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2 changes: 1 addition & 1 deletion docs/getting_started_main.rst
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Expand Up @@ -40,7 +40,7 @@ For development:
- `sphinx`_ (for document generation)
- `ruff`_ (for code style check)

.. _`Python 3.11.x`: https://www.python.org/
.. _`Python 3.12.x`: https://www.python.org/
.. _`NumPy`: https://numpy.org/
.. _`SciPy`: https://scipy.org/
.. _`Matplotlib`: https://matplotlib.org/
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Catmull-Rom Spline Planning
-----------------
----------------------------

.. image:: catmull_rom_path_planning.png

Expand All @@ -10,7 +10,7 @@ exhibits local control, and maintains 𝐶1 continuity.


Catmull-Rom Spline Fundamentals
~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Catmull-Rom splines are a type of cubic spline that passes through a given set of points, known as control points.

Expand All @@ -24,7 +24,7 @@ Where:
* :math:`P_0, P_1, P_2, P_3` are the control points surrounding the parameter :math:`t`.

Types of Catmull-Rom Splines
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are different types of Catmull-Rom splines based on the choice of the **tau** parameter, which influences how the curve
behaves in relation to the control points:
Expand All @@ -51,7 +51,7 @@ behaves in relation to the control points:


Blending Functions
~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~

In Catmull-Rom spline interpolation, blending functions are used to calculate the influence of each control point on the spline at a
given parameter :math:`t`. The blending functions ensure that the spline is smooth and passes through the control points while
Expand Down Expand Up @@ -97,7 +97,7 @@ API


References
~~~~~~~~~~
~~~~~~~~~~~~~~

- `Catmull-Rom Spline - Wikipedia <https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline>`__
- `Catmull-Rom Splines <http://graphics.cs.cmu.edu/nsp/course/15-462/Fall04/assts/catmullRom.pdf>`__
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