- 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;
- shrunk_points[i1] = p1 + ((ccw) ? p13 : -p13);
+ shrunk_points = points;
+ }
+ else
+ {
+ /* shrink polygon in size by 0.5 * blotdiameter */
+
+ // first we need to determine the orientation of the polygon in
+ // order to decide whether shrinking means moving the polygon to the
+ // left or to the right of the outline. We do that by calculating
+ // (double) the oriented area of the polygon. We first determine the
+ // center and do the area calculations relative to it.
+ // Mathematically, the result is not affected by this shift, but
+ // numerically a lot of cancellation is going on and this keeps its
+ // effects in check.
+
+ Offset center;
+ for (vsize i = 0; i < points.size (); i++)
+ center += points[i];
+ center /= points.size ();
+
+ Real area = 0.0;
+ Offset last = points.back () - center;
+
+ for (vsize i = 0; i < points.size (); i++)
+ {
+ Offset here = points[i] - center;
+ area += cross_product (last, here);
+ last = here;
+ }
+
+ bool ccw = area >= 0.0; // true if whole shape is counterclockwise oriented
+
+ shrunk_points.resize (points.size ());
+
+ for (vsize 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 p01 = p1 - p0;
+ Offset p12 = p2 - p1;
+ Offset inward0 = Offset(-p01[Y_AXIS], p01[X_AXIS]).direction ();
+ Offset inward2 = Offset(-p12[Y_AXIS], p12[X_AXIS]).direction ();
+
+ if (!ccw)
+ {
+ inward0 = -inward0;
+ inward2 = -inward2;
+ }
+
+ Offset middle = 0.5*(inward0 + inward2);
+
+ // "middle" now is a vector in the right direction for the
+ // shrinkage. Its size needs to be large enough that the
+ // projection on either of the inward vectors has a size of 1.
+
+ Real proj = dot_product (middle, inward0);
+
+ // What's the size of proj? Assuming that we have a corner
+ // angle of phi where 0 corresponds to a continuing line, the
+ // length of middle is 0.5 |(1+cos phi, sin phi)| = cos (phi/2),
+ // so its projection has length
+ // cos^2 (phi/2) = 0.5 + 0.5 cos (phi).
+ // We don't really want to move inwards more than 3 blob
+ // diameters corresponding to 6 blob radii. So
+ // cos (phi/2) = 1/6 gives phi ~ 161, meaning that a 20 degree
+ // corner necessitates moving 3 blob diameters from the corner
+ // in order to stay inside the lines. Ruler and circle agree.
+ // 0.03 is close enough to 1/36. Basically we want to keep the
+ // shape from inverting from pulling too far inward.
+ // 3 diameters is pretty much a handwaving guess.
+
+ if (abs (proj) < 0.03)
+ proj = proj < 0 ? -0.03 : 0.03;
+
+ shrunk_points[i1] = p1 - (0.5 * blotdiameter / proj) * middle
+ * extroversion;
+ }