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% -%-Fundamental-%- -*-Metafont-*-
% parmesan-macros.mf -- macros for parmesan font
%
% source file of LilyPond's pretty-but-neat music font
%
% (c) 2001--2009 Juergen Reuter <reuter@ipd.uka.de>
%
%
% Find point on `curve' which gives the tangent between point `p'
% and `curve'. To guide the search, two auxiliary points must be
% specified, `p_in' and `p_out'. The line between `p' and `p_in'
% must intersect `curve', while the line between `p' and `p_out'
% must not.
%
def find_tangent (expr p, curve, p_in, p_out) =
begingroup;
save mid, t, t_good, in, out;
pair mid, in, out;
in := p_in;
out := p_out;
forever:
mid := 0.5 [in, out];
exitif abs (out - mid) <= eps;
t := xpart (curve intersectiontimes (p -- mid));
if t > 0:
in := mid;
t_good := t;
else:
out := mid;
fi;
endfor;
point t_good of curve
endgroup
enddef;
%
% Shift `curve' along the line given by the auxiliary points `p_in'
% and `p_out' until `line' is a tangent, and return the shift.
% If `curve' is shifted to position `p_in', it must intersect
% `line', while shifted to `p_out' it must not.
%
def find_tangent_shift (expr line, curve, p_in, p_out) =
begingroup;
save mid, t, in, out;
pair mid, in, out;
in := p_in;
out := p_out;
forever:
mid := 0.5 [in, out];
exitif abs (out - mid) <= eps;
t := xpart ((curve shifted mid) intersectiontimes line);
if t > 0:
in := mid;
else:
out := mid;
fi;
endfor;
mid
endgroup
enddef;
%
% Get subpath specified by `dir_in' and `dir_out' of `curve'
% which is then shifted by `offset'. Assure that result has
% the same orientation as `curve'.
%
def get_subpath (expr curve, dir_in, dir_out, offset) =
begingroup;
save t_in, t_out;
t_in := directiontime dir_in of curve;
t_out := directiontime dir_out of curve;
if t_in > t_out:
t_out := t_out + length curve;
fi;
(subpath (t_in, t_out) of curve) shifted offset
endgroup
enddef;
%
% Get point specified by `dir_' of `curve' which is then
% shifted by `offset'.
%
def get_subpoint (expr curve, dir_, offset) =
(directionpoint dir_ of curve) shifted offset
enddef;
%
% This is the same as `get_subpath', except that the time values
% used to construct the resulting subpath are rounded to integers.
%
def get_subpath_i (expr curve, dir_in, dir_out, offset) =
begingroup;
save t_in, t_out;
t_in := directiontime dir_in of curve;
t_out := directiontime dir_out of curve;
if t_in > t_out:
t_out := t_out + length curve;
fi;
(subpath (floor (t_in + 0.5), floor (t_out + 0.5)) of curve)
shifted offset
endgroup
enddef;
%
% Find envelope cusp created by `object' moved along `curve', using
% step value `s' for initial intermediate points. `s' must be small
% enough so that this macro finds at least one point on the envelope
% between the `entrance' and `exit' points of the cusp which has
% a significantly different direction vector.
%
% This function returns a time value on `curve'; if there is no
% cusp, it returns -1.
%
def find_envelope_cusp (expr object, curve, s) =
begingroup;
save mid, p, t, t_good, delta, start, stop, do_exit;
pair p[];
boolean do_exit;
p0 := (directionpoint (direction 0 of curve) of object)
shifted (point 0 of curve);
p1 := (directionpoint (direction s of curve) of object)
shifted (point s of curve);
t := s;
forever:
t := t + s;
exitif t >= length curve;
p2 := (directionpoint (direction t of curve) of object)
shifted (point t of curve);
if p2 <> p1:
delta := angle (p2 - p1) - angle (p1 - p0);
if delta > 180:
delta := delta - 360;
fi;
% we check for a direction change by more than
% than 45 degrees
if abs (delta) >= 45:
do_exit := true;
else:
do_exit := false;
fi;
p0 := p1;
p1 := p2;
fi;
% having `exitif' within an if-clause doesn't work
exitif do_exit;
endfor;
if t >= length curve:
t_good := -1;
else:
% the wanted point lies between `t - s' and `t'
start := t - s;
stop := t;
t_good := start;
forever:
mid := 0.5 [start, stop];
exitif abs (stop - mid) <= eps;
p0 := (directionpoint (direction start of curve)
of object) shifted (point start of curve);
p1 := (directionpoint (direction mid of curve)
of object) shifted (point mid of curve);
p2 := (directionpoint (direction stop of curve)
of object) shifted (point stop of curve);
exitif (length (p1 - p0) = 0)
or (length (p2 - p1) = 0);
delta := angle (p2 - p1) - angle (p1 - p0);
if delta > 180:
delta := delta - 360;
fi;
if abs (delta) >= 45:
stop := mid;
t_good := mid;
else:
start := mid;
t_good := stop;
fi;
endfor;
fi;
t_good
endgroup
enddef;
% EOF
|
