File:Normal lines to the ellipse.svg
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Summary[edit]
DescriptionNormal lines to the ellipse.svg |
English: Normal lines to the ellipse.[1] The evolute of the ellipse ( = Stretched astroid) can be seen. The streched astroid itself is not not drawn: we see it as the locus of points where the lines are especially close to each other. Stretched = "squashed" astroid = dilated in one direction only= the Lamé curve. Is it generalization of the astroid curve) |
Date | |
Source | Own work |
Author | Adam majewski |
Other versions |
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SVG development InfoField | This plot was created with Gnuplot. This plot uses embedded text that can be easily translated using a text editor. |
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I, the copyright holder of this work, hereby publish it under the following license:
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Maxima CAS src code[edit]
/* =============== Batch file for Maxima CAS save as a c.mac run maxima : maxima and then : batch("e.mac"); ------------text output =-------------- maxima Maxima 5.41.0 http://maxima.sourceforge.net using Lisp GNU Common Lisp (GCL) GCL 2.6.12 Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) batch("e.mac"); read and interpret file: #p/home/a/maxima/batch/curves/ellipse/e2/e.mac (%i2) kill(all) (%o0) done (%i1) remvalue(all) (%o1) [] (%i2) ratprint:false (%o2) false (%i3) display2d:false (%o3) false (%i4) ellipse:x^2/a^2+y^2/b^2-1 (%o4) y^2/b^2+x^2/a^2-1 (%i5) GiveSlopeEquation(e):=block([deriv,m],depends(y,x),deriv:diff(e,x), m:solve(deriv,'diff(y,x)),m:m[1],m:rhs(m),return(m)) (%i6) define(m(x,y),GiveSlopeEquation(ellipse)) (%o6) m(x,y):=-(b^2*x)/(a^2*y) (%i7) t:0.33 (%o7) 0.33 (%i8) a:2 (%o8) 2 (%i9) b:1 (%o9) 1 (%i10) x0:a*cos(t) (%o10) 1.892084687056774 (%i11) y0:b*sin(t) (%o11) 0.3240430283948683 (%i12) m0:m(x0,y0) (%o12) -1.459748028239586 (%i13) tangent:y = m0*(x-x0)+y0 (%o13) y = 0.3240430283948683-1.459748028239586*(x-1.892084687056774) (%i14) normal:y = (-(x-x0))/m0+y0 (%o14) y = 0.3240430283948683-0.6850497350600779*(1.892084687056774-x) (%i15) load(draw) (%o15) "/usr/share/maxima/5.41.0/share/draw/draw.lisp" (%i16) path:"~/maxima/batch/curves/ellipse/e2/" (%i17) draw2d(user_preamble = "set key top right; unset mouse; ", terminal = 'svg,file_name = sconcat(path,"ell3"),font_size = 13, font = "Liberation Sans", title = "Normal and tangent line to the ellipse ", proportional_axes = 'xy,xrange = [-3,3],yrange = [-3,3], ip_grid = [100,100],color = blue,key = "circle", implicit(ellipse,x,-4,4,y,-4,4),key = "tangent",color = red, implicit(tangent,x,-4,4,y,-4,4),key = "normal",color = green, implicit(normal,x,-4,4,y,-4,4),key = "point", point_type = filled_circle,color = black,points([[x0,y0]])) (%o17) "e.mac" */ kill(all); remvalue(all); ratprint:false; /* a message informing the user of the conversion of floating point numbers to rational numbers is displayed. */ display2d:false; /* ---------- functions ---------------------------------------------------- */ /* ellipse in implicit form */ ellipse : x^2/a^2 + y^2/b^2 - 1; /* https://www.linuxjournal.com/content/maximum-calculus-maxima implicit differentiation compute m equation find dy/dx of implicit equation e */ GiveSlopeEquation(e):=block( [deriv,m], depends(y,x), deriv:diff(e,x), m:solve(deriv,'diff(y,x)), m:m[1], m:rhs(m), return(m) )$ /* m(x,y):=-x/y */ define( m(x,y), GiveSlopeEquation(ellipse)); give_line(t):=block( [x0, y0, m0], t:float(t), /* compute point z = x+y*i of the ellipse */ x0: a*cos(t), y0: b*sin(t), /* compute slope */ m0 : m(x0,y0), return(explicit(-(x-x0)/m0 + y0,x,-4,4)) /* normal */ )$ /* ellipse parameters */ a:2; b:1; iMin:1; /* cot: argument 0.0 isn't in the domain of cot. #0: give_line(t=0) */ iMax:200; /* --------------------computations -------------------------------*/ tt: makelist(2*%pi*i/iMax, i, iMin, iMax)$ /* list of angles from 0 to 2 Pi */ lines: map(give_line,tt)$ /* ------- draw --------------------------------------- */ load(draw); path:"~/maxima/batch/curves/ellipse/en/"$ /* pwd, if empty then file is in a home dir , path should end with "/" */ draw2d( user_preamble="set key top right; unset mouse; ", terminal = 'svg, file_name = sconcat(path,"en200_2000_e"), font_size = 50, font = "Liberation Sans", /* https://commons.wikimedia.org/wiki/Help:SVG#Font_substitution_and_fallback_fonts */ title= "Normal lines to the ellipse ", proportional_axes = 'xy, dimensions = [2000,2000], xrange = [-5,5], yrange = [-5,5], ip_grid=[200,200], color= blue, key = "", lines, color=black, implicit(ellipse, x,-4,4, y,-4,4) )$
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 15:50, 22 June 2019 | 2,000 × 2,000 (290 KB) | Soul windsurfer (talk | contribs) | better quality | |
15:44, 22 June 2019 | 2,000 × 2,000 (250 KB) | Soul windsurfer (talk | contribs) | User created page with UploadWizard |
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Short title | Gnuplot |
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Image title | Produced by GNUPLOT 5.3 patchlevel 0 |
Width | 2000 |
Height | 2000 |