.. _auto_curve_cubic_spline:

*FIT THE CUBIC SPLINE*
======================

Fits a cubic (or arbitrary-order) smoothing spline to an input curve using a specified number of knots and regions. Supports optional k-fold cross-validation to automatically select the best spline order and knot count, with a lambda penalty controlling knot contribution. Use this worker to smooth or resample noisy time-history or force-displacement curves.

When to use
-----------

Classification: **process**.

Tagged: ``cross_validation``, ``cubic_spline``, ``curve_smoothing``, ``curve_transform``, ``downsampling``, ``k-fold``, ``knots``, ``lambda``.

Inputs
------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20 20 20

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curve In
     - curve_in
     - vector
     - —
     - 
     - Input curve (x/y vector) to be fitted with a smoothing spline; typically a time-history or force-displacement signal.
   * - Order
     - order
     - scalar
     - 3
     - 
     - Polynomial order of the spline fit (default 3 = cubic); when cross-validation is enabled, this becomes the maximum order evaluated.
   * - Number Of Knots
     - numberof_knots
     - scalar
     - 1
     - 
     - Number of interior knots placed in the spline (default 1); when cross-validation is enabled, this becomes the maximum number of knots evaluated.
   * - Number Of Regions
     - numberof_regions
     - scalar
     - 1
     - 
     - Number of piecewise regions for the spline (default 1); only used when Validation is set to 'None'.
   * - Validation
     - validation
     - scalar
     - none
     - 
     - Cross-validation strategy for automatic order/knot selection: 'None' uses the fixed parameters directly; 'K-Fold 3/5/10' performs k-fold CV to find the optimal configuration (default: None).
   * - Lambda
     - lambda
     - scalar
     - 1
     - 
     - Regularisation penalty factor controlling the contribution of each knot (default 1.0); higher values produce smoother fits with fewer effective knots.

Outputs
-------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20

   * - Label
     - ID
     - Type
     - Description
   * - Cubic Spline Curve
     - curve_cs_output_1
     - vector
     - Fitted cubic spline curve (x/y vector) evaluated over the same domain as the input, representing the smoothed or resampled result.

Disciplines
-----------

- data.curve.transform
- data.signal_processing

Runnable example
----------------

A runnable example is registered for this worker. Open the example workflow on the d3VIEW canvas: `/api/workflow/example?id=curve_cubic_spline <https://www.d3view.com/api/workflow/example?id=curve_cubic_spline>`_

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   Auto-generated from <code>transformation</code> schema. Worker id: <code>curve_cubic_spline</code>. Schema hash: <code>1bca1eb6bc0a</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
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