9.5.2

506 • CHAPTER 8
TOOLS MENU • 507
You may have come across the terms heading, pitch and bank in connection with aircraft. An aeroplane
rotates left or right to change its heading; up or down to changes its pitch; and rolls to change its
bank. When you are changing angles you may nd it helpful to think of an aeroplane.
Unlike HPB, XYZ rotations are non-commutative. In other words, the order in which you rotate the
axes matters. For example, rotating by the X value then the Y value may produce a different result to
rotating Y rst. This makes the XYZ system unsuitable for animation.
On the other hand, in the HPB system the angles are disassociated. You can rst change the heading
and then the pitch, or the other way round, and you’ll still get the same result.
Moreover, the HPB angles create naturally interpolated movements that are particularly useful for
aeroplanes, cars or cameras. When you rotate around a particular axis in the XYZ system this may
cause all three HPB components to change. The result is a tumbling animation. With the HPB system
this cannot happen.
Although the HPB system is excellent for animation, it is useless when it comes to constructing objects.
HPB angles are specied relative to the parent system, which demands a high level of abstraction.
So CINEMA 4D offers you the choice. For rotations in the 3D viewport you have the HPB system
and the (local or global) XYZ system. You’ll nd the Use HPB System option on the Units page of
the preferences. However, note that all numeric input is in HPB angles, even if Use HPB System is
disabled.
Why use HPB?
In this section you’ll learn more about why CINEMA 4D uses the HPB system. However, if you’re the
kind of artist who hates math, you’ll want to skip these optional details.
Some people do not understand why rotations around the Z-axis (the bank angle) are performed in
the object system whereas rotations around Y and X axes (heading and pitch) are always made in
the world system. With animation, even switching to XYZ rotations doesn’t help since CINEMA 4D is
using the HPB system internally. The HPB system is a so-called Euler system where the HPB angles do
not refer in principle to the axes of the object itself.