%% scale_length.ldf %% Created by Laurence D. Finston (LDF) Fri 08 Jul 2022 06:39:54 AM CEST %% * (1) Copyright and License. %%%% Copyright (C) 2022 Laurence Finston %%%% You can redistribute this file and/or modify %%%% it under the terms of the GNU General Public License as published by %%%% the Free Software Foundation; either version 3 of the License, or %%%% (at your option) any later version. %%%% This file is distributed in the hope that it will be useful, %%%% but WITHOUT ANY WARRANTY; without even the implied warranty of %%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the %%%% GNU General Public License for more details. %%%% You should have received a copy of the GNU General Public License %%%% along with this file; if not, write to the Free Software %%%% Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA %%%% The author can be contacted at: %%%% Laurence Finston %%%% Laurence.Finston@gmx.de %% * (1) Top verbatim_metapost "prologues := 3;\noutputtemplate := \"%j%3c.eps\";"; input "plainldf.lmc"; pickup pencircle scaled (.333mm, .333mm, .333mm); numeric wd; numeric n[]; picture v[]; beginfig(1); point p[]; numeric r; r := 1.0595; point a[]; a0 := (1cm, 0); j := 24; for i = 0 upto 24: % message "i == " & decimal i; % message "j == " & decimal j; if i > 0: a[i] := r*a[i-1] shifted a0; fi; p[j] := (-xpart a[i], ypart a[i]); if j < 13: dotlabel.bot("$p_{" & decimal j & "}$", p[j]) shifted (0, -.5cm); fi j -= 1; endfor; %pause; dotlabel.bot("$p_0$", p0) shifted (0, -.5cm); dotlabel.bot("C", p0) shifted (0, -1.5cm); dotlabel.bot("C\#", p1) shifted (0, -1.5cm); dotlabel.bot("D", p2) shifted (0, -1.5cm); dotlabel.bot("D\#", p3) shifted (0, -1.5cm); dotlabel.bot("E", p4) shifted (0, -1.5cm); dotlabel.bot("F", p5) shifted (0, -1.5cm); dotlabel.bot("F\#", p6) shifted (0, -1.5cm); dotlabel.bot("G", p7) shifted (0, -1.5cm); dotlabel.bot("G\#", p8) shifted (0, -1.5cm); dotlabel.bot("A", p9) shifted (0, -1.5cm); dotlabel.bot("A\#", p10) shifted (0, -1.5cm); dotlabel.bot("B", p11) shifted (0, -1.5cm); dotlabel.bot("C", p12) shifted (0, -1.5cm); pickup pencircle scaled (.333mm, .333mm, .333mm); drawarrow p0 -- (p24 shifted (2cm, 0)) with_color dark_gray; p30 := p0 shifted (0, 6cm); dotlabel.lft("$p_{30}$", p30); draw p0 -- p30; p31 := p24 shifted (0, 2cm); dotlabel.llft("$p_{31}$", p31); draw p24 -- p31; p32 := (xpart p0, ypart p31); dotlabel.lft("$p_{32}$", p32); drawarrow p32 -- (p31 shifted (2cm, 0)) with_color dark_gray; draw p30 -- p31 with_pen pencircle scaled (.5mm, .5mm, .5mm); dotlabel.bot("$p_{24}$", p24) shifted (0, -.5cm); p33 := p1 shifted (0, 5cm); dotlabel.lrt("$p_{33}$", p33); draw p1 -- p33; draw p30 -- p33 -- p31 with_color red; p34 := p4 shifted (0, 4cm); dotlabel.lrt("$p_{34}$", p34) shifted (0, -2pt); draw p4 -- p34; draw p30 -- p34 -- p31 with_color blue; p35 := p7 shifted (0, 3cm); dotlabel.llft("$p_{35}$", p35); draw p7 -- p35; draw p30 -- p35 -- p31 with_color dark_green; p36 := p12 shifted (0, 2.333cm); dotlabel.llft("$p_{36}$", p36) shifted (0, -.5cm); draw p36 -- p36 shifted (-.333cm, -.575cm) with_pen pencircle scaled (.25mm, .25mm, .25mm); draw p12 -- p36; draw p30 -- p36 -- p31 with_color purple; p37 := (p7, p35) intersection_point (p30, p31); %dotlabel.llft("$p_{37}$", p37); p38 := (p7, p35) intersection_point (p32, p31); %dotlabel.ulft("$p_{38}$", p38); p39 := (p1, p33) intersection_point (p32, p31); dotlabel.llft("$p_{39}$", p39); p40 := (p1, p33) intersection_point (p30, p31); dotlabel.ulft("$p_{40}$", p40); v0 := current_picture; scale v0 (.667, .667); for i = 13 upto 24: dotlabel.bot("$p_{" & decimal i & "}$", p[i]) shifted (0, -.5cm); endfor; dotlabel.bot("C\#", p13) shifted (0, -1.5cm); dotlabel.bot("D", p14) shifted (0, -1.5cm); dotlabel.bot("D\#", p15) shifted (0, -1.5cm); dotlabel.bot("E", p16) shifted (0, -1.5cm); dotlabel.bot("F", p17) shifted (0, -1.5cm); dotlabel.bot("F\#", p18) shifted (0, -1.5cm); dotlabel.bot("G", p19) shifted (0, -1.5cm); dotlabel.bot("G\#", p20) shifted (0, -1.5cm); dotlabel.bot("A", p21) shifted (0, -1.5cm); dotlabel.bot("A\#", p22) shifted (0, -1.5cm); dotlabel.bot("B", p23) shifted (0, -1.5cm); dotlabel.bot("C", p24) shifted (0, -1.5cm); n0 := magnitude(p31 - p30); label.top("$n_0=\overline{\vbox to 1.5ex{\vss}p_{30}p_{31}}=" & decimal n0 & "$", p37) shifted (0, .25cm); n1 := magnitude(p32 - p31); label.llft("$n_1=" & decimal n1 & "$", p38) shifted (0, -.125cm); label("\setbox0=\hbox{$n_0-n_1$}\vbox{\hbox{$n_0-n_1 = " & decimal (n0 - n1) & "$}" & "\hbox{\hbox to \wd0{$n_0/n_1$\hss} $= " & decimal (n0 / n1) & "$}}", p37 shifted (4cm, 2cm)); n6 := magnitude(p40 - p31); label.urt("$n_6=\overline{\vbox to 1.5ex{\vss}p_{40}p_{31}}=" & decimal n6 & "$", p40) shifted (0, .25cm); p41 := mediate(p30, p33); %dotlabel.lft("$p_{41}$", p41); n7 := magnitude(p30 - p33); label.bot("$n_7=" & decimal n7 & "$", p41) shifted (-10pt, -.25cm) with_color red; p42 := mediate(p33, p34); %dotlabel.lft("$p_{42}$", p42); n8 := magnitude(p33 - p31); label.bot("$n_8=\overline{\vbox to 1.5ex{\vss}p_{33}p_{31}}=" & decimal n8 & "$", p42) shifted (0, -2pt) with_color red; n9 := magnitude(p39 - p31); label.top("$n_9=\overline{\vbox to 1.5ex{}p_{39}p_{31}}=" & decimal n9 & "$", p39 shifted (4cm, 0)); p43 := p42 shifted (.5cm, 4.5cm); %dotlabel.lft("$p_{43}$", p43); label.rt("\setbox0=\hbox{$n_6-n_8$ }" & "\vbox{\hbox{$n_6-n_8=" & decimal (n6 - n8) & "$}" & "\hbox{$n_6-n_9=" & decimal (n6 - n9) & "$}" & "\hbox{$n_8-n_9=" & decimal (n8 - n9) & "$}" & "\hbox{\hbox to \wd0{$n_6/n_8$\hfil}" & "$=" & decimal (n6 / n8) & "$}" & "\hbox{\hbox to \wd0{$n_6/n_9$\hfil}" & "$=" & decimal (n6 / n9) & "$}" & "\hbox{\hbox to \wd0{$n_8/n_9$\hfil}" & "$=" & decimal (n8 / n9) & "$}" & "}", p43); %pause; v10 := current_picture; scale v10 (.667, .667); current_picture := v10; endfig with_projection parallel_x_y; beginfig(2); v1 := v0; scale v1 (.667, 1); output v1 with_projection parallel_x_y; for i = 13 upto 24: drawdot p[i] with_pen pencircle scaled (1mm, 1mm, 1mm); endfor; n2 := .667 * magnitude(p31 - p30); label.top("$n_2=" & decimal n2 & "$", p37) shifted (0, .25cm); n3 := .667 * magnitude(p31 - p32); label.llft("$n_3=" & decimal n3 & "$", p38) shifted (0, -.125cm); label("\setbox0=\hbox{$n_2-n_3$}\vbox{\hbox{$n_2-n_3 = " & decimal (n2 - n3) & "$}" & "\hbox{\hbox to \wd0{$n_2/n_3$\hss} $= " & decimal (n2 / n3) & "$}}", p37 shifted (7cm, 2cm)); n10 := .667 * magnitude(p40 - p31); %% n6 n11 := .667 * magnitude(p30 - p33); %% n7 n12 := .667 * magnitude(p33 - p31); %% n8 n13 := .667 * magnitude(p39 - p31); %% n9 label.urt("$n_{10}=\overline{\vbox to 1.5ex{\vss}p_{40}p_{31}}=" & decimal n10 & "$", p40) shifted (0, .25cm); label.bot("$\scriptstyle n_{11}=" & decimal n11 & "$", p41) shifted (0, -.5cm) with_color red; label.bot("$n_{12}=\overline{\vbox to 1.5ex{\vss}p_{33}p_{31}}=" & decimal n12 & "$", p42) shifted (0, -.25cm) with_color red; label.top("$n_{13}=\overline{\vbox to 1.5ex{}p_{39}p_{31}}=" & decimal n13 & "$", p39 shifted (5cm, 0)); label.rt("\setbox0=\hbox{$n_{10}-n_{12}$ }" & "\vbox{\hbox{$n_{10}-n_{12}=" & decimal (n10 - n12) & "$}" & "\hbox{$n_{10}-n_{13}=" & decimal (n10 - n13) & "$}" & "\hbox{$n_{12}-n_{13}=" & decimal (n12 - n13) & "$}" & "\hbox{\hbox to \wd0{$n_{10}/n_{12}$\hfil}" & "$=" & decimal (n10 / n12) & "$}" & "\hbox{\hbox to \wd0{$n_{10}/n_{13}$\hfil}" & "$=" & decimal (n10 / n13) & "$}" & "\hbox{\hbox to \wd0{$n_{12}/n_{13}$\hfil}" & "$=" & decimal (n12 / n13) & "$}" & "}", p43 shifted (3cm, 0)); scale current_picture (.667, .667); scale current_picture (.667, 1); endfig with_projection parallel_x_y; beginfig(3); v2 := v0; scale v2 (.375, 1); output v2 with_projection parallel_x_y; for i = 13 upto 24: drawdot p[i] with_pen pencircle scaled (1mm, 1mm, 1mm); endfor; n4 := .375 * magnitude(p31 - p30); label.top("$n_4=" & decimal n4 & "$", p37) shifted (0, .25cm); n5 := .375 * magnitude(p31 - p32); label.llft("$n_5=" & decimal n5 & "$", p38) shifted (0, -.125cm); label("\setbox0=\hbox{$n_4-n_5$}\vbox{\hbox{$n_4-n_5 = " & decimal (n4 - n5) & "$}" & "\hbox{\hbox to \wd0{$n_4/n_5$\hss} $= " & decimal (n4 / n5) & "$}}", p37 shifted (13cm, 2cm)); n14 := .375 * magnitude(p40 - p31); %% n6 n15 := .375 * magnitude(p30 - p33); %% n7 n16 := .375 * magnitude(p33 - p31); %% n8 n17 := .375 * magnitude(p39 - p31); %% n9 label.urt("$n_{14}=\overline{\vbox to 1.5ex{\vss}p_{40}p_{31}}=" & decimal n14 & "$", p40) shifted (0, .25cm); label.bot("$n_{15}=\overline{\vbox to 1.5ex{}p_{30}p_{33}}=" & decimal n15 & "$", p30) shifted (0, 3cm) with_color red; label.bot("$n_{16}=\overline{\vbox to 1.5ex{\vss}p_{33}p_{31}}=" & decimal n16 & "$", p30) shifted (0, 2cm) with_color red; label.top("$n_{17}=\overline{\vbox to 1.5ex{}p_{39}p_{31}}=" & decimal n17 & "$", p39 shifted (5cm, 0)); label.rt("\setbox0=\hbox{$n_{14}-n_{16}$ }" & "\vbox{\hbox{$n_{14}-n_{16}=" & decimal (n14 - n16) & "$}" & "\hbox{$n_{14}-n_{17}=" & decimal (n14 - n17) & "$}" & "\hbox{$n_{16}-n_{17}=" & decimal (n16 - n17) & "$}" & "\hbox{\hbox to \wd0{$n_{14}/n_{16}$\hfil}" & "$=" & decimal (n14 / n16) & "$}" & "\hbox{\hbox to \wd0{$n_{14}/n_{17}$\hfil}" & "$=" & decimal (n14 / n17) & "$}" & "\hbox{\hbox to \wd0{$n_{16}/n_{17}$\hfil}" & "$=" & decimal (n16 / n13) & "$}" & "}", p43 shifted (3cm, 0)); scale current_picture (.667, .667); scale current_picture (.375, 1); endfig with_projection parallel_x_y; end_mp; end; %% ** (2) End of 3DLDF code. %% * (1) Emacs-Lisp code for use in indirect buffers when using the %% GNU Emacs editor. The local variable list is not evaluated when an %% indirect buffer is visited, so it's necessary to evaluate the %% following s-expression in order to use the facilities normally %% accessed via the local variables list. %% \initials{LDF 2004.02.12}. %% (progn (metapost-mode) (outline-minor-mode t) (setq fill-column 80)) %% * (1) Local variables for Emacs. %% Local Variables: %% mode:metapost %% eval:(outline-minor-mode t) %% eval:(read-abbrev-file abbrev-file-name) %% outline-regexp:"%% [*\f]+" %% End: