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Don't know if this is what you were thinking, but you did get my imagination going.
Attached is a file that has 4 Dimensions that are projected/skewed into formZs 3D space.
Axes, planes and Tetrans (made up name) Negative portions of the axes are not considered here.
in the Skewed 3D space Negative values of any 4D axis can be regarded as positive values in the other 3 axes. i.e.: -1a = 1b,1c,1d (shown in a layer named as such.) and Visa Versa. Which is why I chose not to show the negative values Meaning, mathematically, orthogonal in 4D is not Orthogonal when projected to 3D
Scale is 1unit(4D) = 1foot(3D)
This is the conceptual leap to consider that 90º gets skewed into 3D space at 109.47º (no negative values) or 70.53º (with negative values)
Not considering the negative values, expands the space instead of compressing it.
1 degree of 4space is equivalent to 1.216333333333333 in 3D or (109.47/90)
If negative values are to be considered, this compresses to
70.53/90 1degree in 4space is equivalent to 0.783666666666667º in 3
I could be WAY off base, but this is the result.
How to script any of this, haven't a clue... Not smart enough to handle the translations needed.
Time Travel any one?
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Ya, this would interest me to have an optional plane locked to the current view, as we might have pondered that years ago, here, no? Or do you mean that the closest orthogonally aligned plane to the line-of-site becomes automatically active? Could that work with previously saved arbitrary planes? A project becomes a stored world of customized planes? Could the xyz cartesian planes be clicked off or made inactive?
I just rediscovered that we can still save customized planes, to be saved under the Menu/Palettes/Custom Reference Planes, but I'm still not 100% sure if a rectilinear mesh shape ought to become the sole grid in tetrahedral work... Or if like you did, one just invents some special grid meshes corresponding to the axes. This subject might get too exponential.
The second option. The active plane changes according to view. Off the top of my head, I don’t see why custom views couldn’t be included... though might get tricky on setting the values of the view angle upon which to switch on.
i don’t think in any current implementation you can actually change the coordinate system to anything other than rect, or polar. So, yea a base mesh would be required to fake it..