.. _auto_curve_slopefromx0:

*COMPUTE THE SECAND MODULUS BASED ON THE INITIAL-POINT AND THE SPECIFIED POINT*
===============================================================================

Computes the secant modulus of a curve by calculating the slope of the line connecting the curve's initial point (x₀) to a specified x-value. Use this worker whenever you need a chord-slope (e.g., engineering modulus) between the origin and an arbitrary point on a stress-strain or force-displacement curve.

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

Classification: **process**.

Tagged: ``chord_slope``, ``curve``, ``modulus``, ``secant_modulus``, ``slope``, ``slopefromx0``, ``stress_strain``.

Inputs
------

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

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curve To Be Looked Up
     - curvetobelookedup
     - vector
     - —
     - 
     - The input XY curve (e.g., stress-strain or force-displacement) on which the secant slope will be computed; provide as a two-column vector of (x, y) pairs.
   * - X Value
     - x_value
     - float
     - 0.0
     - 
     - The x-coordinate of the end-point used to define the secant line from the curve's first point (x₀); defaults to 0.0, meaning the slope from the very start of the curve to this value is computed.

Outputs
-------

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

   * - Label
     - ID
     - Type
     - Description
   * - curve_slopefromx0_output_1
     - curve_slopefromx0_output_1
     - scalar
     - Scalar secant modulus (rise-over-run) computed as Δy/Δx between the curve's initial point and the specified x-value; units match the y-axis units of the input curve divided by its x-axis units.

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

- data.curve.transform
- 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=curve_slopefromx0 <https://www.d3view.com/api/workflow/example?id=curve_slopefromx0>`_

.. raw:: html

   <hr style="margin-top:2em">
   <p style="font-size:11px;color:#888">
   Auto-generated from <code>transformation</code> schema. Worker id: <code>curve_slopefromx0</code>. Schema hash: <code>e43e5c5fdc99</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
   </p>