% -%-Fundamental-%- -*-Metafont-*-
% parmesan-macros.mf -- macros for parmesan font
% 
% source file of LilyPond's pretty-but-neat music font
% 
% (c) 2001--2006 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, 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 shifted mid) intersectiontimes line);
		if (t > 0):
			in := mid;
			t_good := t;
		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;


%
% 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;

% EOF