(draw_petrucci_g_clef): Resolve all self intersections.

The algorithm used by mf2pt1 to compute the correct orientation of an
outline may fail if there are self intersections.  For simple outlines
which don't intersect other outlines this is automatically fixed by
fontforge, but more complicated shapes need the correct orientation.

Note that the recently released metapost 1.0 has an improved version
of the `turningnumber' primitive which gives reliable results in
all cases (including paths with self intersections); however, mf2pt1
hasn't been updated yet to use it.

diff --git a/mf/parmesan-clefs.mf b/mf/parmesan-clefs.mf
index a6980172a67177fbcf66bedac641822b82bf0eeb..3181eaa935a16c1e5467d46f717ec7fe785038d0 100644 (file)
--- a/mf/parmesan-clefs.mf
+++ b/mf/parmesan-clefs.mf
@@ -1385,40 +1385,51 @@ def draw_petrucci_g_clef (expr exact_center, reduction) =
             & subpath (0, times1 - s / 4) of sub_outlines1
             -- cycle;
 
+
        % we approximate `draw paths2'
        for i = 1 step s until (length paths2 - s):
                dirs[i + 20] := direction (i - 1) of paths2;
        endfor;
 
-       fill get_subpath (ellipse, -dirs21, dirs21, z21)
-            for i = (1 + s) step s until (length paths2 - s):
-                    .. get_subpoint (ellipse, dirs[i + 20],
-                                     point (i - 1) of paths2)
-            endfor
-            .. get_subpath (ellipse, up, z26 - z25, z25)
-            -- get_subpath (ellipse, z26 - z25, z25 - z26, z26)
-            -- get_subpoint (ellipse, z25 - z26, z25)
-            -- get_subpoint (ellipse, down, z25)
-            for i = (length paths2 - s) step -s until (t4 + 1):
-                    .. get_subpoint (ellipse, -dirs[i + 20],
-                                     point (i - 1) of paths2)
-            endfor
-            .. get_subpoint (ellipse, -direction t4 of paths2,
-                             point t4 of paths2)
-            -- get_subpoint (ellipse, -direction t3 of paths2,
-                             point t3 of paths2)
-            for i = (floor (t3 / s) * s + 1) step -s until (t2 + 1):
-                    .. get_subpoint (ellipse, -dirs[i + 20],
-                                     point (i - 1) of paths2)
-            endfor
-            .. get_subpoint (ellipse, -direction t2 of paths2,
-                             point t2 of paths2)
-            -- get_subpoint (ellipse, -direction t1 of paths2,
-                             point t1 of paths2)
-            for i = (floor (t1 / s) * s + 1) step -s until (1 + s):
-                    .. get_subpoint (ellipse, -dirs[i + 20],
-                                     point (i - 1) of paths2)
-            endfor
+       sub_outlines21 := get_subpath (ellipse, -dirs21, dirs21, z21)
+                         for i = (1 + s) step s until (length paths2 - s):
+                                 .. get_subpoint (ellipse, dirs[i + 20],
+                                                  point (i - 1) of paths2)
+                         endfor
+                         .. get_subpath (ellipse, up, z26 - z25, z25);
+       sub_outlines22 := get_subpath (ellipse, z26 - z25, z25 - z26, z26)
+                         -- get_subpoint (ellipse, z25 - z26, z25);
+       sub_outlines23 := get_subpoint (ellipse, down, z25)
+                         for i = (length paths2 - s) step -s until (t4 + 1):
+                                 .. get_subpoint (ellipse, -dirs[i + 20],
+                                                  point (i - 1) of paths2)
+                         endfor
+                         .. get_subpoint (ellipse, -direction t4 of paths2,
+                                          point t4 of paths2);
+       sub_outlines24 := get_subpoint (ellipse, -direction t3 of paths2,
+                                       point t3 of paths2)
+                         for i = (floor (t3 / s) * s + 1) step -s until (t2 + 1):
+                                 .. get_subpoint (ellipse, -dirs[i + 20],
+                                                  point (i - 1) of paths2)
+                         endfor
+                         .. get_subpoint (ellipse, -direction t2 of paths2,
+                                          point t2 of paths2);
+       sub_outlines25 := get_subpoint (ellipse, -direction t1 of paths2,
+                                       point t1 of paths2)
+                         for i = (floor (t1 / s) * s + 1) step -s until (1 + s):
+                                 .. get_subpoint (ellipse, -dirs[i + 20],
+                                                  point (i - 1) of paths2)
+                         endfor;
+
+       (times2223, times2322) = sub_outlines22 intersectiontimes sub_outlines23;
+       (times2324, times2423) = sub_outlines23 intersectiontimes sub_outlines24;
+       (times2425, times2524) = sub_outlines24 intersectiontimes sub_outlines25;
+
+       fill sub_outlines21
+            -- subpath (0, times2223) of sub_outlines22
+            -- subpath (times2322, times2324) of sub_outlines23
+            -- subpath (times2423, times2425) of sub_outlines24
+            -- subpath (times2524, infinity) of sub_outlines25
             .. cycle;
 
        labels (1, 2, 3, 4, 5, 6, 7, 8, 9, 10);