util: tune point_in_poly test for polys in screen coords

This makes a change to the original point_in_poly algorithm from:
http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html

The aim was to tune the test so that tests against screen aligned
rectangles are more resilient to some in-precision in how we transformed
that rectangle into screen coordinates. In particular gnome-shell was
finding that for some stage sizes then row 0 of the stage would become a
dead zone when going through the software picking fast-path and this was
because the y position of screen aligned rectangles could end up as
something like 0.00024 and the way the algorithm works it doesn't have
any epsilon/fuz factor to consider that in-precision.

We've avoided introducing an epsilon factor to the comparisons since we
feel there's a risk of changing some semantics in ways that might not be
desirable. One of those is that if you transform two polygons which
share an edge and test a point close to that edge then this algorithm
will currently give a positive result for only one polygon.

Another concern is the way this algorithm resolves the corner case where
the horizontal ray being cast to count edge crossings may cross directly
through a vertex. The solution is based on the "idea of Simulation of
Simplicity" and "pretends to shift the ray infinitesimally down so that
it either clearly intersects, or clearly doesn't touch". I'm not
familiar with the idea myself so I expect a misplaced epsilon is likely
to break that aspect of the algorithm.

The simple solution this patch applies is to pixel align the polygon
vertices which should eradicate most noise due to in-precision.

https://bugzilla.gnome.org/show_bug.cgi?id=641197

1 files changed, 36 insertions, 5 deletions

diff --git a/cogl/cogl-point-in-poly.c b/cogl/cogl-point-in-poly.c
index fc38d1d6..87e090ec 100644
--- a/cogl/cogl-point-in-poly.c
+++ b/cogl/cogl-point-in-poly.c
@@ -38,14 +38,40 @@
 #include "config.h"
 #endif
 
+#include "cogl-util.h"
+
 #include <glib.h>
 
+/* We've made a notable change to the original algorithm referenced
+ * above to make sure we have reliable results for screen aligned
+ * rectangles even though there may be some numerical in-precision in
+ * how the vertices of the polygon were calculated.
+ *
+ * We've avoided introducing an epsilon factor to the comparisons
+ * since we feel there's a risk of changing some semantics in ways that
+ * might not be desirable. One of those is that if you transform two
+ * polygons which share an edge and test a point close to that edge
+ * then this algorithm will currently give a positive result for only
+ * one polygon.
+ *
+ * Another concern is the way this algorithm resolves the corner case
+ * where the horizontal ray being cast to count edge crossings may
+ * cross directly through a vertex. The solution is based on the "idea
+ * of Simulation of Simplicity" and "pretends to shift the ray
+ * infinitesimally down so that it either clearly intersects, or
+ * clearly doesn't touch". I'm not familiar with the idea myself so I
+ * expect a misplaced epsilon is likely to break that aspect of the
+ * algorithm.
+ *
+ * The simple solution we've gone for is to pixel align the polygon
+ * vertices which should eradicate most noise due to in-precision.
+ */
 int
-_cogl_util_point_in_poly (float point_x,
-                          float point_y,
-                          void *vertices,
-                          size_t stride,
-                          int n_vertices)
+_cogl_util_point_in_screen_poly (float point_x,
+                                 float point_y,
+                                 void *vertices,
+                                 size_t stride,
+                                 int n_vertices)
 {
   int i, j, c = 0;
 
@@ -58,6 +84,11 @@ _cogl_util_point_in_poly (float point_x,
       float vert_yj = *(float *)((guint8 *)vertices + j * stride +
                                  sizeof (float));
 
+      vert_xi = COGL_UTIL_NEARBYINT (vert_xi);
+      vert_xj = COGL_UTIL_NEARBYINT (vert_xj);
+      vert_yi = COGL_UTIL_NEARBYINT (vert_yi);
+      vert_yj = COGL_UTIL_NEARBYINT (vert_yj);
+
       if (((vert_yi > point_y) != (vert_yj > point_y)) &&
            (point_x < (vert_xj - vert_xi) * (point_y - vert_yi) /
             (vert_yj - vert_yi) + vert_xi) )