.. _auto_curves_fit_polynomial:

*FIT THE CURVES WITH POLYNOMIALS*
=================================

Fits one or more input curves with a polynomial of selectable order (1–5) using least-squares regression, optionally restricting the fit to a user-defined x-range and resampling the result to a specified number of points. Use this worker to smooth noisy curves, extract trend lines, or prepare regularised representations of test or simulation data for downstream processing.

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

Classification: **process**.

Tagged: ``curve_fit``, ``digitize``, ``force_origin``, ``knot_adjust``, ``least_squares``, ``optimize``, ``polynomial``, ``regression``.

Inputs
------

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

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curves
     - curves
     - vector
     - —
     - ✓
     - One or more input curves (x/y vector pairs) to be fitted; accepts multiple curve objects passed as a vector collection.
   * - Order
     - order
     - list
     - 1
     - ✓
     - Polynomial degree for the fit — integer 1 (linear) through 5 (quintic); defaults to 1 (linear).
   * - DIG POINTS
     - digitize
     - list
     - -1
     - 
     - Number of evenly-spaced points used to re-digitise the fitted curve for output; set to -1 (default) to keep the original x-spacing of the input curve.
   * - XMIN - Optional
     - xmi_n-optional
     - scalar
     - 0
     - 
     - Lower bound of the x-range over which the polynomial is fitted and evaluated; leave at 0 (default) to use the curve's own minimum x value.
   * - XMAX - Optional
     - xma_x-optional
     - scalar
     - 0
     - 
     - Upper bound of the x-range over which the polynomial is fitted and evaluated; leave at 0 (default) to use the curve's own maximum x value.
   * - Step
     - step-optional
     - scalar
     - 0.001
     - 
     - X-axis step size used when resampling the output curve; default is 0.001 — only active when digitize is not -1.
   * - Remove Intercept
     - remove_intercept
     - list
     - no
     - 
     - Line is rotated about the mean point until it passes through the origin. For segmented linear, the window_size is used as number of knots whose positions are to be optimized
   * - Window Size
     - window_size
     - scalar
     - —
     - 
     - Percentage of points to use over which the regression is built. By default the entire curve is used as the window size
   * - Type Of Fit
     - optimize
     - list
     - no
     - 
     - Type of fit
   * - Smallest Segment To Consider For Fit
     - increment_ratio
     - text
     - 0.01
     - 
     - Ratio of points in the curve to use for as increments for the fit
   * - R2 Cut Off For Fit Optimization
     - r2_cutoff
     - text
     - 0.995
     - 
     - When the R2 of a fit is below this to the previous fit, the fit considered goog
   * - Force Zero Origin
     - force_zero_origin
     - list
     - no
     - 
     - This option fores the fit to pass through 0,0 point
   * - Limit to 100 points while searching for Knots
     - limit_to_100_points
     - list
     - no
     - 
     - By default all points are used while searching. This option may help reduce execution time
   * - Adjust Knots
     - adjust_knots
     - list
     - no
     - 
     - In some instances, the auto-knots might find knots points that could create noise in the fit. This option helps to re-adjust those knots to minimize noise
   * - Number of Knot Adjustments
     - num_adjusts
     - text
     - 3
     - 
     - When <b> Adjust Knots </b> is turned on, number of adjustments is determined by this number

Outputs
-------

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

   * - Label
     - ID
     - Type
     - Description
   * - curves_fit_polynomial_output_1
     - curves_fit_polynomial_output_1
     - vector
     - Collection of polynomial-fitted curves (one per input curve), each containing the evaluated polynomial as an x/y vector at the requested resolution and x-range.

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

- ai_ml.supervised.regression
- data.curve.transform

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

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

.. raw:: html

   <hr style="margin-top:2em">
   <p style="font-size:11px;color:#888">
   Auto-generated from <code>transformation</code> schema. Worker id: <code>curves_fit_polynomial</code>. Schema hash: <code>6cedb2847032</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
   </p>