-shaped; Sigmoidal function
مُنْحَنَى سينِيّ
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)
Examples of use of S curve
1. Before nightfall, the wall of smoke extended an estimated 2,000 feet into the air and bent in a giant S–curve, blanketing the capital skyline.
2. This preserves the natural S curve of the spine." Up to 80 per cent of people in Britain suffer back pain at some point.
3. He stood, thin and tall, his body in an S–curve with his hands on his hips and with lips set in a permanent purple sneer as he examined the man before him.
4. Against this the effective increase allowed by the Government in response to OGRA’s recommendation was only '.5% for Domestic customers in the lowest slab, using up to 100 units and 22.2% for other domestic, commercial and industrial customers (excluding fertilizer plants using gas for feed stock). This relatively smaller increase is due to the S–curve pricing formula which the New Gas/Petroleum Policy 2001 incorporated as a prudent measure for the benefit of the vast majority of citizens of Pakistan that continues to get gas supplies at a rate considerably lower than in most countries.