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--- tutorials:xl-turtle-geometry [2024/11/29 11:13] – [Transformation] tim
+++ tutorials:xl-turtle-geometry [2024/12/18 10:02] (current) – [3D objects] Tim
@@ Line 54: / Line 54: @@
 The **moving** part is already covered by the M node for now.
-You can **rotate** the turtle along the three axes x, y and z. We can see an example of the rotation tool on the right with the possible rotations in colors: x=red, y=blue and z=green. In the turtle geometry we can rotate these axes with the commands ''RL(angle)'', ''RU(angle)'' and ''RH(angle)''. RL rotates around the local X-axis (the red circle in the picture), RU around the Y-axis (the blue circle) and RH around the Z-axis. If we imagine to look from the perspective of the turtle, the names make more sense: RL rotates to the __l__left (with negative values to the right), RU rotates __u__p and RH rotates around the __h__head axes.
+You can **rotate** the turtle along the three axes x, y and z. We can see an example of the rotation tool on the right with the possible rotations in colors: x=red, y=blue and z=green. In the turtle geometry we can rotate these axes with the commands ''RL(angle)'', ''RU(angle)'' and ''RH(angle)''. RL rotates around the local X-axis (the red circle in the picture), RU around the Y-axis (the blue circle) and RH around the Z-axis. If we imagine to look from the perspective of the turtle, the names make more sense: RL rotates to the __l__eft (with negative values to the right), RU rotates __u__p and RH rotates around the __h__ead axes.
 Following up on our little example above you could think about rotation the short cylinder 30 degrees up like:
@@ Line 65: / Line 65: @@
 |{{:tutorials:turtle_tut_fruf.png?direct&240 |}}{{ :tutorials:turtle_tut_fruf_graph.png?direct&240|}}|
-||
+|The result of rotating the second cylinder up 30 degrees|
-===== Local transformation =====
-===== Modules =====
+You can try this also with the RL command and will a very similar result, with RH on the other hand you will see nothing because a cylinder is round and you cant see if it is rotated on the head axes.
-==== Instantiation rules ====
+That brings us to the next step: **combining transformations**, because even so the RH command does not give us a visible result it changes the orientation of the turtle and therefore influences all following commands for instance other rotations:
+<code java>
+protected void init ()
+[
+   Axiom ==> F RH(150)RU(30) F(0.2,2);
+]
+</code>
-===== Edge types =====
+|{{:tutorials:turtle_tut_frurhf.png?direct&240 |}}{{ :tutorials:turtle_tut_frurhf_graph.png?direct&240|}}|
+|The result of rotating the turtle first on the head axes and then rotate it up|
-==== Branches ====
+You can now try to switch the order of the commands to ''F RU(30) RH(150)F(0.2,2)'' and you will see the same result as without the RH because only the already up-rotated cylinder is now rotated around its head.
-==== Decomposition & custom ====
+Looking at the list of turtle commands, you can see that there are more rotations such as RV or RD you can explore.
+There are also more computer graphics oriented approaches embedded in the GroIMP turtle commands: Translate(x,y,z) Rotate(x,y,z) and Scale(x,y,z).
+**Translate** is moving the turtle for the given values on the local x,y,z axes:
+<code java>
+protected void init ()
+[
+	Axiom ==> F Translate(3,0,1)F(0.2,2);
+]
+</code>
+|{{:tutorials:turtle_tut_ftranslatef.png?direct&240 |}}{{ :tutorials:turtle_tut_ftranslatef_graph.png?direct&240|}}|
+Similarly the **Rotation** command is rotating around all 3 local axes at the same time. They do not influence each other that way so a rotation on the head axes would once again be not that impressive in our case.
+<code java>
+protected void init ()
+[
+	Axiom ==> F Rotate(20,30,0)F(0.2,2);
+]
+</code>
+|{{:tutorials:turtle_tut_frotatef.png?direct&240 |}}{{ :tutorials:turtle_tut_frotatef_graph.png?direct&240|}}|
+Finally the **scale** command can be used to change the size of all following commands, either proportionally or depending on the axes. For example if you want your howl model to be halve the size without chaining any parameter you could just add a Scale(0.5) in the beginning:
+<code java>
+protected void init ()
+[
+	Axiom ==> Scale(0.5) F Rotate(20,30,0)F(0.2,2);
+]
+</code>
+This will give us the same result as before only a smaller...
+Additionally, if we would like to be our cylinders to be not round but oval we can use the scale command as well, but with three parameters for the axes. For example we can turn the upper F in to a oval like this:
+<code java>
+protected void init ()
+[
+	Axiom ==> F Rotate(20,30,0)Scale(0.2,1,1)F(0.2,2);
+]
+</code>
+|{{:tutorials:turtle_tut_frotatescalef.png?direct&240| }}{{ :tutorials:turtle_tut_frotatescalef_graph.png?direct&240|}}|
+===== 3D objects =====
+As mentioned above in GroIMP we are not limited to the turtle commands but we can also use geometrical objects.
+<code java>
+protected void init ()
+[
+	Axiom ==> F Sphere(1);
+]
+</code>