(get_subpoint, find_envelope_cusp): New macros.

diff --git a/mf/parmesan-macros.mf b/mf/parmesan-macros.mf
index 6fd040c53168d10077b981311a993cea3261a83d..e72bcbf1fca8060b7ec85c8081550a44f0863044 100644 (file)
--- a/mf/parmesan-macros.mf
+++ b/mf/parmesan-macros.mf
@@ -26,7 +26,7 @@ def find_tangent (expr p, curve, p_in, p_out) =
                mid := 0.5 [in, out];
                exitif abs (out - mid) <= eps;
                t := xpart (curve intersectiontimes (p -- mid));
-               if (t > 0):
+               if t > 0:
                        in := mid;
                        t_good := t;
                else:
@@ -47,7 +47,7 @@ enddef;
 %
 def find_tangent_shift (expr line, curve, p_in, p_out) =
        begingroup;
-       save mid, t, t_good, in, out;
+       save mid, t, in, out;
        pair mid, in, out;
 
        in := p_in;
@@ -57,9 +57,8 @@ def find_tangent_shift (expr line, curve, p_in, p_out) =
                mid := 0.5 [in, out];
                exitif abs (out - mid) <= eps;
                t := xpart ((curve shifted mid) intersectiontimes line);
-               if (t > 0):
+               if t > 0:
                        in := mid;
-                       t_good := t;
                else:
                        out := mid;
                fi;
@@ -91,6 +90,15 @@ def get_subpath (expr curve, dir_in, dir_out, offset) =
 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.
@@ -111,4 +119,97 @@ def get_subpath_i (expr curve, dir_in, dir_out, 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