Add splitting and decomposition docs

orbingol · Feb 12, 2018 · cf11d84 · cf11d84
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diff --git a/docs/images/split_curve2d_translate.png b/docs/images/split_curve2d_translate.png
diff --git a/docs/images/split_curve3d.png b/docs/images/split_curve3d.png
diff --git a/docs/images/split_decompose_circle1.png b/docs/images/split_decompose_circle1.png
diff --git a/docs/images/split_decompose_circle2.png b/docs/images/split_decompose_circle2.png
diff --git a/docs/images/split_decompose_surface1.png b/docs/images/split_decompose_surface1.png
diff --git a/docs/images/split_decompose_surface2.png b/docs/images/split_decompose_surface2.png
diff --git a/docs/images/split_surface_combined.jpg b/docs/images/split_surface_combined.jpg
diff --git a/docs/images/split_surface_multi.png b/docs/images/split_surface_multi.png
diff --git a/docs/images/split_surface_translate.png b/docs/images/split_surface_translate.png
diff --git a/docs/index.rst b/docs/index.rst
@@ -37,6 +37,7 @@ This documentation is organized into a couple sections:
     examples
     file_formats
     visualization
+    visualization_splitting
 
 .. _modules:
 

diff --git a/docs/visualization_splitting.rst b/docs/visualization_splitting.rst
@@ -0,0 +1,67 @@
+Splitting and Decomposition
+^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+NURBS-Python is also capable of splitting the curves and the surfaces, as well as applying Bézier decomposition.
+Splitting of 2D/3D curves can be achieved via ``split()`` method. For the surfaces, there are 2 different splitting
+methods, ``split_u()`` for splitting the surface in U-direction and ``split_v()`` for V-direction. Bézier decomposition
+can be applied via ``decompose()`` method for all curve and surface classes. Please refer to the documentation for more
+details.
+
+The following figures are generated from the examples provided in the Examples_ repository.
+
+Splitting
+=========
+
+The following 2D curve is split at ``u = 0.6`` and applied translation by the tangent vector via ``translate()`` method.
+
+.. image:: images/split_curve2d_translate.png
+    :alt: 3D curve splitting example with translation
+
+Splitting can also be applied to 3D curves (split at ``u = 0.3``) without any translation.
+
+.. image:: images/split_curve3d.png
+    :alt: 3D curve splitting example
+
+Surface splitting is also possible. The following figure compares splitting at ``u = 0.5`` and ``v = 0.5``.
+
+.. image:: images/split_surface_combined.png
+    :alt: Surface split combined
+
+Surfaces can also be translated too before or after splitting operation. The following figure illustrates translation
+after splitting the surface at ``u = 0.5``.
+
+.. image:: images/split_surface_translate.png
+    :alt: Surface split and translation
+
+Multiple splitting is also possible for all curves and surfaces. The following figure describes multi splitting in
+surfaces. The initial surface is split at ``u = 0.25`` and then, one of the resultant surfaces is split at ``v = 0.75``,
+finally resulting 3 surfaces.
+
+.. image:: images/split_surface_multi.png
+    :alt: Surface multi split
+
+Bézier Decomposition
+====================
+
+The following figures illustrate Bézier cecomposition capabilities of NURBS-Python. Let's start with the most obvious
+one, a full circle with 9 control points. It also is possible to directly  generate this shape via ``geomdl.shapes``
+module.
+
+.. image:: images/split_decompose_circle1.png
+    :alt: 2D curve decomposition 1
+
+The following is a circle-like shape generated with 7 control points as illustrated on page 301 of *The NURBS Book*
+(2nd Edition) by Piegl and Tiller. There is also an option to generate this shape via ``geomdl.shapes`` module.
+
+.. image:: images/split_decompose_circle2.png
+    :alt: 2D curve decomposition 2
+
+The following figures illustrate the possibility of Bézier decomposition in B-Spline and NURBS surfaces.
+
+.. image:: images/split_decompose_surface1.png
+    :alt: B-Spline surface decomposition
+
+.. image:: images/split_decompose_surface2.png
+    :alt: NURBS surface decomposition
+
+.. _Examples: https://github.com/orbingol/NURBS-Python_Examples