🧵 Hexagon in Ellipse
Anonymous at Thu, 17 Oct 2024 13:31:03 UTC No. 16436259
Hi!
If I have a hexagon inscribed in a circle, and would rotate it over the X axis such that I would have a hexagon inscribed in an ellipse. Is there a solution where all the angles are a multiple of 22.5 degrees?
Could someone help me to calculate this, or give me the dimensions of the resulting hexagon?(Height and width?)
Asking because I want to make a hexagon base in Factorio with the new 22.5 degree rail segments and I think this might give the most pleasing ratio for the hexagon.
Anonymous at Thu, 17 Oct 2024 13:34:00 UTC No. 16436266
>>16436259
This is not a rotation. You’re deforming a circle to an ellipse. This is an affine transformation.
Anonymous at Thu, 17 Oct 2024 13:37:27 UTC No. 16436271
>>16436266
Oh, and to answer your question, affine transformations don’t preserve angles.
Anonymous at Thu, 17 Oct 2024 13:39:40 UTC No. 16436275
>>16436266
If I print out a large circle on a piece of paper, and move it from a vertical position perpendicular to me, and rotate over the X axis towards being horizontal, what's the resulting shape the circle gets then in perspective?
Anonymous at Thu, 17 Oct 2024 13:41:27 UTC No. 16436279
>>16436271
If you read my message you'd realize that's the goal. I want 30 degree increments to turn into 22.5 degree increments.
Anonymous at Thu, 17 Oct 2024 14:10:08 UTC No. 16436324
>>16436279
So work it out yourself. I told you about what type of transformation you need to perform. Not here to do your Factorio homework. It's a basic set of equations.
Anonymous at Thu, 17 Oct 2024 22:42:49 UTC No. 16437062
🗑️ Anonymous at Fri, 18 Oct 2024 00:08:06 UTC No. 16437186
>homework thread
Anonymous at Fri, 18 Oct 2024 01:52:37 UTC No. 16437309
>>16436259
Sum of all angles of a hexagon is 720. By symmetry after shrinking/rotation angles B,C,F,E are all still the same and angles A,D are each equal to (720-4*B)/2 = 22.5*(16-2*(B/22.5)) so all angles will be multiples of 22.5 if B is and we only need to worry about B.
No matter how much rotation there is B will always be between 90 and 120, so B must =112.5, or the yellow angle in the pic =22.5. Shrinking vertically will scale the .5 length segments but not the .866, and if the scale factor is X we need .5 * X/.866 = tan(22.5) = .4142, so X = .7174. Coords are
A,D = (0, +/-.717)
B,C,F,E = (+/-.866, +/-.359)
Scale it up or down by just multiplying every coordinate by some fixed number.
Anonymous at Fri, 18 Oct 2024 12:36:26 UTC No. 16437808
>>16437309
Thank you anon, you're the best. Have a good weekend.
Anonymous at Sat, 19 Oct 2024 16:40:04 UTC No. 16439941
>>16436259
i wish my KSP comms relay looked like that.