.. highlightlang:: us

.. _rspline:

rspline
=======

.. index:: rspline

.. us.tag  rspline ENGLISH New550 Interpolation

:ref:`rspline` computes a rational spline under tension for a given x and y vector.

.. function::  rmXY = rspline(rvX, rvY, p)
    rmXY = rspline(rvX, rvY, p, rsTensionFactor)
    rmXY = rspline(rvX, rvY, p, rsTensionFactor, flag)

.. us.return

**Return Value**

The return value *rmXY* is a real matrix with two columns. The first column
contains the x-coordinates of the spline and the second column contains the
y-coordinates of the spline. In case of an error *rmXY* has only one element
with an error number: 

.. list-table::
   :header-rows: 0

   * - 1
     - not enough memory
   * - 2
     - x-coordinates are not strictly increasing
   * - 3
     - less than 3 datapoints specified.

.. us.params

**Parameters**

.. uparam:: rvX

   *rvX* is a real vector with at least 3 elements.

.. uparam:: rvY

   *rvY* is a real vector with at least 3 elemetns.

.. uparam:: rsTensionFactor

   *rsTensionFactor* is a value in the range 0 to 100. For 0 the spline is similar
   to a cubic spline and for values close to 100 the result is a polygon.
   Default value is 1.

.. uparam:: p

   The meaning of *p* depends on the value of the parameter *flag*

.. uparam:: flag

   *flag* can be one of the following values:

   .. list-table::
      :header-rows: 1

      * - Value
        - Meaning
      * - 1
        - p is the number of x-, y-coordinates calculated.
      * - 2
        - p is the number of x-, y-coordinates calculated. The original x-coordinates are added to the total.
      * - 3
        - p is a strictly increasing vector of x-coordinates.

   Default value is 1.

.. us.example

**Example**

.. image:: S:/uniplot-obj/images/rspline.*

.. us.history

**History**

.. list-table::
   :header-rows: 1

   * - Version
     - Description
   * - 5.5.0
     - New

.. seealso::
   :ref:`overview-mathematic`,
   :ref:`pspline`,
   :ref:`fspline`,
   :ref:`akimaspline`,
   :ref:`interpol`

:sub:`id-1612071`