%% sinewaves.ldf %% Created by Laurence D. Finston (LDF) Do 10. Aug 09:53:53 CEST 2023 %% * (1) Copyright and License. %%%% Copyright (C) 2023 Laurence Finston %%%% This file is free software; you can redistribute it 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 %%%% Please send bug reports to Laurence.Finston@gmx.de %%%% The author can be contacted at: %%%% Laurence Finston %%%% Laurence.Finston@gmx.de input "plainldf.lmc"; medium_pen := pencircle scaled (.333mm, .333mm, .333mm); verbatim_tex "\magnification=3000"; verbatim_metapost "dotlabeldiam := 3mm;"; %verbatim_metapost "prologues := 3;outputtemplate := \"%j_%3c.eps\";"; verbatim_metapost "outputformat:=\"png\";outputtemplate := \"%j_%3c.png\";" & "outputformatoptions := \"antialias=none\";"; %% * (1) point p[]; point a[]; path Q; path q[]; reg_polygon r[]; circle c[]; ellipse e[]; picture v[]; transform t[]; string s; boolean b; bool_point bp; bool_point_vector bpv; focus f; set f with_position (0, 10, -40) with_direction (0, 10, 10) with_distance 45; numeric frame_wd; numeric frame_ht; % \special{papersize=400mm, 225mm} %% Frame size, proportion 16x9 % \hsize=400mm % \vsize=225mm %% (* (/ 400 16.0) 9) 225.0 frame_wd := 400mm; frame_ht := 225mm; path frame[]; frame1 := (-.5frame_wd, -.5frame_ht) -- (.5frame_wd, -.5frame_ht) -- (.5frame_wd, .5frame_ht) -- (-.5frame_wd, .5frame_ht) -- cycle; frame0 := frame1 scaled (.9, .9); % (* 400 .9) 360.0 % (* 225 .9) 202.5 %% * (1) pickup medium_pen; plane M; line L[]; input "sinewaves.lmc"; %% * (1) for j = 0 upto 3: p[j] := get_point (j) frame0; endfor; for j = 0 upto 3: p[4+j] := mediate(p[j], p[(j+1) mod 4]); endfor; pickup big_pen; save_offset := 0.03125pi; offset := save_offset; increment := pi/120; period := 5pi-1.5increment; amplitude := 5; frequency_val := 4.5; amplitude_sign_val := 1; increment_sign_val := 1; boolean do_labels; do_labels := false; % true; % %% * (1) if false: beginfig(400); draw frame0; draw frame1; fill p0 -- p1 -- p5 -- p7 -- cycle with_color red; fill p2 -- p3 -- p7 -- p5 -- cycle with_color blue; endfig with_projection parallel_x_y; fi %% * (1) for i = 0 upto 300: beginfig(i); draw frame0; %draw p7 -- p5; if do_labels: dotlabel.bot("$p_0$", p0); dotlabel.bot("$p_1$", p1); dotlabel.top("$p_2$", p2); dotlabel.top("$p_3$", p3); dotlabel.bot("$p_4$", p4); dotlabel.rt("$p_5$", p5); dotlabel.top("$p_6$", p6); dotlabel.lft("$p_7$", p7); fi; % if (i == 238) or (i == 239): % message "increment: " & decimal increment; % pause; % fi; sinewave (Q) {p7, p5, period, amplitude, increment, frequency_val, offset}; q0 := Q; %draw q0 with_color red; dot_pen := pencircle scaled (3mm, 3mm, 3mm); p8 := get_point 0 q0; %drawdot p8 with_color red with_pen dot_pen; p9 := get_last_point q0; %drawdot p9 with_color red with_pen dot_pen; p10 := (xpart p5, ypart p9); %drawdot p10 with_color green with_pen dot_pen; q1 := q0 .. p10 -- p2 -- p3 -- p8; q1 += cycle; draw frame1; draw frame0; %draw q1 with_color blue; fill frame0 with_color blue; fill q1 with_color red; q2 := q0 .. p10 -- p1 -- p0 -- p8; q2 += cycle; %draw q2 with_color red; % fill frame0 with_color red on_picture v2; % fill q2 with_color blue on_picture v2; endfig with_projection parallel_x_y; %% ** (2) offset += save_offset; if magnitude(amplitude) >= 9: amplitude_sign_val *= -1; fi; amplitude += .125 * amplitude_sign_val; if magnitude(increment) > pi: increment_sign_val *= -1; fi; increment += (pi/120) * increment_sign_val; if increment == 0: increment := pi/120; fi; message "Fig. " & decimal i; endfor; bye; % beginfig(1); % draw frame0; % draw frame1; % endfig; %% * (1) Sine wave with moving dot, three colors. %% * (1) Fig. 1 pen big_dot_pen; big_dot_pen := pencircle scaled (.25, .25, .25); %show length q0; %pause; beginfig(1); draw frame1; fill frame0 with_color dark_green; fill q1 with_color red; v0 := current_picture; clip v0 to frame0; output v0 with_projection parallel_x_y; clear current_picture; clear v0; draw frame0; draw frame1; endfig with_projection parallel_x_y; %% * (1) Fig. 2--66 n := length q0; n -= 1; for i = 0 upto n: beginfig(i+2); fill frame0 with_color dark_green; fill q1 with_color red; if i > 0: draw subpath(0, i) of q0 with_color blue with_pen big_dot_pen; fi; drawdot p[i+8] with_color blue with_pen big_dot_pen; v0 := current_picture; clip v0 to frame0; output v0 with_projection parallel_x_y; clear current_picture; clear v0; draw frame0; draw frame1; message "Fig. " & decimal (i+2); endfig with_projection parallel_x_y; endfor; %pause; %% * (1) Fig. 67--131 for i = 0 upto n: beginfig(67+i); fill frame0 with_color dark_green; fill q1 with_color red; draw q0 with_color blue with_pen big_dot_pen; if i > 0: draw subpath(0, i) of q0 with_color orange with_pen big_dot_pen; fi; drawdot p[i+8] with_color orange with_pen big_dot_pen; v0 := current_picture; clip v0 to frame0; output v0 with_projection parallel_x_y; clear current_picture; clear v0; draw frame0; draw frame1; message "Fig. " & decimal (67+i); endfig with_projection parallel_x_y; endfor; %% * (1) Fig. 132-- 196 for i = 0 upto n: beginfig(132+i); fill frame0 with_color dark_green; fill q1 with_color red; draw q0 with_color orange with_pen big_dot_pen; if i > 0: draw subpath(0, i) of q0 with_color violet with_pen big_dot_pen; fi; drawdot p[i+8] with_color violet with_pen big_dot_pen; v0 := current_picture; clip v0 to frame0; output v0 with_projection parallel_x_y; clear current_picture; clear v0; draw frame0; draw frame1; message "Fig. " & decimal (132+i); endfig with_projection parallel_x_y; endfor; bye; %% * (1) Fig. 1. beginfig(1); rectangle r[]; r0 := unit_rectangle scaled (4, 0, 4); for i = 0 upto 3: p[i] := get_point (i) r0; endfor; dotlabel.bot("$p_0$", p0); dotlabel.bot("$p_1$", p1); dotlabel.top("$p_2$", p2); dotlabel.top("$p_3$", p3); p4 := (1, -2); p5 := (-2, 2); draw r0; q0 := p4 -- p5; draw q0; draw r0; dotlabel.lft("$p_4$", p4); dotlabel.lft("$p_5$", p5); b := q2 is_colinear r0; % message "b:"; % show b; p7 := p2 shifted (1, 1); p8 := p1 shifted (2, -1); dotlabel.rt("$p_7$", p7); dotlabel.rt("$p_8$", p8); q1 := p7 -- p8; draw q1; L0 := get_line q0; % message "L0:"; % show L0; L1 := get_line q1; p9 := mediate(p8, p7); p10 := mediate(p8, p7, 1.5); dotlabel.lft("$p_{9}$", p9) with_color blue; dotlabel.lft("$p_{10}$", p10) with_color blue; q2 := p9 -- p10; draw q2 with_color blue; L2 := get_line q2; % message "L1:"; % show L1; % message "L2:"; % show L2; %p11 := get_direction L1; % message "p11:"; % show p11; % p12 := get_direction L2; % message "p12:"; % show p12; % b := L1 ~= L2; % message "b:"; % show b; % if L1 ~= L2: % message "Equivalent."; % else: % message "Not equivalent."; % fi; % pause; b := L1 is_parallel L2; message "b:"; show b; pause; q3 := q2 shifted (1, 0); L3 := get_line q3; % b := L2 is_parallel L3; % message "b:"; % show b; % pause; endfig with_focus f; bye; %% ** (2) %% * (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. %% LDF 2004.02.12. %% (progn (metafont-mode) (outline-minor-mode t) (setq fill-column 80) (ignore '( %% )) (setq outline-regexp "%% [*\f]+")) %% * (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: