QCAD.org Forum

Hello again everyone! I hope everyone is enjoying their weekend and living well!

Anyway, as I mentioned later on in my previous angle unit related thread, another idea for another arguably missing angle display unit occurred to me in the course of thinking about our related discussions.

There are only three angular units I know of that occur naturally (aren't arbitrary human-made scales): radians, cycles, and complex numbers.

So, the idea occurred to me that it could conceivably be useful in some cases if the complex numbers cases was given some representation and ease of quick reference by making it so that there's an option to display angles as normalized unit circle coordinates (essentially the complex number coefficients in other words) so that the user can instantly know what unit circle coordinates correspond to any given position as they move their mouse around the grid and so on.

Admittedly, I can't immediately think of pragmatic uses I have in mind for such a case, but I have little/no doubt that there are circumstances where it may be desired by someone.

And after all, what is the purpose of a CAD program but to automate away the tedium of these kinds of mundane computations that get in the way of high level sense of design sometimes?

Such a display unit would make it so that the user doesn't have to compute normalized unit circle coordinates corresponding to any given angle.

Thus, I have created this new thread advocating for another angle display unit to be considered for an automated implementation.

I am much less attached to this idea than to the merits of cycles (a.k.a. turns or revolutions), but I think some people out there may find it useful too potentially.

Anyway, thank you for your time and for reading!

QCAD is such wonderfully expressive software. Even more differentiating points that let users express themselves however they want or need will inevitably add value potential. Some features will be used more or less, but one of the things that makes this software so great I feel is that it offers such an abundance of different ways of expressing exactly what the user means, which is exactly where so much of the value of QCAD comes from I think, though I've only been using it shortly so far!

Oh, another thing I should mention for further clarification of additional reasons one may want this and why complex numbers can indeed be thought of as a kind of angle unit:

Complex numbers have the extremely useful, computationally efficient, and surprising property that if you multiple any complex number by another complex number then this has the effect of rotating the first complex number by the angle between the zero line and the second complex number an also scaling by the magnitude (length) of the complex number's Cartesian coordinates.

Thus, multiplying any given coordinate by a complex number corresponding to the normalized (rescaled to have length 1) unit circle coordinates of an angle is actually equivalent to the corresponding rotation.

This property is even used in modern game engines (in a generalized form of complex numbers via 4-dimensional rotations using what is called quaternions) in order to perform rotations in a more computationally efficient form than using angles or matrices. This was a major improvement in rotation performance in 3D graphics technology when someone first had the idea to use it!

WraithGlade wrote: ↑

Sun Feb 18, 2024 7:39 pm

And after all, what is the purpose of a CAD program but to automate away the tedium of these kinds of mundane computations that get in the way of high level sense of design sometimes?

I disagree! The purpose of a CAD program is to design digital models etc. before even manufactured or in a reingeneering matter. It is not meant or designed to do complex calculation. Yes, it is able to cover basic geometrical math but that is a sideeffect benefit.
If I use a texteditor like MS Word I can also draw a basic drawing with it. Sure, it is heavyly limited to basic geometry but no one would ask the developer's to improve those abilities to make it a CAD program.

It is also remarkable to me that except you noone has ever ask in this forum for those changes. Looks to me nobody is missing it. Same with your tau / circle / turn request. Looks like there are more out there like me. 50 years in the drafting business and never did a calculation with tau. Well...one... two days ago ...
I learned on PI and never noticed they prefer now to teach to use tau (they don't!) ... because it is much more safisticated.

This said - I tent to agreeing with you findings but if the user mass isn't missing it why fix a non broken machine?

And that is probably the most important point. If an improvement idea doesn't benefits mass QCAD user then the idea is basically dead at arrival.

With other words: Cobbler, stick to your last!

However - we appreciate you are sharing your thoughts on Qcad. In my case my comments are based on 50 years drafter by trade / Instructor technical draftsman, 35 years CAD and 15+ years QCAD experience. Parallel many software consulting jobs on the way and still no idea how to code anything ...

WraithGlade wrote: ↑

Sun Feb 18, 2024 7:39 pm

There are only three angular units I know of that occur naturally

Can't agree that Radians and complex numbers are naturally occurring quantities.
Radians is based on PI and we humans are still defining PI for the moment aka squaring the circle.
Complex numbers are an invention to solve sqrt(-xxx).

On turns I can agree.
For QCAD drop the plural, angles are normalized aka 1 turn or 1 revolution or 1 cycle.

Regards,
CVH

In the related feature request I included an example.
https://qcad.org/bugtracker/index.php?d ... sk_id=2529

0.965926 + 0.258819j would represent an angle of 15.0 degrees.
Decide for yourself what would be more appropriate.
What it means is 0.965926 units to the right and 0.258819 units up, normalized and thus always 1 unit away.
Correction, almost 1 unit away because of the truncated values.

Let us pretend to enter a relative polar coordinate using this notation:
@100<0.965926 + 0.258819j ... And then I would personally prefer @100<15

Not normalized would already say more to most people:
@96.5926 + 25.8819j or 96.5926 units to the right and 25.8819 units up ... We know this as the relative notation: @96.5926, 25.8819

The problem lies in the accuracy ...
@100<0.965926 + 0.258819j results in 100.00001561184886... away with an angle of about 14.99999493... degrees.

Rather more beneficial when not normalized and with somewhat rounded values.
@4.2 + 5.25j or 4.2 units to the right and 5.25 units up ... aka @4.2, 5.25
Now the distance (6.72328045...) and the angle (51.34019175...) are no neat values.
You can not have it both ways except for some orientations: 0-90-180-270-... degrees.
While neat when not normalized ...
... The normalized counterpart is again very hard to grasp: @6.72328045...<0.624695... + 0.7808688...j
Nothing in this notation tells me that it is merely 4.2 right and 5.25 up.

Regards,
CVH