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.
This commit is contained in:
Manuel Stoeckl 2023-10-01 16:25:39 -04:00 committed by Simon Ser
parent d817ebb80f
commit d180f4d9b3
3 changed files with 168 additions and 0 deletions

76
include/util/rect_union.h Normal file
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@ -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

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@ -5,6 +5,7 @@ wlr_files += files(
'env.c',
'global.c',
'log.c',
'rect_union.c',
'region.c',
'set.c',
'shm.c',

91
util/rect_union.c Normal file
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@ -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;
}