]pts =. _2 ]\ 1 1 2 2 3 4 NB. points as (x,y)
1 1
2 2
3 4
]zpts =. j./ |: pts NB. points in complex plane
1j1 2j2 3j4
zorigin =. 0j0
NB. verb to rotate points y counterclockwise by angle x
rot =. {{ zorigin + (y-zorigin) * ^ j. x }}"0 _
NB. Get the angles to use. Each pairwise point difference is a
vector. Calculate them, run
NB. into a list, discard 0s, find the angle. Negate the angle so as
to rotate CW (which puts y
NB. values the same, and append a copy with pi/2 added (which
rotation puts x values the same).
NB. Force to quadrants I and II, discard duplicates, sort.
]angles =. /:~ ~. 1p1 | (, 0.5p1&+) - 12 o. 0 -.~ , -/~ zpts
0.463648 0.588003 0.785398 2.03444 2.1588 2.35619
NB. Rotate by each angle to see that coordinates match
angles rot zpts
0.447214j1.34164 0.894427j2.68328 0.894427j4.91935
0.27735j1.38675 0.5547j2.7735 0.27735j4.9923
0j1.41421 0j2.82843 _0.707107j4.94975
_1.34164j0.447214 _2.68328j0.894427 _4.91935j0.894427
_1.38675j0.27735 _2.7735j0.5547 _4.9923j0.27735
_1.41421j1.11022e_16 _2.82843j2.22045e_16 _4.94975j_0.707107
Henry Rich
On 11/16/2023 9:44 AM, 'PMA' via Programming wrote:
Dear J-Programming Forum,
I want to make a script that, given the X/Y values of a 2D dot-graph,
will rotate the graph around its designated origin, looking for
instances of 2 or more points coming into new horizontal &/or vertical
alignment, and at each such instance output the full set of current
X/Y values (integer-rounded).
Could you point me to the main needed ingredients?
Thanks in advance,
Peter Armstrong
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