.. _auto_curve_fit_polynomial:

*FIT THE CURVE WITH POLYNOMIALS*
================================

Fits a 2-D curve with a polynomial of a specified (or automatically selected) order using least-squares regression. Supports optional x-range clipping, digitization, sliding-window fitting, R² optimisation, and origin-forcing. Use this worker to smooth noisy curves or extract a compact polynomial representation for further processing.

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

Classification: **process**.

Tagged: ``curve_fit``, ``digitize``, ``least_squares``, ``optimize``, ``polynomial_fit``, ``r2``, ``regression``, ``sliding_window``.

Inputs
------

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

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curve
     - curve
     - vector
     - —
     - ✓
     - Input curve (x-y vector) to be fitted; must be a valid d3VIEW curve object — this is the only required input.
   * - Order
     - order
     - scalar
     - 1
     - ✓
     - Polynomial order for the fit (integer 1–9, default 1); pass "auto" to select the order with the highest R², or "auto_parsimony" to select the lowest order whose R² is within 0.005 of the best — recommended for noisy data to avoid overfitting. When optimize=yes this becomes the maximum order to search.
   * - DIG POINTS
     - digitize
     - list
     - -1
     - 
     - Number of evenly-spaced points to which the input curve is re-sampled before fitting (options: -1 = no re-sampling, 10/100/200/400/1000; default -1); increase to normalise high-density or irregular curves.
   * - XMIN - Optional
     - xmi_n-optional
     - scalar
     - 0
     - 
     - Minimum x-value of the fitting domain (default 0, meaning use the curve's natural start); set to clip the fit to a sub-range.
   * - XMAX - Optional
     - xma_x-optional
     - scalar
     - 0
     - 
     - Maximum x-value of the fitting domain (default 0, meaning use the curve's natural end); set in conjunction with XMIN to restrict the polynomial to a specific interval.
   * - Step
     - step-optional
     - scalar
     - 0.001
     - 
     - X-step size used when generating the output fitted curve (default 0.001); reduce for smoother output or increase for coarser/faster results.
   * - Remove Intercept
     - remove_intercept
     - list
     - no
     - 
     - Whether to suppress the constant term (intercept) in the fitted polynomial — "yes" or "no" (default "no"); set to "yes" when the fitted curve must pass through y=0 at x=0.
   * - Window Size
     - window_size
     - scalar
     - —
     - 
     - Number of x-points in each sliding window for a piecewise/local polynomial fit (default null = global fit over the whole curve); set to a positive integer to enable local fitting.
   * - Type Of Fit
     - optimize
     - list
     - no
     - 
     - When set to "yes", iteratively increments the polynomial order up to the value of `order`, accepting each increment only when R² improves by more than `per_inc` (default "no").
   * - 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
     - r2cutoff
     - 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 certain number of points while searching for Knots
     - limit_to_100_points
     - list
     - no
     - 
     - Limit the input data to a maximum of 100 points before fitting — "yes" or "no" (default "no"); can speed up fitting on very dense curves with minimal accuracy loss.
   * - 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
     - 
     - Maximum number of auto-adjustment iterations performed when auto_adjusts=yes (default 3); increase for tighter convergence at the cost of additional compute time.

Outputs
-------

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

   * - Label
     - ID
     - Type
     - Description
   * - curve_fit_polynomial_output_1
     - curve_fit_polynomial_output_1
     - vector
     - Fitted polynomial curve as an x-y vector evaluated at the specified step size over the fitting domain; ready for downstream curve comparison, visualisation, or further transformation.

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=curve_fit_polynomial <https://www.d3view.com/api/workflow/example?id=curve_fit_polynomial>`_

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   Auto-generated from <code>transformation</code> schema. Worker id: <code>curve_fit_polynomial</code>. Schema hash: <code>74d5d9e9231f</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
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