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 >> >>---------------------------------------------------------------------- >>For information about J forums see http://www.jsoftware.com/forums.htm >> >> >> >---------------------------------------------------------------------- >For information about J forums see http://www.jsoftware.com/forums.htm > >---------------------------------------------------------------------- >For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
