stroke: Use round-joins near inflection points of splines

Near an inflection, the angle between two segments of a spline increases
rapidly (as the radius of curvature decreases for the cusp). The angle
may increase so much that a simple line connecting the two outside
points of the spline is not within the user specified geometric
tolerance (with the result that you can generate severe ugliness around
a cusp). Extend the current detection of the exact inflection to cover
the sharp joins near the cusp by inspecting whether the bisection angle
is larger than acceptable.

Fixes bug-spline.

Signed-off-by: Chris Wilson <chris@chris-wilson.co.uk>

1 files changed, 14 insertions, 3 deletions

diff --git a/src/cairo-path-stroke-polygon.c b/src/cairo-path-stroke-polygon.c
index 88527f5b..e8e7bb23 100644
--- a/src/cairo-path-stroke-polygon.c
+++ b/src/cairo-path-stroke-polygon.c
@@ -67,6 +67,7 @@ struct stroker {
     const cairo_matrix_t *ctm;
     const cairo_matrix_t *ctm_inverse;
     double tolerance;
+    double spline_cusp_tolerance;
     cairo_bool_t ctm_det_positive;
 
     cairo_pen_t pen;
@@ -1152,8 +1153,8 @@ spline_to (void *closure,
     } else {
 	compute_face (point, tangent, stroker, &face);
 
-	if (face.dev_slope.x * stroker->current_face.dev_slope.x +
-	    face.dev_slope.y * stroker->current_face.dev_slope.y < 0)
+	if ((face.dev_slope.x * stroker->current_face.dev_slope.x +
+	     face.dev_slope.y * stroker->current_face.dev_slope.y) < stroker->spline_cusp_tolerance)
 	{
 	    const cairo_point_t *inpt, *outpt;
 	    struct stroke_contour *outer;
@@ -1304,7 +1305,17 @@ _cairo_path_fixed_stroke_to_polygon (const cairo_path_fixed_t	*path,
     stroker.ctm = ctm;
     stroker.ctm_inverse = ctm_inverse;
     stroker.tolerance = tolerance;
-
+    /* To test whether we need to join two segments of a spline using
+     * a round-join or a bevel-join, we can inspect the angle between the
+     * two segments. If the difference between the chord distance
+     * (half-line-width times the cosine of the bisection angle) and the
+     * half-line-width itself is greater than tolerance then we need to
+     * inject a point.
+     */
+    stroker.spline_cusp_tolerance = 1 - 2 * tolerance / style->line_width;
+    stroker.spline_cusp_tolerance *= stroker.spline_cusp_tolerance;
+    stroker.spline_cusp_tolerance *= 2;
+    stroker.spline_cusp_tolerance -= 1;
     stroker.ctm_det_positive =
 	_cairo_matrix_compute_determinant (ctm) >= 0.0;