timetrans               package:qualV               R Documentation

_B_i_j_e_c_t_i_v_e _T_r_a_n_s_f_o_r_m_a_t_i_o_n_s _o_f _T_i_m_e

_D_e_s_c_r_i_p_t_i_o_n:

     Various function models for isoton bijective transformation of a
     time interval to itself.

_U_s_a_g_e:

     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))

_A_r_g_u_m_e_n_t_s:

       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 'timeTransME'. The chosen values are quite
          restrictive to avoid stupid extreme transformation.

    pmax: provides similar to 'pmin' the upper useful bounds for the
          parameters.

      p0: provides similar to 'pmin' and 'pmax' the parameterization
          for the identify transform.

_D_e_t_a_i_l_s:

'_t_r_a_n_s_B_e_t_a' 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.  

'_t_r_a_n_s_S_i_m_p_l_e_x' 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.

'_t_r_a_n_s_B_e_z_i_e_r' 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.    

_V_a_l_u_e:

     The value is a vector of the same length as 'x' providing the
     transformed values.

_S_e_e _A_l_s_o:

     'timeTransME'

_E_x_a_m_p_l_e_s:

     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")

