+ return Stencil (b,at);
+}
+
+
+
+/*
+ * Create Stencil that represents a filled polygon with round edges.
+ *
+ * LIMITATIONS:
+ *
+ * (a) Only outer (convex) edges are rounded.
+ *
+ * (b) This algorithm works as expected only for polygons whose edges
+ * do not intersect. For example, the polygon ((0, 0), (q, 0), (0,
+ * q), (q, q)) has an intersection at point (q/2, q/2) and therefore
+ * will give a strange result. Even non-adjacent edges that just
+ * touch each other will in general not work as expected for non-null
+ * blotdiameter.
+ *
+ * (c) Given a polygon ((x0, y0), (x1, y1), ... , (x(n-1), y(n-1))),
+ * if there is a natural number k such that blotdiameter is greater
+ * than the maximum of { | (x(k mod n), y(k mod n)) - (x((k+1) mod n),
+ * y((k+1) mod n)) |, | (x(k mod n), y(k mod n)) - (x((k+2) mod n),
+ * y((k+2) mod n)) |, | (x((k+1) mod n), y((k+1) mod n)) - (x((k+2)
+ * mod n), y((k+2) mod n)) | }, then the outline of the rounded
+ * polygon will exceed the outline of the core polygon. In other
+ * words: Do not draw rounded polygons that have a leg smaller or
+ * thinner than blotdiameter (or set blotdiameter to a sufficiently
+ * small value -- maybe even 0.0)!
+ *
+ * NOTE: Limitations (b) and (c) arise from the fact that round edges
+ * are made by moulding sharp edges to round ones rather than adding
+ * to a core filled polygon. For details of these two different
+ * approaches, see the thread upon the ledger lines patch that started
+ * on March 25, 2002 on the devel mailing list. The below version of
+ * round_filled_polygon() sticks to the moulding model, which the
+ * majority of the list participants finally voted for. This,
+ * however, results in the above limitations and a much increased
+ * complexity of the algorithm, since it has to compute a shrinked
+ * polygon -- which is not trivial define precisely and unambigously.
+ * With the other approach, one simply could move a circle of size
+ * blotdiameter along all edges of the polygon (which is what the
+ * postscript routine in the backend effectively does, but on the
+ * shrinked polygon). --jr
+ */
+Stencil
+Lookup::round_filled_polygon (Array<Offset> points, Real blotdiameter)
+{
+ /* TODO: Maybe print a warning if one of the above limitations
+ applies to the given polygon. However, this is quite complicated
+ to check. */
+
+ /* remove consecutive duplicate points */
+ const Real epsilon = 0.01;
+ for (int i = 0; i < points.size ();)
+ {
+ int next_i = (i + 1) % points.size ();
+ Real d = (points[i] - points[next_i]).length ();
+ if (d < epsilon)
+ points.del (next_i);
+ else
+ i++;
+ }
+
+ /* special cases: degenerated polygons */
+ if (points.size () == 0)
+ return Stencil ();
+ if (points.size () == 1)
+ return dot (points[0], 0.5 * blotdiameter);
+ if (points.size () == 2)
+ return Line_interface::make_line (blotdiameter, points[0], points[1]);
+
+ /* shrink polygon in size by 0.5 * blotdiameter */
+ Array<Offset> shrinked_points;
+ shrinked_points.set_size (points.size ());
+ bool ccw = 1; // true, if three adjacent points are counterclockwise ordered
+ for (int i = 0; i < points.size (); i++)
+ {
+ int i0 = i;
+ int i1 = (i + 1) % points.size ();
+ int i2 = (i + 2) % points.size ();
+ Offset p0 = points[i0];
+ Offset p1 = points[i1];
+ Offset p2 = points[i2];
+ Offset p10 = p0 - p1;
+ Offset p12 = p2 - p1;
+ if (p10.length () != 0.0)
+ { // recompute ccw
+ Real phi = p10.arg ();
+ // rotate (p2 - p0) by (-phi)
+ Offset q = complex_multiply (p2 - p0, complex_exp (Offset (1.0, -phi)));
+
+ if (q[Y_AXIS] > 0)
+ ccw = 1;
+ else if (q[Y_AXIS] < 0)
+ ccw = 0;
+ else {} // keep ccw unchanged
+ }
+ else {} // keep ccw unchanged
+ Offset p10n = (1.0 / p10.length ()) * p10; // normalize length to 1.0
+ Offset p12n = (1.0 / p12.length ()) * p12;
+ Offset p13n = 0.5 * (p10n + p12n);
+ Offset p14n = 0.5 * (p10n - p12n);
+ Offset p13;
+ Real d = p13n.length () * p14n.length (); // distance p3n to line(p1..p0)
+ if (d < epsilon)
+ // special case: p0, p1, p2 are on a single line => build
+ // vector orthogonal to (p2-p0) of length 0.5 blotdiameter
+ {
+ p13[X_AXIS] = p10[Y_AXIS];
+ p13[Y_AXIS] = -p10[X_AXIS];
+ p13 = (0.5 * blotdiameter / p13.length ()) * p13;
+ }
+ else
+ p13 = (0.5 * blotdiameter / d) * p13n;
+ shrinked_points[i1] = p1 + ((ccw) ? p13 : -p13);
+ }
+
+ /* build scm expression and bounding box */
+ SCM shrinked_points_scm = SCM_EOL;
+ Box box;
+ for (int i = 0; i < shrinked_points.size (); i++)
+ {
+ SCM x = gh_double2scm (shrinked_points[i][X_AXIS]);
+ SCM y = gh_double2scm (shrinked_points[i][Y_AXIS]);
+ shrinked_points_scm = gh_cons (x, gh_cons (y, shrinked_points_scm));
+ box.add_point (points[i]);
+ }
+ SCM polygon_scm = scm_list_n (ly_symbol2scm ("polygon"),
+ ly_quote_scm (shrinked_points_scm),
+ gh_double2scm (blotdiameter),
+ SCM_UNDEFINED);
+
+ Stencil polygon = Stencil (box, polygon_scm);
+ shrinked_points.clear ();
+ return polygon;