util: add struct to track union of rectangles

The new struct rect_union is designed to make it easier to
efficiently accumulate a list of rectangles, and then operate
on an exact cover of their union.

Using rect_union, the times needed to added t rectangles, and then
compute their exact cover will be O(t), and something between Ω(t) and
O(t^2), depending on the rectangle arrangement. If one tries to do
the same by storing a pixman_region32_t and updating it with
pixman_region32_union_rect(), then total time needed would be between
Ω(t^2) and O(t^3), depending on the input. Without changing the public
API (data structure + rectangle ordering rules) for pixman_region32_t,
it is impossible to improve its worst case time.

3 files changed, 168 insertions, 0 deletions

diff --git a/include/util/rect_union.h b/include/util/rect_union.h
new file mode 100644
index 00000000..2d74f94d
--- /dev/null
+++ b/include/util/rect_union.h
@@ -0,0 +1,76 @@
+#ifndef UTIL_RECT_UNION_H
+#define UTIL_RECT_UNION_H
+
+#include <stdlib.h>
+#include <stdbool.h>
+#include <pixman.h>
+#include <wayland-util.h>
+
+/**
+ * `struct rect_union` is a data structure to efficiently accumulate a number
+ * of rectangles and then, when needed, compute a disjoint cover of their union.
+ * (That is: produce a list of disjoint rectangles which covers every point
+ * that was contained in one of the added rectangles.)
+ *
+ * Add rectangles to the union with `rect_union_add()`; to compute the disjoint
+ * union, run `rect_union_evaluate()`, which will place the result in `.region`.
+ * If there were any allocation failures, `.region` will instead contain the
+ * bounding box for the entire list of rectangles.
+ *
+ * Example usage:
+ *
+ *     struct rect_union r;
+ *     rect_union_init(&r);
+ *     for (j in ...) {
+ *         rect_union_add(&r, box[j]);
+ *     }
+ *     const pixman_region32_t *reg = rect_union_evaluate(&r);
+ *     int nboxes;
+ *     pixman_box32_t *boxes = pixman_region32_rectangles(reg, nboxes);
+ *     for (int i = 0; i < nboxes; i++) {
+ *         do_stuff(boxes[i]);
+ *     }
+ *     rect_union_destroy(&r);
+ *
+ */
+struct rect_union {
+	pixman_box32_t bounding_box; // Always up-to-date bounding box
+	pixman_region32_t region; // Updated only on _evaluate()
+
+	struct wl_array unsorted; // pixman_box32_t
+	bool alloc_failure; // If this is true, fall back to computing a bounding box
+};
+
+/**
+ * Initialize *r, disregarding any previous contents.
+ */
+void rect_union_init(struct rect_union *r);
+
+/**
+ * Free heap data associated with *r; should only be called after rect_union_init.
+ * Leaves *r in an invalid state.
+ */
+void rect_union_finish(struct rect_union *r);
+
+/**
+ * Add a rectangle to the union. If `box` is empty or invalid (x2 > x1 || y2 > y1),
+ * do nothing.
+ *
+ * Amortized time: O(1)
+ */
+void rect_union_add(struct rect_union *r, pixman_box32_t box);
+
+/**
+ * Compute an exact cover of the rectangles added so far, and return
+ * a pointer to a pixman_region32_t giving that cover. The pointer will
+ * remain valid until the next time *r is modified. If there was an allocation
+ * failure, this function may return a single-rectangle bounding box instead.
+ *
+ * This may be called multiple times and interleaved with rect_union_add().
+ *
+ * Worst case time: O(t^2), where t is the number of rectangles in the list.
+ * Best case time: O(t), if rectangles are disjoint and have y-x band structure
+ */
+const pixman_region32_t *rect_union_evaluate(struct rect_union *r);
+
+#endif
diff --git a/util/meson.build b/util/meson.build
index 1cd7f65c..1c3dcd5a 100644
--- a/util/meson.build
+++ b/util/meson.build
@@ -5,6 +5,7 @@ wlr_files += files(
 	'env.c',
 	'global.c',
 	'log.c',
+	'rect_union.c',
 	'region.c',
 	'set.c',
 	'shm.c',
diff --git a/util/rect_union.c b/util/rect_union.c
new file mode 100644
index 00000000..8cd26d76
--- /dev/null
+++ b/util/rect_union.c
@@ -0,0 +1,91 @@
+#include <limits.h>
+#include "util/rect_union.h"
+
+static void box_union(pixman_box32_t *dst, pixman_box32_t box) {
+	dst->x1 = dst->x1 < box.x1 ? dst->x1 : box.x1;
+	dst->y1 = dst->y1 < box.y1 ? dst->y1 : box.y1;
+	dst->x2 = dst->x2 > box.x2 ? dst->x2 : box.x2;
+	dst->y2 = dst->y2 > box.y2 ? dst->y2 : box.y2;
+}
+
+static bool box_empty_or_invalid(pixman_box32_t box) {
+	return box.x1 >= box.x2 || box.y1 >= box.y2;
+}
+
+void rect_union_init(struct rect_union *ru) {
+	*ru = (struct rect_union) {
+		.alloc_failure = false,
+		.bounding_box = (pixman_box32_t) {
+			.x1 = INT_MAX,
+			.x2 = INT_MIN,
+			.y1 = INT_MAX,
+			.y2 = INT_MIN,
+		}
+	};
+	pixman_region32_init(&ru->region);
+	wl_array_init(&ru->unsorted);
+};
+
+void rect_union_finish(struct rect_union *ru) {
+	pixman_region32_fini(&ru->region);
+	wl_array_release(&ru->unsorted);
+}
+
+static void handle_alloc_failure(struct rect_union *ru) {
+	ru->alloc_failure = true;
+	wl_array_release(&ru->unsorted);
+	wl_array_init(&ru->unsorted);
+}
+
+void rect_union_add(struct rect_union *ru, pixman_box32_t box) {
+	if (box_empty_or_invalid(box)) {
+		return;
+	}
+
+	box_union(&ru->bounding_box, box);
+
+	if (!ru->alloc_failure) {
+		pixman_box32_t *entry = wl_array_add(&ru->unsorted, sizeof(*entry));
+		if (entry) {
+			*entry = box;
+		} else {
+			handle_alloc_failure(ru);
+		}
+	}
+}
+
+const pixman_region32_t *rect_union_evaluate(struct rect_union *ru) {
+	if (ru->alloc_failure) {
+		goto bounding_box;
+	}
+
+	int nrects = (int)(ru->unsorted.size / sizeof(pixman_box32_t));
+	pixman_region32_t reg;
+	bool ok = pixman_region32_init_rects(&reg, ru->unsorted.data, nrects);
+	if (!ok) {
+		handle_alloc_failure(ru);
+		goto bounding_box;
+	}
+	ok = pixman_region32_union(&reg, &reg, &ru->region);
+	if (!ok) {
+		pixman_region32_fini(&reg);
+		handle_alloc_failure(ru);
+		goto bounding_box;
+	}
+	pixman_region32_fini(&ru->region);
+	// pixman_region32_t is safe to move
+	ru->region = reg;
+	wl_array_release(&ru->unsorted);
+	wl_array_init(&ru->unsorted);
+
+	return &ru->region;
+bounding_box:
+	pixman_region32_fini(&ru->region);
+	if (box_empty_or_invalid(ru->bounding_box)) {
+		pixman_region32_init(&ru->region);
+	} else {
+		pixman_region32_init_with_extents(&ru->region, &ru->bounding_box);
+	}
+	return &ru->region;
+}
+