.. _auto_curves_derivative_exceeds_threshold:

*DETECT SIGN CHANGES BASED ON 3RD DERIVATIVE SIGN CHANGE*
=========================================================

Detects sign changes in a curve by computing its Nth-order derivative and flagging points where the derivative exceeds a ratio-based threshold. Use this worker to identify inflection points, oscillations, or instabilities in time-history or spatial curves via higher-order derivative analysis.

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

Classification: **process**.

Tagged: ``curve_analysis``, ``derivative``, ``higher_order``, ``inflection_point``, ``sign_change``, ``threshold``.

Inputs
------

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

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curve
     - curve
     - vector
     - —
     - 
     - One or more input curves (x-y vector pairs) to analyse; accepts multiple curves — leave empty only if curves are provided downstream via a connected node.
   * - Order
     - order
     - scalar
     - 3
     - 
     - Derivative order to compute before applying the threshold check (dimensionless integer, default 3 for the 3rd derivative); increase to detect higher-order sign changes, decrease for smoother sensitivity.
   * - Ratio
     - ratio
     - scalar
     - 0.75
     - 
     - Fraction of the peak derivative magnitude used as the detection threshold (dimensionless, default 0.75); points whose derivative exceeds ratio × peak are flagged — lower values flag more points, higher values flag only sharp changes.

Outputs
-------

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

   * - Label
     - ID
     - Type
     - Description
   * - curves_derivative_exceeds_threshold_output_1
     - curves_derivative_exceeds_threshold_output_1
     - vector
     - Output curve(s) containing the flagged points or annotated signal where the Nth-order derivative exceeds the ratio threshold, returned as an x-y vector in the same domain as the input.

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

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   Auto-generated from <code>transformation</code> schema. Worker id: <code>curves_derivative_exceeds_threshold</code>. Schema hash: <code>1d24ae22f3b7</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
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