# What is the purpose of inertial space and what are its uses?

I'm currently reading about left-handed and right-handed coordinate systems when working with 3D and it's all very fascinating. These systems are made up of world space, object space, and inertial space. I believe I have a firm grip on world space and object space, however I'm not entirely sure what inertial space is used for? If my understanding is correct - it is simply a way to convert local space to world space, and vice versa? Is inertial reference frame the same as inertial space? • You're reading in reference to physics, right? I've never heard of inertial-anything outside of physics and a quick Google search of "inertial space" is backing that up. The main point of the text you may be reading is that there are literally an infinite number of bases or vector spaces that you can define depending on your needs. – Sean Middleditch Jan 21 '14 at 0:35
• I would migrate this question to Physics.SE. Eventhough people here might know the answer, I don't believe it's suited or you will get the best answer here. – concept3d Jan 21 '14 at 0:50
• In 3D graphics, we generally have "model, world, view and clip" space (plus a few extra that are less commonly referred to. I have never seen the term inertial space in reference to 3D graphics and I'm not sure what more common term it is in reference to. Can you provide more details on what this inertial space is described as? – Josh Jan 21 '14 at 1:50
• Inertial space is more commonly a physics topic. – Josh Jan 21 '14 at 1:52
• I think this term was used in the book '3D Math Primer for Graphics and Game Development' but I don't think it is really used in rendering. – Archy Jan 21 '14 at 9:08

Disclaimer: I am not a physics expert, neither I guarantee the following explanation to be entirely accurate, but I will try to make things simpler.

First: Let's us break it down into two keywords, obviously space and interia.

Space (or a frame of reference) in 3D : is a combination of rotation and translation. So when we say a point is relative to a specific space, we mean that its coordinates are measured relative to that space orientation and translation. More on this here.

When you measure temperature you measure it relative to a certain reference (could be the zero or other value in your thermometer). When you say 10C you mean 10°C relative to 0°C where 0°C was defined as the freezing point of water. (Note: This is not entirely accurate more info here.

The same goes for bodies motion, we measure them relative to something else, whether it was an observer space or any other body space.

Inertial space is a reference frame that is itself not accelerating; that is said, objects being observed should appear appear to experience constant speed relative to each other.

Remember that constant speed means zero acceleration,

Newton's second law states:

F = mass * acceleration

hence,

acceleration = F / mass

And according to Newton's first law:

When a object is viewed in an inertial reference frame, an object either is at rest or moves at a constant velocity, unless acted upon by an external force.

Inertial space is a space where Newton's laws holds true. This is important for calculations to remain simple. For example choosing a non-inertial space (an accelerating space) will make objects appear to have ambient acceleration even without having force acting on them, at this state Newtons laws of motion doesn't hold anymore.

It's easy to connect the first and the second law. If it was not for inertial space, neither will hold true.

An example of a non-inertial frame, an observer setting on an accelerating rotating disk, this will particularly complicate calculation, and will complicate even the slightest observations; such as the linear motion of two balls as observer from that location, (this needs some imagination) the balls will have acceleration relative to the observer, which makes Newton's first law no hold anymore.

## Inertial frame of reference in Gamedev and graphics

We just assume it exists, we never select a frame of reference that is accelerating, physics simulations are calculated relative to world coordinates, which is fixed. If you want to calculate physics relative to an accelerating camera (please don't mix the coordinates where things are rendered and the coordinates where physics is calculated) don't do that, the calculation will be redundantly complex. We never calculate physics an relative to an accelerating eye coordinates (even if you did you should select the coordinates that have Zero or constant velocity).

## Why did the chicken cross the road?

### Aristotle:

It is the nature of chickens to cross the road.

### Newton:

Because no force caused the chicken's state of uniform road crossing to change.

### Einstein:

Is the chicken crossing the road or is the road moving under the chicken?