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World/Inertial/Object space

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Right now im reading the 3d math primer book and the author goes into a bit of detail about World, Inertial, and object space. Say you have an object,around (400,400) in world space. Now if you look at its Inertial space (which is parallel to the world space) the object will be located at (0,0) inertial space and (0,0) object space. Now say we rotate our object 60degrees to towards the y axis. The object space stays the same(0,0) but the inertial space changes since it is parallel to the world space, so intertial space is something like (-100,100); Here is what we end up with Object relative to World space (400,400) Object relative to Inertial space (-100,100) Object relative to Object space (0,0) Now the author claims to get to world space all the object must do is rotate to line up with the Inertial space, then translate to the world space. My friend says that its not actually used that much in open gl or direct x. So i dont know if i need to know this, or do the API''s usually do this by themsleves. It seems a it redundent to do it like this, but at the same time i can see its usefullness from an object oriented standpoint. Anyone have any insight on the practicality of the 3 differnt spaces?

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Welcome to the wonderful world of coordinate systems and tranformations. This stuff is really worth understanding well, as it allows you to make heirachical objects as well as being the basic principle in transforming 3d objects to 2d screen space.

Think about a wheel on a car. If you had to rotate it in world space directly each frame, it would be a pain. But by having a matrix describing the transformation between coordinate systems, you can simply rotate the wheel in its own object space and then transform the points to the car object space, then to the world space. All this is not handled by the API, you have total control over which matrices you are working with at all times.

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