Position Independent Principle
PhD Chris Thorne (see this link) introduces the principle of position independence regarding 3D graphics here at the following link: https://www.researchgate.net/publication/342510617_Position_Independent_Principle?fbclid=IwAR2u77O2nZiRoPK_IoEO
As PhD Thorne explains, the floating point precision decreases exponentially with the distance from the origin of a simulation / animation, if we assume, all the animation, simulation and graphics are calculated with respect to the common origin "O".
Additionally, we would like to add the consideration that the assumption of some "external", "absolute", "independent", "master", "global" *) coordinate system / origin seems to be problematic with respect to nowadays philosophy of relativity in physics.
*) those words ("external", "absolute", "independent", "master", "global", ......) are more or less deprecated in modern physics
So let's try to collect the information in a picture:
When we meditate the picture, then we can conclude that the available floating point precision will be a maximum, if we move the whole scene ("virtual roaming area") relative to and with the camera "C" into the origin "O", hence setting "offset" := 0.
Depending on the used software, this might have the disadvantage, each camera move must be accompanied by a complete transformation of the whole scene *).
*) Some frameworks or game engines might reveal this as advantage, on the other hand, if the whole scene must be transformed anyway to be stored relative to the view frustum
In general, we can imagine three approaches:
- Approach "A": never mind the "offset"
- Approach "B": keep the "offset" small in relation the rmax by transforming the scene every now and then
- Approach "C": keep the "offset" strictly at "offset" := 0
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OK, you need to separate the variable resolution of digital space from relocating an equation. The principal says equations can be moved: change their absolute location - and still produce a valid result. More specifically this applies to equations that are positional closures.
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Position independence cann then be applied together with the observation that greater accuracy can be achieved by calculating closer to the origin. I.e. the two separate ideas are combined to achieve optimal accuracy that is invariant to the actual absolute location of the equation.
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This invariance is not achievable by conventional methods. It means, for example, jitter I'd minimized and invariant for the rendering calculation, for proximity and distance calculations, and physics, to name a few.
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Btw. the diagram is a good idea. Just keep in mind the variation in resolution and geometric error is linear but the variation in calculation accuracy becomes exponential with complexity of equation because of error propagation.
Tbd.