timetrans | R Documentation |
Various function models for isoton bijective transformation of a time interval to itself.
transBeta(x, p, interval = c(0, 1), inv = FALSE,
pmin = -3, pmax = 3, p0 = c(0, 0))
transSimplex(x, p, interval = c(0, 1), inv = FALSE,
pmin = -2, pmax = 2, p0 = c(0, 0, 0, 0, 0))
transBezier(x, p, interval = c(0, 1), inv = FALSE,
pmin = 0, pmax = 1, p0 = c(0.25, 0.25, 0.75, 0.75))
x |
a vector of values to be transformed, |
p |
the vector of parameters for the transformation, |
interval |
a vector of length 2 giving the minimum and maximum value in the transformation interval. |
inv |
a boolean, if true the inverse transform is computed. |
pmin |
a number or a vector giving the minimal useful value for
the parameters. This information is not used by the function itself,
but rather provides a meta information about the function used in
|
pmax |
provides similar to |
p0 |
provides similar to |
transBeta
The transformation provided is the distribution function of the
Beta-Distribution with parameters exp(p[1])
and
exp(p[2])
scaled to the given interval. This function is
guaranteed to be strictly isotonic for every choice of p. p has
length 2. The strength of the Beta transformation is the reasonable
behavior for strong time deformations.
transSimplex
The transformation provided a simple linear interpolation. The interval is separated into equidistant time spans, which are transformed to non-equidistant length. The length of the new time spans is the proportional to exp(c(p, 0)). This function is guaranteed to be strictly isotonic for every choice of p. p can have any length. The strength of the Simplex transformation is the possibility to have totally different speeds at different times.
transBezier
The transformation is provided by a Bezier-Curve of order
length(p) / 2 + 1
. The first and last control point are given by
c(0, 0)
and c(1, 1)
and the intermediate control points
are given by p[c(1, 2) + 2 * i - 2]
. This function is not guaranteed
to be isotonic for length(p) > 4
. However it seams useful. A
major theoretical advantage is that this model is symmetric between
image and coimage. The strength of the Bezier transformation is fine
tuning of transformation.
The value is a vector of the same length as x
providing the
transformed values.
timeTransME
t <- seq(0, 1, length.out = 101)
par(mfrow = c(3, 3))
plot(t, transBeta(t, c(0, 0)), type = "l")
plot(t, transBeta(t, c(0, 1)), type = "l")
plot(t, transBeta(t, c(-1,1)), type = "l")
plot(t, transSimplex(t, c(0)), type = "l")
plot(t, transSimplex(t, c(3, 2, 1)), type = "l")
plot(t, transSimplex(t, c(0, 2)), type = "l")
plot(t, transBezier(t, c(0, 1)), type = "l")
plot(t, transBezier(t, c(0, 1, 1, 0)), type = "l")
plot(t, transBezier(t, c(0.4, 0.6)), type = "l")
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