Remove the hyperbola and run with aspect 1. The hyperbola is messing it
up as the plot boundary is square so there is compression along the x
axis (aspect 0.926 works when the hyperbola is included ).
Don Kelly
On 20/09/2013 6:39 PM, Linda Alvord wrote:
Square isn't so square either. Linda (Yet again, life is a series of
approximations.)
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Bo Jacoby
Sent: Wednesday, September 18, 2013 9:52 PM
To: [email protected]
Subject: Re: [Jprogramming] Plotting complex lists
Thanks Linda! The 'aspect 1' makes the plot square. Do you know how to make
circles circular?
________________________________
Fra: Linda Alvord <[email protected]>
Til: [email protected]
Sendt: 2:48 torsdag den 19. september 2013
Emne: Re: [Jprogramming] Plotting complex lists
Try replacing the last line with:
'aspect 1' plot circle,ellipse,:hyperbola
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Bo
Jacoby
Sent: Tuesday, September 17, 2013 12:00 PM
To: [email protected]
Subject: Re: [Jprogramming] Plotting complex lists
One benefit of using complex numbers is that you may forget about
trigonometry.
load'plot'
circle=._1^n=.(%~i:)60
ellipse=.(circle*-.a)+(+circle)*a=.0.8
hyperbola=.-:((+%)j.(-%))^n
plot circle,ellipse,:hyperbola
________________________________
Fra: km <[email protected]>
Til: "[email protected]" <[email protected]>
Sendt: 0:40 tirsdag den 17. september 2013
Emne: Re: [Jprogramming] Plotting complex lists
Summary of results. The strategy of hyperbola below (plotting a
complex
table) is not well known. Henry Rich found it and reported it.
Bo Jacoby gave the best way to change the sign of the real part of a
complex number.
Simply do [: + - .
NB. Complex Analytic Geometry
NB. How to calculate complex number lists and tables for NB. plotting
lines, circles, ellipses, and hyperbolas. How to NB. modify these
tables to achieve translations, rotations, NB. and reflections. Begin
with preliminaries:
steps =: {.@] + -~/@] * [ %~ [: i. >:@[
NB. n steps a,b produces n+1 equally spaced values from a to b
to =: 512 steps , NB. Usage a to b for 512 steps from a to b
sin =: 1&o.
cos =: 2&o.
sinh =: 5&o.
cosh =: 6&o.
arcsinh =: _5&o.
NB. Now, results
line =: 2 : 'm + (n-m)*]'
NB. A line B [ t is point "t of the way from A to B". Command NB.
NB. plot 0 line 1j1 [ _1 to 2
NB.
NB. shows the line segment from _1j_1 to 2j2
NB. You are plotting a list of 513 complex numbers.
parabola =: 1 : '] j. (1 % 4 * m) * *:'
NB. p parabola x produces point x j. y on parabola NB. (*: x) = 4*p*y
. Command NB.
NB. plot 1r4 parabola _2 to 2
NB.
NB. plots parabola y = *: x for x from _2 to 2
NB. You are plotting a list of 513 complex numbers.
ellipse =: 2 : '((m * cos) j. n * sin) 0 to 2p1'
NB. Suggested by Henry Rich
NB. Command
NB.
NB. plot a ellipse b
NB.
NB. plots the ellipse 1 = (*: x % a) + *: y % b .
NB. If a = b you get the circle (*: x) + (*: y) = *: a
hyperbola =: 2 : '[: (,: +) (n * sinh) j. m * cosh'
NB. Suggested by Henry Rich
toh =: [: to/ [: arcsinh %~
NB. b toh c,d is (arcsinh c%b) to (arcsinh d%b)
NB. Command
NB.
NB. plot a hyperbola b [ b toh c,d
NB.
NB. plots y^2/a^2 - x^2/b^2 = 1 for x from c to d.
NB. Remember the pattern b [ b toh c,d
NB. You are plotting rows of a 2 by 513 table to get the two NB.
branches of the hyperbola.
NB. Rotations, translations, and reflections
NB. Multiply a complex number list or table by (^&j. theta) NB. to
rotate all of its points by theta radians. The center NB. of rotation
is the origin 0 = 0j0 .
NB. Add 5j3 to a complex list or table to move all of its points NB.
the distance and direction of 5j3 from 0j0.
NB. Use (+ list) or (+ table) (monadic + is conjugate) to NB. reflect
all the points of the list or table across the NB. line through 0j0
and
1j0 -- the x-axis. Afterwards NB. multiply by (^&j. theta) to achieve
a reflection across NB. the line through 0j0 and (^&j. theta).
NB. Multiply a positive number p times a list or table to NB. achieve
an expansion from 0 or compression toward 0 NB. according as p > 1
or p < 1 .
NB. If you want to combine several operations do the NB. reflection
first and the translation last.
NB. Example
NB.
NB. plot (^&j. theta) * p parabola _2 to 3 NB.
NB. plots a parabola rotated by theta radians, with 0j0 NB. the center
of rotation. If theta is _1r2p1 (that is NB. - pi%2 radians) you have
converted a (*: x) = 4 * p * y NB. parabola into a (*: y) = 4 * p *
x parabola.
--Kip Murray
Sent from my iPad
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