documentation: Add 4. tutorial

CE3D2/doc/GettingStarted-WritingTransformations-example.md

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+# Getting Started - Part 4 - Example code
+
+Contains all snippets from the fourth tutorial you can directly include. For
+simplicity reasons no cpp-files were used.
+
+## XTranslation.h
+
+```cpp
+#ifndef _XTRANSLATION_H
+#define _XTRANSLATION_H
+
+#include <CE3D2/transformation/Transformation.h>
+
+class XTranslation : public CE3D2::Transformation::Transformation
+{
+public:
+    void
+    transform_vector(CE3D2::Vector& vector) const override
+    {
+        vector[0] += 1;
+    }
+};
+
+#endif
+```
+
+## ShoppingListTransformation.h
+
+```cpp
+#ifndef _SHOPPING_LIST_TRANSFORMATION_H
+#define _SHOPPING_LIST_TRANSFORMATION_H
+
+#include <CE3D2/Matrix.h>
+#include <CE3D2/transformation/LinearTransformation.h>
+
+class ShoppingListTransformation :
+    public CE3D2::Transformation::LinearTransformation
+{
+protected:
+    virtual CE3D2::Matrix
+    on_update() const override
+    {
+        CE3D2::Matrix cashbox(1, 3);
+        cashbox(0, 0) = 10.0f; // Pizza,
+        cashbox(0, 1) = 3.0f; // energy-drinks
+        cashbox(0, 2) = 5.0f; // and the good ice cream.
+        return cashbox;
+    }
+};
+
+#endif
+```

CE3D2/doc/GettingStarted-WritingTransformations.md

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+# Getting Started - Part 4
+
+## Writing your own transformations
+
+### Non-linear transformations
+
+Like described in the chapter before a transformation in CE3D2 maps a vector
+onto another vector. Exactly this behaviour is manifested inside a function
+of `CE3D2::Transformation::Transformation`:
+
+```cpp
+virtual void
+transform_vector(CE3D2::Vector &vector) const;
+```
+
+So all you need to do is override this member and modify the vector as you wish.
+
+For example let's take a translation in x-direction of the length 1.
+
+```cpp
+#include <CE3D2/transformation/Transformation.h>
+
+class XTranslation : public CE3D2::Transformation::Transformation
+{
+public:
+    void
+    transform_vector(CE3D2::Vector& vector) const override
+    {
+        vector[0] += 1;
+    }
+};
+```
+
+That's all! This transformation can now be used like any other transformation.
+
+### Linear transformations
+
+If your transformation you want to implement fits into a matrix, you should use
+the `CE3D2::Transformation::LinearTransformation` instead.
+
+Let us directly take another example: We want a matrix that shall apply
+something like a weighting algorithm, so each element of the given vector is
+weighted with a factor and added together with the others. We imagine some kind
+of shopping list with 3 items: Pizza, energy drinks and ice cream. The
+weightings represent prices, a pizza costs 10$, a single energy drink 3$ and a
+bucket of ice cream 5$ (yeah we buy the good ice cream, not the cheapest one
+:D). We could implement this inside a transformation like this:
+
+```cpp
+#include <CE3D2/Matrix.h>
+#include <CE3D2/transformation/LinearTransformation.h>
+
+class ShoppingListTransformation :
+    public CE3D2::Transformation::LinearTransformation
+{
+protected:
+    virtual CE3D2::Matrix
+    on_update() const override
+    {
+        CE3D2::Matrix cashbox(1, 3);
+        cashbox(0, 0) = 10.0f; // Pizza,
+        cashbox(0, 1) = 3.0f; // energy-drinks
+        cashbox(0, 2) = 5.0f; // and the good ice cream.
+        return cashbox;
+    }
+};
+```
+
+Applying this transformation on a 3D-vector would serve us now a one-dimensional
+vector where the entry holds the all round price.
+
+Now we need to override another member, called `on_update()`. Linear
+transformations use a lazy update system, this means if someone wants to
+retrieve the matrix via `get_matrix()`, it's only calculated once (if no
+changes were performed until the next call, more on that instantly). So
+calling `get_matrix()` repeatedly does not impact that much on performance,
+since the last calculated matrix is stored and retrieved directly on demand.
+
+But what if changes occur? Maybe you provide a value inside your transformation
+your matrix depends on? That's what the `update()` method is for. You **must**
+call it if you detected changes that affect your matrix so it can be updated
+again from your values inside `on_update()`.
+
+So you know now also how linear transformations work in CE3D2, you should have
+no problems to advance even further!