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`trajectory, `

`gx`, `gy`, `vx`, `vy` [[, `n`],
`ox`, `oy`]

`trajectory, `

`gx`, `gy`, `v` [[, `n`], `ox`,
`oy`]

`[develop package]`

Calculates trajectories of particles
under guidance of a specified flow field. The two starting coordinates
of each particle are taken from

and `gx`

which must be real numerical arrays with the same number of elements.
The velocity field which guides the particles has coordinates either
given by two arguments `gy`

and `vx`

, or by a
single argument `vy`

. `v`

and `vx`

must be two-dimensional real numerical arrays with the same dimensional
structures. Alternatively, `vy`

must be a three-dimensional
real numerical array with 2 elements in its first dimension (which count
the x and y coordinates).
`v`

The coordinates in

and `gx`

are interpreted
such that the first velocity vector resides at coordinates `gy``(0,0)`

and the second one at `(1,0)`

.

If

is specified, then it must be a scalar that indicates
(after transformation of its value to type `n``long`

) over how many
time steps the particles are to be followed. The integer value of

must be positive.
`n`

If

and `ox`

are specified, then they must be
named writeable variables, and the resulting coordinates are returned in
them. If these arguments are not specified, then `oy`

cannot
be specified either (and a value of 1 is taken for it), and then the
results are returned in `n`

and `gx`

. The
results get all dimensions of `gy`

, plus one dimension at the
beginning equal to `gx`

(but only if `n`

is greater
than 1).
`n`

Currently, the flow field depends only on the integer part of the coordinates. In other words, there is no interpolation of the flow field for non-integer coordinates, and the flow vectors may change discontinuously when one crosses an integer coordinate line. The trajectory within each integer-coordinate box is a straight line with a direction corresponding to the flow vector. Because of the discontinuous flow field, it is possible that the velocity on both sides of an integer coordinate line points to the other side of the coordinate line. Any trajectory that reaches such an integer coordinate line stops there.

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