File:Circle2heart.png
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[edit]DescriptionCircle2heart.png |
English: Circle to non-cardioid heart curve mapping. |
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Date | |||
Source |
Own work by uploader in Maxima and Gnuplot with help of many people ( see references ) This plot was created with Gnuplot by n. |
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Author | Adam majewski | ||
Other versions |
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Long description
[edit]"It's not complex-analytic, but
makes nice-looking heart shapes out of circles centered on the origin (different for different radii)" [1]
so in Maxima notation :
- point of circle is w :
w:x+y*%i;
- point of heart curve is
c:x+f(w)*%i;
where
f(w):=sqrt(abs(realpart(w)))-imagpart(w);
Compare it with
[edit]- Image showing non-cardioid heart curve as a shadow of ring
- similar image, but different position of ring
- Conformal mapping from circle to cardioid
- Image GJL-fft-herz.png
- File:Simple 4-quadrant heart curve.svg
- Image made by Monguin61 using MATLAB
Maxima source code
[edit]/* batch file for maxima mapping from : the circle with center=0 and radius=r given by equation : abs(2*z)=1 where : z:x+y*%i=r*cos(t)+%i*r*sin(t) = onto non-cardioid heart curve is given by equation: c:x+(sqrt(abs(x))- y)*%i; */ /* */ f(w):=sqrt(abs(realpart(w)))-imagpart(w); iMax:1000; /* number of points to draw */ dt:1/iMax; r:4; /* radius of circle */ /* circle D={w:abs(2w)=1 } where w=l(t) t is angle in turns ; 1 turn = 360 degree = 2*Pi radians */ l(t):=r*%e^(%i*t*2*%pi)/2; /* point to point method of drawing */ t:0; /* angle in turns */ /* compute first point of curve, create list and save point to this list */ /* point of unit circle w:l(t); */ w:rectform(ev(l(t), numer)); /* "exponential form prevents allroots from working", code by Robert P. Munafo */ circleList:makelist (w, j, 1, 1); for i:1 thru iMax step 1 do block (t:t+dt, w:rectform(ev(l(t), numer)), /* "exponential form prevents allroots from working", code by Robert P. Munafo */ circleList:cons(w,circleList) ); /* convert one list into 2 lists */ xxCircle:map(realpart, circleList); yyCircle:map(imagpart, circleList); /* convert one list into 2 lists and maps */ xxHeart:map(realpart, circleList); yyHeart:map(f, circleList); load(draw); /* Mario Rodríguez Riotorto http://www.telefonica.net/web2/biomates/maxima/gpdraw/index.html archive copy at the Wayback Machine */ draw(file_name = "a", terminal = 'png, pic_width = 1000, pic_height = 500, columns = 2, gr2d(title = " circle D={w:abs(2*w)=4 } ", points_joined =true, color = red, point_type = 0, points(xxCircle,yyCircle)), gr2d(title = "non-cardioid heart shape curve ", points_joined =true, color = blue, point_type = 0, points(xxHeart,yyHeart)) );
References
[edit]- ↑ Answer by wiki user BenRG on Reference desk
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 20:56, 9 December 2008 | 1,000 × 500 (8 KB) | Soul windsurfer (talk | contribs) | {{Information |Description=more points gives better image |Source= |Date= |Author= |Permission= |other_versions= }} | |
16:37, 9 December 2008 | 1,000 × 500 (8 KB) | Soul windsurfer (talk | contribs) | {{Information |Description={{en|1=Circle to non-cardioid heart curve mapping}} |Source=Own work by uploader |Author=Adam majewski |Date=2008.12.09 |Permission= |other_versions= }} <!--{{ImageUpload|full}}--> |
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