Understanding orientation in a 3D World

In a 2D plane, the turtle's orientation was only defined by its heading. In a 3D world, the turtle's orientation is given by 3 angles:

• Roll: The turtle's angle around axis $(Oy)$
• Pitch: The turtle's angle around axis $(Ox)$
• Heading: The turtle's angle around axis $(Oz)$

In fact, to move itself in the 3D World, the turtle is very similar to an aircraft. Here is a little illustration which represents these 3 values:

Roll

Pitch

Heading

It seems quite complex at first, but you will see that a lot of things stay very similar to moving in a 2D plane. Here are the basic primitives for moving in the 3D world:

• forward, fd, back, bk: Same behaviour as in 2D plane.
• right, rt, left, lt: Same behaviour as in 2D plane.
• rightroll, rr: The turtle turns $n$ degrees to the right around its longitudinal axis.
• leftroll, lr: The turtle turns $n$ degrees to the left around its longitudinal axis.
• up, uppitch: The turtle goes $n$ degrees up around its transversal axis.
• down, downpitch: The turtle goes $n$ degrees down around its transversal axis.

In the 2D plane, when we want to draw a square of side 200 steps, we write:

repeat 4[fd 200 rt 90]

These instructions are still available in the 3D world, where the square is drawn in perspective mode. If the turtle goes down $90$ degrees, we can draw another square and we obtain:

cs
repeat 4[fd 200 rt 90]
down 90
repeat 4[fd 200 rt 90]

You just have to try some examples to understand these orientations and become an expert!
You must understand that the 3 rotation primitives are linked together, for example try this:

cs
leftroll 90 up 90 rightroll 90

The turtles movement is equivalent to left 90 (You can try with your hand simulating the turtle if you don't understand)