HAVSIN

Given a specific $x$ value, the Havsin function evaluates the $y$ value of a Haversine function that smoothly transitions from $(x_{0}, y_{0})$ to $(x_{1}, y_{1})$ .

Format

$Havsin (x, x_{0}, y_{0}, x_{1}, y_{1})$

Arguments

$x$: The independent variable. For example, to specify time as the independent variable, specify $x$ as TIME.
$x_{0}$: The $x$ value at which the Haversine function begins.
$y_{0}$: The value of the Haversine function desired at $x_{0}$ .
$x_{1}$: The $x$ value at which the Haversine function ends.
$y_{1}$: The value of the Haversine function desired at $x_{1}$ .

Definition

(1)

\begin{array}{l} havsin = {\begin{cases} y_{0}, if x < x_{0} \\ \bar{y} + \frac{Δ y}{2} \sin (\tilde{x} π - \frac{π}{2}), if x_{0} \leq x \leq x_{1} \\ y_{1}, if x > x_{1} \end{cases} \\ where, \\ \bar{y} = \frac{(y_{0} + y_{1})}{2} \\ Δ y = (y_{1} - y_{0}) \\ \tilde{x} = \frac{(x - x_{0})}{(x_{1} - x_{0})} \end{array}

Example

<Post_Request
     comment             = "WM-WDTM-HAVSIN-FORSIN-DIM-ACOS"
     id                  = "3"
     type                = "EXPRESSION"
     expr1               = "NULL"
     expr2               = "WM(30102010)"
     expr3               = "WDTM(30102010)"
     expr4               = "HAVSIN(TIME,1.,0.,4.,1.)"
     expr5               = "NULL"
     expr6               = "FORSIN(TIME,0.1,6.28,0.1,0.2)"
     expr7               = "DIM(TIME,1.0)"
     expr8               = "ACOS(COS(TIME))"
/>