.. _auto_curves_area_between:

*AREA BETWEEN TWO CURVES*
=========================

Computes the area between two arbitrary XY curves over an X range. The two curves are resampled onto a common dense grid of 1000 points and the trapezoidal integral of (Curve 2 minus Curve 1) is returned. Use the 'absolute' mode when the curves cross and you want the total enclosed area; use 'signed' when sign carries physical meaning (e.g. loading vs unloading, gain vs loss).

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

Classification: **process**.

Tagged: ``area_between``, ``curve_difference``, ``enclosed_area``, ``hysteresis``, ``loading_unloading``, ``scalar_output``, ``signed_area``, ``trapezoidal_integration``.

Inputs
------

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

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curve 1
     - curve_1
     - vector
     - —
     - 
     - First XY curve. The output is the integral of (Curve 2 minus Curve 1) over the overlapping X range, so Curve 1 is the lower / reference curve in the sign convention.
   * - Curve 2
     - curve_2
     - vector
     - —
     - 
     - Second XY curve. The signed area returned is positive where Curve 2 is above Curve 1 and negative where it dips below.
   * - X Left
     - x_left
     - string
     - —
     - 
     - Left X integration limit. Leave blank to use the left edge of the curves' overlapping X range.
   * - X Right
     - x_right
     - string
     - —
     - 
     - Right X integration limit. Leave blank to use the right edge of the curves' overlapping X range.
   * - Area Mode
     - area_mode
     - select
     - signed
     - 
     - 'Signed' returns the net integral of (Curve 2 - Curve 1), so regions where Curve 2 is below Curve 1 subtract from the total. 'Absolute' returns the integral of the absolute difference, i.e. the total enclosed area between the two curves regardless of which one is on top; zero crossings are handled by splitting each segment at the crossing point.

Outputs
-------

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

   * - Label
     - ID
     - Type
     - Description
   * - curves_area_between_output_1
     - curves_area_between_output_1
     - scalar
     - Scalar area in natural units of X x Y. With area_mode = 'signed' this is the net integral of (Curve 2 - Curve 1) over [x_left, x_right]; with 'absolute' it is the total enclosed area between the two curves regardless of which is on top.

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

- data.curve.pair
- data.curve.transform
- data.statistics
- engineering.material.characterization

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

A runnable example is registered for this worker. Open the example workflow on the d3VIEW canvas: `/api/workflow/example?id=cs_432_area_between_curves <https://www.d3view.com/api/workflow/example?id=cs_432_area_between_curves>`_

.. raw:: html

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   Auto-generated from <code>transformation</code> schema. Worker id: <code>curves_area_between</code>. Schema hash: <code>f98632dac142</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
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