Eliminate self-intersecting strokes.

We refactor the surface fallbacks to convert full strokes and fills to the
intermediate polygon representation (as opposed to before where we
returned the trapezoidal representation). This allow greater flexibility
to choose how then to rasterize the polygon. Where possible we use the
local spans rasteriser for its increased performance, but still have the
option to use the tessellator instead (for example, with the current
Render protocol which does not yet have a polygon image).

In order to accommodate this, the spans interface is tweaked to accept
whole polygons instead of a path and the tessellator is tweaked for speed.

Performance Impact
==================

...
Still measuring, expecting some severe regressions.
...

1 files changed, 1189 insertions, 0 deletions

diff --git a/util/show-edges.c b/util/show-edges.c
new file mode 100644
index 00000000..d3b94bc0
--- /dev/null
+++ b/util/show-edges.c
@@ -0,0 +1,1189 @@
+#define _GNU_SOURCE
+#include <gtk/gtk.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <gdk/gdkkeysyms.h>
+#include <math.h>
+
+typedef struct _point {
+    gdouble x, y;
+} point_t;
+typedef struct _box {
+    point_t p1, p2;
+} box_t;
+typedef struct _line {
+    point_t p1, p2;
+} line_t;
+typedef struct _trapezoid {
+    gdouble top, bottom;
+    line_t left, right;
+} trapezoid_t;
+typedef struct _traps {
+    struct _traps *next, *prev;
+    box_t extents;
+    int num_traps;
+    int size;
+    trapezoid_t traps[0];
+} traps_t;
+
+typedef struct _edge {
+    line_t line;
+    gdouble top, bottom;
+    point_t p1, p2;
+    int dir;
+} edge_t;
+typedef struct _edges {
+    struct _edges *next, *prev;
+    box_t extents;
+    int num_edges;
+    int size;
+    edge_t edges[0];
+} edges_t;
+
+typedef struct _TrapView {
+    GtkWidget widget;
+
+    struct _TrapView *group_head;
+    struct _TrapView *group_next;
+    struct _TrapView *group_prev;
+
+    traps_t *traps_list;
+    traps_t *current_traps;
+
+    edges_t *edges_list;
+    edges_t *current_edges;
+
+    double px, py;
+
+    gint mag_x, mag_y;
+    gint mag_size;
+    gdouble mag_zoom;
+    gboolean in_mag_drag;
+    gint mag_drag_x, mag_drag_y;
+} TrapView;
+
+typedef struct _TrapViewClass {
+    GtkWidgetClass parent_class;
+} TrapViewClass;
+
+G_DEFINE_TYPE (TrapView, trap_view, GTK_TYPE_WIDGET)
+
+static gdouble
+_compute_intersection_x_for_y (const line_t *line,
+			       gdouble y)
+{
+    gdouble dx = line->p2.x - line->p1.x;
+    gdouble dy = line->p2.y - line->p1.y;
+    gdouble x;
+
+    if (y == line->p1.y)
+	return line->p1.x;
+    if (y == line->p2.y)
+	return line->p2.x;
+
+    x = line->p1.x;
+    if (dy != 0)
+	x +=  (y - line->p1.y)*dx/dy;
+    return x;
+}
+
+static void
+_compute_intersection_point (const line_t *line,
+			     gdouble y,
+			     point_t *p)
+{
+    p->x = _compute_intersection_x_for_y (line, p->y = y);
+}
+
+static void
+trap_view_draw (TrapView *self, cairo_t *cr)
+{
+    traps_t *traps;
+    edges_t *edges;
+    gdouble sf_x, sf_y, sf;
+    gdouble mid, dim;
+    gdouble x0, x1,  y0, y1;
+    double dash[2] = {8, 8};
+    double dots[2] = {0., 1.};
+    int n;
+    box_t extents;
+    point_t p;
+
+    cairo_save (cr);
+    cairo_save (cr);
+    cairo_set_source_rgb (cr, 1, 1, 1);
+    cairo_paint (cr);
+    cairo_restore (cr);
+
+    traps = self->current_traps;
+    edges = self->current_edges;
+    if (traps == NULL && edges == NULL)
+	return;
+
+    if (traps != NULL) {
+	extents = traps->extents;
+	if (edges != NULL) {
+	    if (edges->extents.p1.x < extents.p1.x)
+		extents.p1.x = edges->extents.p1.x;
+	    if (edges->extents.p1.y < extents.p1.y)
+		extents.p1.y = edges->extents.p1.y;
+	    if (edges->extents.p2.x > extents.p2.x)
+		extents.p2.x = edges->extents.p2.x;
+	    if (edges->extents.p2.y > extents.p2.y)
+		extents.p2.y = edges->extents.p2.y;
+	}
+    } else
+	extents = edges->extents;
+
+    mid = (extents.p2.x + extents.p1.x) / 2.;
+    dim = (extents.p2.x - extents.p1.x) / 2. * 1.25;
+    sf_x = self->widget.allocation.width / dim / 2;
+
+    mid = (extents.p2.y + extents.p1.y) / 2.;
+    dim = (extents.p2.y - extents.p1.y) / 2. * 1.25;
+    sf_y = self->widget.allocation.height / dim / 2;
+
+    sf = MIN (sf_x, sf_y);
+
+    mid = (extents.p2.x + extents.p1.x) / 2.;
+    dim = sf_x / sf * (extents.p2.x - extents.p1.x) / 2. * 1.25;
+    x0 = mid - dim;
+    x1 = mid + dim;
+    mid = (extents.p2.y + extents.p1.y) / 2.;
+    dim = sf_y / sf * (extents.p2.y - extents.p1.y) / 2. * 1.25;
+    y0 = mid - dim;
+    y1 = mid + dim;
+
+    if (traps != NULL) {
+	cairo_save (cr);
+	cairo_scale (cr, sf, sf);
+	cairo_translate (cr, -x0, -y0);
+	cairo_set_source_rgba (cr, 0, 1, 0, .2);
+	for (n = 0; n < traps->num_traps; n++) {
+	    const trapezoid_t *t = &traps->traps[n];
+
+	    _compute_intersection_point (&t->left, t->top, &p);
+	    cairo_move_to (cr, p.x, p.y);
+	    _compute_intersection_point (&t->right, t->top, &p);
+	    cairo_line_to (cr, p.x, p.y);
+	    _compute_intersection_point (&t->right, t->bottom, &p);
+	    cairo_line_to (cr, p.x, p.y);
+	    _compute_intersection_point (&t->left, t->bottom, &p);
+	    cairo_line_to (cr, p.x, p.y);
+	    cairo_close_path (cr);
+	    cairo_fill (cr);
+	}
+	cairo_restore (cr);
+    }
+
+    if (edges == NULL) {
+	cairo_save (cr);
+
+	/* top, bottom */
+	cairo_save (cr); {
+	    cairo_matrix_t m;
+	    cairo_matrix_init_scale (&m, sf, sf);
+	    cairo_matrix_translate (&m, -x0, -y0);
+
+	    cairo_set_line_width (cr, 1.);
+	    cairo_set_line_cap (cr, CAIRO_LINE_CAP_BUTT);
+	    for (n = 0; n < traps->num_traps; n++) {
+		const trapezoid_t *t = &traps->traps[n];
+
+		_compute_intersection_point (&t->left, t->top, &p);
+		cairo_matrix_transform_point (&m, &p.x, &p.y);
+		cairo_move_to (cr, floor (p.x), floor (p.y) + .5);
+		cairo_set_dash (cr, dash, 2, fmod (floor (p.x), dash[0] + dash[1]));
+
+		_compute_intersection_point (&t->right, t->top, &p);
+		cairo_matrix_transform_point (&m, &p.x, &p.y);
+		cairo_line_to (cr, ceil (p.x), floor (p.y) + .5);
+		cairo_stroke (cr);
+
+		_compute_intersection_point (&t->left, t->bottom, &p);
+		cairo_matrix_transform_point (&m, &p.x, &p.y);
+		cairo_move_to (cr, floor (p.x), floor (p.y) + .5);
+		cairo_set_dash (cr, dash, 2, fmod (floor (p.x), dash[0] + dash[1]));
+
+		_compute_intersection_point (&t->right, t->bottom, &p);
+		cairo_matrix_transform_point (&m, &p.x, &p.y);
+		cairo_line_to (cr, ceil (p.x), floor (p.y) + .5);
+		cairo_stroke (cr);
+	    }
+	} cairo_restore (cr);
+
+	/* left extents */
+	cairo_save (cr); {
+	    cairo_save (cr); {
+		cairo_scale (cr, sf, sf);
+		cairo_translate (cr, -x0, -y0);
+
+		for (n = 0; n < traps->num_traps; n++) {
+		    const trapezoid_t *t = &traps->traps[n];
+		    cairo_move_to (cr, t->left.p1.x, t->left.p1.y);
+		    cairo_line_to (cr, t->left.p2.x, t->left.p2.y);
+		}
+	    } cairo_restore (cr);
+	    cairo_set_source_rgb (cr, 1, 0, 0);
+	    cairo_set_line_width (cr, 1.);
+	    cairo_set_dash (cr, dash, 2, 0.);
+	    cairo_stroke (cr);
+	} cairo_restore (cr);
+
+	/* left line */
+	cairo_save (cr); {
+	    cairo_save (cr); {
+		cairo_scale (cr, sf, sf);
+		cairo_translate (cr, -x0, -y0);
+
+		for (n = 0; n < traps->num_traps; n++) {
+		    const trapezoid_t *t = &traps->traps[n];
+		    _compute_intersection_point (&t->left, t->top, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    _compute_intersection_point (&t->left, t->bottom, &p);
+		    cairo_line_to (cr, p.x, p.y);
+		}
+	    } cairo_restore (cr);
+	    cairo_set_source_rgb (cr, 1, 0, 0);
+	    cairo_stroke (cr);
+	} cairo_restore (cr);
+
+	/* right extents */
+	cairo_save (cr); {
+	    cairo_save (cr); {
+		cairo_scale (cr, sf, sf);
+		cairo_translate (cr, -x0, -y0);
+
+		for (n = 0; n < traps->num_traps; n++) {
+		    const trapezoid_t *t = &traps->traps[n];
+		    cairo_move_to (cr, t->right.p1.x, t->right.p1.y);
+		    cairo_line_to (cr, t->right.p2.x, t->right.p2.y);
+		}
+	    } cairo_restore (cr);
+	    cairo_set_source_rgb (cr, 0, 0, 1);
+	    cairo_set_line_width (cr, 1.);
+	    cairo_set_dash (cr, dash, 2, 0.);
+	    cairo_stroke (cr);
+	} cairo_restore (cr);
+
+	/* right line */
+	cairo_save (cr); {
+	    cairo_save (cr); {
+		cairo_scale (cr, sf, sf);
+		cairo_translate (cr, -x0, -y0);
+
+		for (n = 0; n < traps->num_traps; n++) {
+		    const trapezoid_t *t = &traps->traps[n];
+		    _compute_intersection_point (&t->right, t->top, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    _compute_intersection_point (&t->right, t->bottom, &p);
+		    cairo_line_to (cr, p.x, p.y);
+		} cairo_restore (cr);
+		cairo_set_source_rgb (cr, 0, 0, 1);
+		cairo_stroke (cr);
+	    } cairo_restore (cr);
+	}
+
+	/* end-points */
+	cairo_save (cr); {
+	    cairo_save (cr); {
+		cairo_scale (cr, sf, sf);
+		cairo_translate (cr, -x0, -y0);
+
+		for (n = 0; n < traps->num_traps; n++) {
+		    const trapezoid_t *t = &traps->traps[n];
+		    _compute_intersection_point (&t->left, t->top, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    cairo_close_path (cr);
+		    _compute_intersection_point (&t->left, t->bottom, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    cairo_close_path (cr);
+		    _compute_intersection_point (&t->right, t->top, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    cairo_close_path (cr);
+		    _compute_intersection_point (&t->right, t->bottom, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    cairo_close_path (cr);
+		}
+	    } cairo_restore (cr);
+	    cairo_set_source_rgb (cr, 0, 0, 0);
+	    cairo_set_dash (cr, dots, 2, 0.);
+	    cairo_set_line_cap (cr, CAIRO_LINE_CAP_ROUND);
+	    cairo_set_line_width (cr, 4.);
+	    cairo_stroke (cr);
+	} cairo_restore (cr);
+
+	cairo_restore (cr);
+    } else {
+	cairo_save (cr);
+
+	for (n = 0; n < edges->num_edges; n++) {
+	    const edge_t *e = &edges->edges[n];
+
+	    cairo_save (cr); {
+		cairo_scale (cr, sf, sf);
+		cairo_translate (cr, -x0, -y0);
+		cairo_move_to (cr, e->p1.x, e->p1.y);
+		cairo_line_to (cr, e->p2.x, e->p2.y);
+	    } cairo_restore (cr);
+
+	    if (e->dir < 0) {
+		cairo_set_source_rgb (cr, 0, 0, 1);
+		cairo_set_dash (cr, dash, 2, dash[0]);
+	    } else {
+		cairo_set_source_rgb (cr, 1, 0, 0);
+		cairo_set_dash (cr, dash, 2, 0.);
+	    }
+
+	    cairo_set_line_cap (cr, CAIRO_LINE_CAP_BUTT);
+	    cairo_set_line_width (cr, 1.);
+	    cairo_stroke (cr);
+
+	    cairo_save (cr); {
+		cairo_scale (cr, sf, sf);
+		cairo_translate (cr, -x0, -y0);
+		cairo_move_to (cr, e->p1.x, e->p1.y);
+		cairo_close_path (cr);
+		cairo_move_to (cr, e->p2.x, e->p2.y);
+		cairo_close_path (cr);
+	    } cairo_restore (cr);
+	    cairo_set_source_rgb (cr, 0, 0, 0);
+	    cairo_set_dash (cr, dots, 2, 0.);
+	    cairo_set_line_cap (cr, CAIRO_LINE_CAP_ROUND);
+	    cairo_set_line_width (cr, 4.);
+	    cairo_stroke (cr);
+	}
+
+	cairo_restore (cr);
+    }
+
+    /* draw a zoom view of the area around the mouse */
+    {
+	cairo_save (cr);
+	double zoom = self->mag_zoom;
+	int size = self->mag_size;
+
+	/* bottom right */
+	cairo_rectangle (cr, self->mag_x, self->mag_y, size, size);
+	cairo_stroke_preserve (cr);
+	cairo_set_source_rgb (cr, 1, 1, 1);
+	cairo_fill_preserve (cr);
+	cairo_clip (cr);
+
+	/* compute roi in extents */
+	cairo_translate (cr, self->mag_x + size/2, self->mag_y + size/2);
+
+	if (traps != NULL) {
+	    cairo_save (cr);
+	    cairo_scale (cr, zoom, zoom);
+	    cairo_translate (cr, -(self->px / sf + x0), -(self->py /sf + y0));
+	    for (n = 0; n < traps->num_traps; n++) {
+		const trapezoid_t *t = &traps->traps[n];
+
+		_compute_intersection_point (&t->left, t->top, &p);
+		cairo_move_to (cr, p.x, p.y);
+		_compute_intersection_point (&t->right, t->top, &p);
+		cairo_line_to (cr, p.x, p.y);
+		_compute_intersection_point (&t->right, t->bottom, &p);
+		cairo_line_to (cr, p.x, p.y);
+		_compute_intersection_point (&t->left, t->bottom, &p);
+		cairo_line_to (cr, p.x, p.y);
+		cairo_close_path (cr);
+		cairo_set_source_rgba (cr, 0, 1, 0, .2);
+		cairo_fill (cr);
+	    }
+	    cairo_restore (cr);
+	}
+
+	if (edges == NULL) {
+	    cairo_save (cr); {
+		cairo_matrix_t m;
+		cairo_matrix_init_scale (&m, zoom, zoom);
+		cairo_matrix_translate (&m, -(self->px / sf + x0), -(self->py /sf + y0));
+
+		cairo_set_source_rgb (cr, 0, 0, 0);
+		cairo_set_line_width (cr, 1.);
+		cairo_set_line_cap (cr, CAIRO_LINE_CAP_BUTT);
+		for (n = 0; n < traps->num_traps; n++) {
+		    const trapezoid_t *t = &traps->traps[n];
+
+		    _compute_intersection_point (&t->left, t->top, &p);
+		    cairo_matrix_transform_point (&m, &p.x, &p.y);
+		    cairo_move_to (cr, floor (p.x), floor (p.y) + .5);
+		    cairo_set_dash (cr, dash, 2, fmod (floor (p.x), dash[0] + dash[1]));
+
+		    _compute_intersection_point (&t->right, t->top, &p);
+		    cairo_matrix_transform_point (&m, &p.x, &p.y);
+		    cairo_line_to (cr, ceil (p.x), floor (p.y) + .5);
+		    cairo_stroke (cr);
+
+		    _compute_intersection_point (&t->left, t->bottom, &p);
+		    cairo_matrix_transform_point (&m, &p.x, &p.y);
+		    cairo_move_to (cr, floor (p.x), floor (p.y) + .5);
+		    cairo_set_dash (cr, dash, 2, fmod (floor (p.x), dash[0] + dash[1]));
+
+		    _compute_intersection_point (&t->right, t->bottom, &p);
+		    cairo_matrix_transform_point (&m, &p.x, &p.y);
+		    cairo_line_to (cr, ceil (p.x), floor (p.y) + .5);
+		    cairo_stroke (cr);
+		}
+	    } cairo_restore (cr);
+
+	    cairo_save (cr); { /* left extents */
+		cairo_save (cr); {
+		    cairo_scale (cr, zoom, zoom);
+		    cairo_translate (cr, -(self->px / sf + x0), -(self->py /sf + y0));
+		    for (n = 0; n < traps->num_traps; n++) {
+			const trapezoid_t *t = &traps->traps[n];
+			cairo_move_to (cr, t->left.p1.x, t->left.p1.y);
+			cairo_line_to (cr, t->left.p2.x, t->left.p2.y);
+		    }
+		} cairo_restore (cr);
+		cairo_set_source_rgb (cr, 1, 0, 0);
+		cairo_set_line_width (cr, .5);
+		cairo_set_dash (cr, dash, 2, 0.);
+		cairo_stroke (cr);
+	    } cairo_restore (cr);
+	    cairo_save (cr); { /* right extents */
+		cairo_save (cr); {
+		    cairo_scale (cr, zoom, zoom);
+		    cairo_translate (cr, -(self->px / sf + x0), -(self->py /sf + y0));
+
+		    for (n = 0; n < traps->num_traps; n++) {
+			const trapezoid_t *t = &traps->traps[n];
+			cairo_move_to (cr, t->right.p1.x, t->right.p1.y);
+			cairo_line_to (cr, t->right.p2.x, t->right.p2.y);
+		    }
+		} cairo_restore (cr);
+		cairo_set_source_rgb (cr, 0, 0, 1);
+		cairo_set_line_width (cr, .5);
+		cairo_set_dash (cr, dash, 2, 0.);
+		cairo_stroke (cr);
+	    } cairo_restore (cr);
+
+	    cairo_save (cr); { /* left lines */
+		cairo_save (cr);
+		cairo_scale (cr, zoom, zoom);
+		cairo_translate (cr, -(self->px / sf + x0), -(self->py /sf + y0));
+		for (n = 0; n < traps->num_traps; n++) {
+		    const trapezoid_t *t = &traps->traps[n];
+		    _compute_intersection_point (&t->left, t->top, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    _compute_intersection_point (&t->left, t->bottom, &p);
+		    cairo_line_to (cr, p.x, p.y);
+		}
+		cairo_restore (cr);
+		cairo_set_source_rgb (cr, 1, 0, 0);
+		cairo_stroke (cr);
+	    } cairo_restore (cr);
+	    cairo_save (cr); { /* right lines */
+		cairo_save (cr);
+		cairo_scale (cr, zoom, zoom);
+		cairo_translate (cr, -(self->px / sf + x0), -(self->py /sf + y0));
+		for (n = 0; n < traps->num_traps; n++) {
+		    const trapezoid_t *t = &traps->traps[n];
+		    _compute_intersection_point (&t->right, t->top, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    _compute_intersection_point (&t->right, t->bottom, &p);
+		    cairo_line_to (cr, p.x, p.y);
+		}
+		cairo_restore (cr);
+		cairo_set_source_rgb (cr, 0, 0, 1);
+		cairo_stroke (cr);
+	    } cairo_restore (cr);
+
+	    /* end-points */
+	    cairo_save (cr); {
+		double dots[2] = {0., 1.};
+
+		cairo_save (cr);
+		cairo_scale (cr, zoom, zoom);
+		cairo_translate (cr, -(self->px / sf + x0), -(self->py /sf + y0));
+		for (n = 0; n < traps->num_traps; n++) {
+		    const trapezoid_t *t = &traps->traps[n];
+		    _compute_intersection_point (&t->left, t->top, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    cairo_close_path (cr);
+		    _compute_intersection_point (&t->left, t->bottom, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    cairo_close_path (cr);
+		    _compute_intersection_point (&t->right, t->top, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    cairo_close_path (cr);
+		    _compute_intersection_point (&t->right, t->bottom, &p);
+		    cairo_move_to (cr, p.x, p.y);
+		    cairo_close_path (cr);
+		}
+		cairo_restore (cr);
+		cairo_set_source_rgb (cr, 0, 0, 0);
+		cairo_set_dash (cr, dots, 2, 0.);
+		cairo_set_line_cap (cr, CAIRO_LINE_CAP_ROUND);
+		cairo_set_line_width (cr, 4.);
+		cairo_stroke (cr);
+	    } cairo_restore (cr);
+	} else {
+	    cairo_save (cr);
+
+	    for (n = 0; n < edges->num_edges; n++) {
+		const edge_t *e = &edges->edges[n];
+
+		cairo_save (cr); {
+		    cairo_scale (cr, zoom, zoom);
+		    cairo_translate (cr, -(self->px / sf + x0), -(self->py /sf + y0));
+		    cairo_move_to (cr, e->p1.x, e->p1.y);
+		    cairo_line_to (cr, e->p2.x, e->p2.y);
+		} cairo_restore (cr);
+
+		if (e->dir < 0) {
+		    cairo_set_source_rgb (cr, 0, 0, 1);
+		    cairo_set_dash (cr, dash, 2, dash[0]);
+		} else {
+		    cairo_set_source_rgb (cr, 1, 0, 0);
+		    cairo_set_dash (cr, dash, 2, 0.);
+		}
+
+		cairo_set_line_cap (cr, CAIRO_LINE_CAP_BUTT);
+		cairo_set_line_width (cr, 1.);
+		cairo_stroke (cr);
+
+		cairo_save (cr); {
+		    cairo_scale (cr, zoom, zoom);
+		    cairo_translate (cr, -(self->px / sf + x0), -(self->py /sf + y0));
+		    cairo_move_to (cr, e->p1.x, e->p1.y);
+		    cairo_close_path (cr);
+		    cairo_move_to (cr, e->p2.x, e->p2.y);
+		    cairo_close_path (cr);
+		} cairo_restore (cr);
+		cairo_set_source_rgb (cr, 0, 0, 0);
+		cairo_set_dash (cr, dots, 2, 0.);
+		cairo_set_line_cap (cr, CAIRO_LINE_CAP_ROUND);
+		cairo_set_line_width (cr, 4.);
+		cairo_stroke (cr);
+	    }
+
+	    cairo_restore (cr);
+	}
+
+	/* grid */
+	cairo_save (cr); {
+	    int i;
+
+	    cairo_translate (cr,
+			     -zoom*fmod (self->px/sf + x0, 1.),
+			     -zoom*fmod (self->py/sf + y0, 1.));
+	    for (i = -size/2/zoom - 1; i <= size/2/zoom + 1; i++) {
+		cairo_move_to (cr, zoom*i, -size/2);
+		cairo_line_to (cr, zoom*i, size/2 + zoom);
+		cairo_move_to (cr, -size/2, zoom*i);
+		cairo_line_to (cr, size/2 + zoom, zoom*i);
+	    }
+	    cairo_set_source_rgba (cr, .7, .7, .7, .5);
+	    cairo_set_line_width (cr, 1.);
+	    cairo_stroke (cr);
+	} cairo_restore (cr);
+    }
+
+    cairo_restore (cr);
+}
+
+static gdouble
+trapezoid_area (const trapezoid_t *t)
+{
+    gdouble inner_left, inner_right;
+    gdouble outer_left, outer_right;
+    gdouble height;
+    gdouble area;
+
+    /* split into 3 sections: a rectangle with a pair of triangular bookends */
+    inner_left = _compute_intersection_x_for_y (&t->left, t->top);
+    outer_left = _compute_intersection_x_for_y (&t->left, t->bottom);
+    if (outer_left > inner_left) {
+	gdouble t = outer_left;
+	outer_left = inner_left;
+	inner_left = t;
+    }
+
+    inner_right = _compute_intersection_x_for_y (&t->right, t->top);
+    outer_right = _compute_intersection_x_for_y (&t->right, t->bottom);
+    if (outer_right > inner_right) {
+	gdouble t = outer_right;
+	outer_right = inner_right;
+	inner_right = t;
+    }
+
+    if (outer_left > outer_right) { /* reverse */
+	gdouble t;
+
+	t = outer_left;
+	outer_left = inner_right;
+	inner_right = t;
+
+	t = inner_left;
+	inner_left = outer_right;
+	outer_right = t;
+    }
+
+    height = t->bottom - t->top;
+    area  = (inner_left - outer_left) * height / 2;
+    area += (outer_right - inner_right) * height / 2;
+    area += (inner_right - inner_left) * height;
+
+    return area;
+}
+
+static gdouble
+traps_compute_total_area (const traps_t *traps)
+{
+    int n;
+    gdouble area = 0.;
+    for (n = 0; n < traps->num_traps; n++)
+	area += trapezoid_area (&traps->traps[n]);
+    return area;
+}
+
+static void
+trap_view_draw_labels (TrapView *self, cairo_t *cr)
+{
+    PangoLayout *layout;
+    gint width, height;
+    gdouble total_area;
+    gchar *str;
+    traps_t *traps;
+
+    traps = self->current_traps;
+    if (traps == NULL)
+	return;
+
+    /* convert total area from fixed-point (assuming 24.8) */
+    total_area = traps_compute_total_area (traps) / (256. * 256.);
+    str = g_strdup_printf ("Number of trapezoids:\t%d\n"
+			   "Total area of trapezoids:\t%.2f",
+			   traps->num_traps,
+			   total_area);
+    layout = gtk_widget_create_pango_layout (&self->widget, str);
+    g_free (str);
+
+    pango_layout_get_pixel_size (layout, &width, &height);
+
+    cairo_move_to (cr, 10, 10 + height);
+    pango_cairo_show_layout (cr, layout);
+    g_object_unref (layout);
+}
+
+static gboolean
+trap_view_expose (GtkWidget *w, GdkEventExpose *ev)
+{
+    TrapView *self = (TrapView *) w;
+    cairo_t *cr;
+
+    cr = gdk_cairo_create (w->window);
+    gdk_cairo_region (cr, ev->region);
+    cairo_clip (cr);
+
+    trap_view_draw (self, cr);
+    trap_view_draw_labels (self, cr);
+
+    cairo_destroy (cr);
+    return FALSE;
+}
+
+static void
+trap_view_advance (TrapView *self)
+{
+    if (self->current_traps && self->current_traps->prev)
+	self->current_traps = self->current_traps->prev;
+    if (self->current_edges && self->current_edges->prev)
+	self->current_edges = self->current_edges->prev;
+    gtk_widget_queue_draw (&self->widget);
+}
+
+static void
+trap_view_back (TrapView *self)
+{
+    if (self->current_traps && self->current_traps->next)
+	self->current_traps = self->current_traps->next;
+    if (self->current_edges && self->current_edges->next)
+	self->current_edges = self->current_edges->next;
+    gtk_widget_queue_draw (&self->widget);
+}
+
+static void
+trap_view_group_foreach (TrapView *group, GFunc func, gpointer data)
+{
+    while (group) {
+	func (group, data);
+	group = group->group_next;
+    }
+}
+
+static gboolean
+trap_view_key_press (GtkWidget *w, GdkEventKey *ev)
+{
+    TrapView *self = (TrapView *) w;
+
+    switch (ev->keyval) {
+    case GDK_BackSpace:
+	trap_view_group_foreach (self->group_head,
+				 (GFunc) trap_view_back,
+				 NULL);
+	break;
+
+    case GDK_space:
+	trap_view_group_foreach (self->group_head,
+				 (GFunc) trap_view_advance,
+				 NULL);
+	break;
+
+    case GDK_Return:
+	trap_view_group_foreach (self->group_head,
+				 (GFunc) trap_view_advance,
+				 NULL);
+	break;
+
+    case GDK_Escape:
+    case GDK_Q:
+	gtk_main_quit ();
+	break;
+    }
+
+    return FALSE;
+}
+
+static gboolean
+trap_view_button_press (GtkWidget *w, GdkEventButton *ev)
+{
+    TrapView *self = (TrapView *) w;
+
+    if (ev->x < self->mag_x ||
+	ev->y < self->mag_y ||
+	ev->x > self->mag_x + self->mag_size ||
+	ev->y > self->mag_y + self->mag_size)
+    {
+	if (ev->type == GDK_BUTTON_PRESS) {
+	    if (self->current_traps == NULL)
+		return FALSE;
+
+	    if (ev->button == 1) {
+		trap_view_group_foreach (self->group_head,
+					 (GFunc) trap_view_advance,
+					 NULL);
+	    } else if (ev->button == 3) {
+		trap_view_group_foreach (self->group_head,
+					 (GFunc) trap_view_back,
+					 NULL);
+	    }
+	}
+    }
+    else
+    {
+	self->in_mag_drag = TRUE;
+	self->mag_drag_x = ev->x;
+	self->mag_drag_y = ev->y;
+    }
+
+    return FALSE;
+}
+
+static gboolean
+trap_view_button_release (GtkWidget *w, GdkEventButton *ev)
+{
+    TrapView *self = (TrapView *) w;
+
+    self->in_mag_drag = FALSE;
+
+    return FALSE;
+}
+
+static void
+trap_view_update_mouse (TrapView *self, GdkEventMotion *ev)
+{
+    self->px = ev->x;
+    self->py = ev->y;
+
+    gtk_widget_queue_draw (&self->widget);
+}
+
+static void
+trap_view_update_magnifier (TrapView *self, gint *xy)
+{
+    self->mag_x = xy[0];
+    self->mag_y = xy[1];
+
+    gtk_widget_queue_draw (&self->widget);
+}
+
+static gboolean
+trap_view_motion (GtkWidget *w, GdkEventMotion *ev)
+{
+    TrapView *self = (TrapView *) w;
+
+    if (self->in_mag_drag) {
+	int xy[2];
+
+	xy[0] = self->mag_x + ev->x - self->mag_drag_x;
+	xy[1] = self->mag_y + ev->y - self->mag_drag_y;
+
+	trap_view_group_foreach (self->group_head,
+				 (GFunc) trap_view_update_magnifier,
+				 xy);
+
+	self->mag_drag_x = ev->x;
+	self->mag_drag_y = ev->y;
+    } else if (ev->x < self->mag_x ||
+	       ev->y < self->mag_y ||
+	       ev->x > self->mag_x + self->mag_size ||
+	       ev->y > self->mag_y + self->mag_size)
+    {
+	trap_view_group_foreach (self->group_head,
+				 (GFunc) trap_view_update_mouse,
+				 ev);
+    }
+
+    return FALSE;
+}
+
+static void
+trap_view_realize (GtkWidget *widget)
+{
+    GdkWindowAttr attributes;
+
+    GTK_WIDGET_SET_FLAGS (widget, GTK_REALIZED);
+
+    attributes.window_type = GDK_WINDOW_CHILD;
+    attributes.x = widget->allocation.x;
+    attributes.y = widget->allocation.y;
+    attributes.width  = widget->allocation.width;
+    attributes.height = widget->allocation.height;
+    attributes.wclass = GDK_INPUT_OUTPUT;
+    attributes.visual = gtk_widget_get_visual (widget);
+    attributes.colormap = gtk_widget_get_colormap (widget);
+    attributes.event_mask = gtk_widget_get_events (widget) |
+	                    GDK_BUTTON_PRESS_MASK |
+	                    GDK_BUTTON_RELEASE_MASK |
+	                    GDK_KEY_PRESS_MASK |
+	                    GDK_KEY_RELEASE_MASK |
+			    GDK_POINTER_MOTION_MASK |
+			    GDK_BUTTON_MOTION_MASK |
+	                    GDK_EXPOSURE_MASK;
+
+    widget->window = gdk_window_new (gtk_widget_get_parent_window (widget),
+				     &attributes,
+				     GDK_WA_X | GDK_WA_Y |
+				     GDK_WA_VISUAL | GDK_WA_COLORMAP);
+    gdk_window_set_user_data (widget->window, widget);
+
+    widget->style = gtk_style_attach (widget->style, widget->window);
+    gtk_style_set_background (widget->style, widget->window, GTK_STATE_NORMAL);
+}
+
+static void
+trap_view_size_allocate (GtkWidget *w, GdkRectangle *r)
+{
+    TrapView *self = (TrapView *) w;
+
+    GTK_WIDGET_CLASS (trap_view_parent_class)->size_allocate (w, r);
+
+    self->mag_x = w->allocation.width - self->mag_size - 10;
+    self->mag_y = w->allocation.height - self->mag_size - 10;
+}
+
+static void
+trap_view_finalize (GObject *obj)
+{
+    G_OBJECT_CLASS (trap_view_parent_class)->finalize (obj);
+}
+
+static void
+trap_view_class_init (TrapViewClass *klass)
+{
+    GObjectClass *object_class = (GObjectClass *) klass;
+    GtkWidgetClass *widget_class = (GtkWidgetClass *) klass;
+
+    object_class->finalize = trap_view_finalize;
+
+    widget_class->realize = trap_view_realize;
+    widget_class->size_allocate = trap_view_size_allocate;
+    widget_class->expose_event = trap_view_expose;
+    widget_class->key_press_event = trap_view_key_press;
+    widget_class->button_press_event = trap_view_button_press;
+    widget_class->button_release_event = trap_view_button_release;
+    widget_class->motion_notify_event = trap_view_motion;
+}
+
+static void
+trap_view_init (TrapView *self)
+{
+    self->mag_zoom = 10;
+    self->mag_size = 200;
+
+    GTK_WIDGET_SET_FLAGS (self, GTK_CAN_FOCUS);
+}
+
+static traps_t *
+_traps_add_trapezoid (TrapView *tv, traps_t *traps, const trapezoid_t *trap)
+{
+    if (trap->top < traps->extents.p1.y)
+	traps->extents.p1.y = trap->top;
+    if (trap->bottom > traps->extents.p2.y)
+	traps->extents.p2.y = trap->bottom;
+
+    if (trap->left.p1.x < traps->extents.p1.x)
+	traps->extents.p1.x = trap->left.p1.x;
+    if (trap->left.p2.x < traps->extents.p1.x)
+	traps->extents.p1.x = trap->left.p2.x;
+
+    if (trap->right.p1.x > traps->extents.p2.x)
+	traps->extents.p2.x = trap->right.p1.x;
+    if (trap->right.p2.x > traps->extents.p2.x)
+	traps->extents.p2.x = trap->right.p2.x;
+
+    if (traps->num_traps == traps->size) {
+	int newsize = 2 * traps->size;
+	void *newtraps;
+
+	newtraps = g_realloc (traps,
+			      sizeof (traps_t) + newsize * sizeof (trapezoid_t));
+	if (newtraps == NULL)
+	    return traps;
+
+	if (tv->current_traps == traps)
+	    tv->current_traps = newtraps;
+
+	traps = newtraps;
+	traps->size = newsize;
+
+	if (traps->next != NULL)
+	    traps->next->prev = newtraps;
+	if (traps->prev != NULL)
+	    traps->prev->next = newtraps;
+	else
+	    tv->traps_list = newtraps;
+    }
+
+    traps->traps[traps->num_traps++] = *trap;
+
+    return traps;
+}
+
+static traps_t *
+traps_new (TrapView *tv)
+{
+    traps_t *t;
+
+    t = g_malloc (sizeof (traps_t) + 16 * sizeof (trapezoid_t));
+    t->prev = NULL;
+    t->next = tv->traps_list;
+    if (tv->traps_list)
+	tv->traps_list->prev = t;
+    tv->traps_list = t;
+
+    if (tv->current_traps == NULL)
+	tv->current_traps = t;
+
+    t->size = 16;
+    t->num_traps = 0;
+    t->extents.p1.x = G_MAXDOUBLE;
+    t->extents.p1.y = G_MAXDOUBLE;
+    t->extents.p2.x = -G_MAXDOUBLE;
+    t->extents.p2.y = -G_MAXDOUBLE;
+
+    return t;
+}
+
+static edges_t *
+_edges_add_edge (TrapView *tv, edges_t *edges, edge_t *e)
+{
+    if (e->top < edges->extents.p1.y)
+	edges->extents.p1.y = e->top;
+    if (e->bottom > edges->extents.p2.y)
+	edges->extents.p2.y = e->bottom;
+
+    _compute_intersection_point (&e->line, e->top, &e->p1);
+    _compute_intersection_point (&e->line, e->bottom, &e->p2);
+
+    if (e->p1.x < edges->extents.p1.x)
+	edges->extents.p1.x = e->p1.x;
+    if (e->p2.x < edges->extents.p1.x)
+	edges->extents.p1.x = e->p2.x;
+
+    if (e->p1.x > edges->extents.p2.x)
+	edges->extents.p2.x = e->p1.x;
+    if (e->p2.x > edges->extents.p2.x)
+	edges->extents.p2.x = e->p2.x;
+
+    if (edges->num_edges == edges->size) {
+	int newsize = 2 * edges->size;
+	void *newedges;
+
+	newedges = g_realloc (edges,
+			      sizeof (edges_t) + newsize * sizeof (edge_t));
+	if (newedges == NULL)
+	    return edges;
+
+	if (tv->current_edges == edges)
+	    tv->current_edges = newedges;
+
+	edges = newedges;
+	edges->size = newsize;
+
+	if (edges->next != NULL)
+	    edges->next->prev = newedges;
+	if (edges->prev != NULL)
+	    edges->prev->next = newedges;
+	else
+	    tv->edges_list = newedges;
+    }
+
+    edges->edges[edges->num_edges++] = *e;
+
+    return edges;
+}
+
+static edges_t *
+edges_new (TrapView *tv)
+{
+    edges_t *t;
+
+    t = g_malloc (sizeof (edges_t) + 16 * sizeof (edge_t));
+    t->prev = NULL;
+    t->next = tv->edges_list;
+    if (tv->edges_list)
+	tv->edges_list->prev = t;
+    tv->edges_list = t;
+
+    if (tv->current_edges == NULL)
+	tv->current_edges = t;
+
+    t->size = 16;
+    t->num_edges = 0;
+    t->extents.p1.x = G_MAXDOUBLE;
+    t->extents.p1.y = G_MAXDOUBLE;
+    t->extents.p2.x = -G_MAXDOUBLE;
+    t->extents.p2.y = -G_MAXDOUBLE;
+
+    return t;
+}
+
+int
+main (int argc, char **argv)
+{
+    TrapView *tv, *tv2, *group_head = NULL, *group_prev = NULL;
+    traps_t *traps;
+    edges_t *edges;
+    GtkWidget *window, *hbox;
+    FILE *file;
+    char *line = NULL;
+    size_t len = 0;
+
+    gtk_init (&argc, &argv);
+
+    hbox = gtk_hbox_new (TRUE, 0);
+
+    tv = g_object_new (trap_view_get_type (), NULL);
+    gtk_box_pack_start (GTK_BOX (hbox), &tv->widget, TRUE, TRUE, 0);
+    gtk_widget_show (&tv->widget);
+
+    tv->group_prev = group_prev;
+    tv->group_next = NULL;
+    if (group_prev)
+	group_prev->group_next = tv;
+    group_prev = tv;
+    if (group_head == NULL)
+	group_head = tv;
+    tv->group_head = group_head;
+
+    file = fopen (argv[1], "r");
+    if (file != NULL) {
+	edges = edges_new (tv);
+	while (getline (&line, &len, file) != -1) {
+	    edge_t e;
+
+	    if (sscanf (line,
+			"(%lf, %lf), (%lf, %lf) %lf %lf %d",
+			&e.line.p1.x, &e.line.p1.y,
+			&e.line.p2.x, &e.line.p2.y,
+			&e.top, &e.bottom,
+			&e.dir) == 7) {
+		edges = _edges_add_edge (tv, edges, &e);
+	    } else {
+		if (edges->num_edges) {
+		    g_print ("read %d edges\n", edges->num_edges);
+		    g_print ("extents=(%lg, %lg), (%lg, %lg)\n",
+			     edges->extents.p1.x, edges->extents.p1.y,
+			     edges->extents.p2.x, edges->extents.p2.y);
+		    edges = edges_new (tv);
+		}
+	    }
+	}
+
+	if (edges->num_edges) {
+	    g_print ("read %d edges\n", edges->num_edges);
+	    g_print ("extents=(%lg, %lg), (%lg, %lg)\n",
+		     edges->extents.p1.x, edges->extents.p1.y,
+		     edges->extents.p2.x, edges->extents.p2.y);
+	}
+
+	fclose (file);
+    }
+
+    file = fopen (argv[2], "r");
+    if (file != NULL) {
+	traps = traps_new (tv);
+	while (getline (&line, &len, file) != -1) {
+	    trapezoid_t t;
+
+	    if (sscanf (line,
+			"%lf %lf L:(%lf, %lf), (%lf, %lf) R:(%lf, %lf), (%lf, %lf)",
+			&t.top, &t.bottom,
+			&t.left.p1.x, &t.left.p1.y,
+			&t.left.p2.x, &t.left.p2.y,
+			&t.right.p1.x, &t.right.p1.y,
+			&t.right.p2.x, &t.right.p2.y) == 10) {
+		traps = _traps_add_trapezoid (tv, traps, &t);
+	    } else {
+		if (traps->num_traps) {
+		    g_print ("read %d trapezoids\n", traps->num_traps);
+		    g_print ("extents=(%lg, %lg), (%lg, %lg)\n",
+			     traps->extents.p1.x, traps->extents.p1.y,
+			     traps->extents.p2.x, traps->extents.p2.y);
+		    traps = traps_new (tv);
+		}
+	    }
+	}
+
+	if (traps->num_traps) {
+	    g_print ("read %d trapezoids\n", traps->num_traps);
+	    g_print ("extents=(%lg, %lg), (%lg, %lg)\n",
+		     traps->extents.p1.x, traps->extents.p1.y,
+		     traps->extents.p2.x, traps->extents.p2.y);
+	}
+
+	fclose (file);
+    }
+
+    free (line);
+
+    tv2 = g_object_new (trap_view_get_type (), NULL);
+    gtk_box_pack_start (GTK_BOX (hbox), &tv2->widget, TRUE, TRUE, 0);
+    gtk_widget_show (&tv2->widget);
+
+    tv2->traps_list = tv->traps_list;
+    tv2->current_traps = tv->current_traps;
+
+    tv2->group_prev = group_prev;
+    tv2->group_next = NULL;
+    group_prev->group_next = tv2;
+    group_prev = tv2;
+    tv2->group_head = group_head;
+
+    window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+    g_signal_connect (window, "delete-event",
+		      G_CALLBACK (gtk_main_quit), NULL);
+    gtk_widget_set_size_request (window, 512, 512);
+    gtk_container_add (GTK_CONTAINER (window), hbox);
+    gtk_widget_show (hbox);
+    gtk_widget_show (window);
+
+    gtk_main ();
+    return 0;
+}