在二维区域内为物体寻找空间的算法

Question

我正在构建一个使用 jQuery 的网站，以允许用户将小部件添加到页面，拖动它们并调整它们的大小（页面是固定宽度和无限高。）我遇到的问题是添加时页面的新小部件我必须为它找到一个可用空间（小部件不能重叠，我希望页面顶部有空间。）

我一直在研究各种打包算法，但似乎没有一个适合。原因是它们是为将所有对象打包到容器中而设计的，这意味着之前的所有矩形都以统一的方式布局。它们通常排列矩形的边缘，以便形成行/列，这简化了计算出适合下一行/列的位置的内容。当用户可以随意移动/调整小部件的大小时，这些算法就不能正常工作了。

我以为我有一个部分解决方案，但在这里写了一些伪代码后，我意识到它不起作用。基于蛮力的方法会起作用，但如果可能的话，我更喜欢更有效的方法。谁能推荐一个合适的算法？这是我正在寻找的打包算法还是其他更好的方法？

谢谢

Answer 1

好的，我已经找到了解决方案。我不喜欢基于蛮力的方法的想法，因为我认为它效率低下，但我意识到，如果您可以查看哪些现有小部件妨碍放置小部件，那么您可以跳过大部分网格。

这是一个示例：（在此示例中，放置的小部件为 20x20，页面宽度为 100px。）

This diagram is 0.1 scale and got messed up so I've had to add an extra column

*123456789A*
1+---+ +--+1
2|   | |  |2
3|   | +--+3
4|   |     4
5+---+     5
*123456789A*

1. 我们尝试将小部件放置在 0x0 处，但它不适合，因为该坐标处有一个 50x50 小部件。
2. 然后我们将当前正在扫描的 x 坐标推进到 51 并再次检查。
3. 然后我们在 0x61 处找到一个 40x30 的小部件。
4. 然后我们将 x 坐标提高到 90，但这并没有为要放置的小部件留下足够的空间，因此我们增加了 y 坐标并将 x 重置回 0。
5. 从之前的尝试中我们知道，上一行的小部件至少有 30 像素高，因此我们将 y 坐标增加到 31。
6. 我们在 0x31 处遇到相同的 50x50 小部件。
7. 所以我们将 x 增加到 51，发现可以在 51x31 处放置一个小部件

这里是javascript：

function findSpace(width, height) {
    var $ul = $('.snap-layout>ul');
    var widthOfContainer = $ul.width();
    var heightOfContainer = $ul.height();
    var $lis = $ul.children('.setup-widget'); // The li is on the page and we dont want it to collide with itself

    for (var y = 0; y < heightOfContainer - height + 1; y++) {
        var heightOfShortestInRow = 1;
        for (var x = 0; x < widthOfContainer - width + 1; x++) {
            console.log(x + '/' + y);
            var pos = { 'left': x, 'top': y };
            var $collider = $(isOverlapping($lis, pos, width, height));
            if ($collider.length == 0) {
                // Found a space
                return pos;
            }

            var colliderPos = $collider.position();
            // We have collided with something, there is no point testing the points within this widget so lets skip them
            var newX = colliderPos.left + $collider.width() - 1; // -1 to account for the ++ in the for loop
            x = newX > x ? newX : x; // Make sure that we are not some how going backwards and looping forever

            var colliderBottom = colliderPos.top + $collider.height();
            if (heightOfShortestInRow == 1 || colliderBottom - y < heightOfShortestInRow) {
                heightOfShortestInRow = colliderBottom - y; // This isn't actually the height its just the distance from y to the bottom of the widget, y is normally at the top of the widget tho
            }
        }
        y += heightOfShortestInRow - 1;
    }

    //TODO: Add the widget to the bottom
}

这是更长且更不优雅的版本，它还调整了容器的高度（我现在只是将它一起破解，但稍后会清理并编辑）

function findSpace(width, height,
        yStart, avoidIds // These are used if the function calls itself - see bellow
    ) {
    var $ul = $('.snap-layout>ul');
    var widthOfContainer = $ul.width();
    var heightOfContainer = $ul.height();
    var $lis = $ul.children('.setup-widget'); // The li is on the page and we dont want it to collide with itself

    var bottomOfShortestInRow;
    var idOfShortestInRow;

    for (var y = yStart ? yStart : 0; y <= heightOfContainer - height + 1; y++) {
        var heightOfShortestInRow = 1;
        for (var x = 0; x <= widthOfContainer - width + 1; x++) {
            console.log(x + '/' + y);
            var pos = { 'left': x, 'top': y };
            var $collider = $(isOverlapping($lis, pos, width, height));
            if ($collider.length == 0) {
                // Found a space
                return pos;
            }

            var colliderPos = $collider.position();
            // We have collided with something, there is no point testing the points within this widget so lets skip them
            var newX = colliderPos.left + $collider.width() - 1; // -1 to account for the ++ in the for loop
            x = newX > x ? newX : x; // Make sure that we are not some how going backwards and looping forever

            colliderBottom = colliderPos.top + $collider.height();
            if (heightOfShortestInRow == 1 || colliderBottom - y < heightOfShortestInRow) {
                heightOfShortestInRow = colliderBottom - y; // This isn't actually the height its just the distance from y to the bottom of the widget, y is normally at the top of the widget tho
                var widgetId = $collider.attr('data-widget-id');
                if (!avoidIds || !$.inArray(widgetId, avoidIds)) { // If this is true then we are calling ourselves and we used this as the shortest widget before and it didnt work
                    bottomOfShortestInRow = colliderBottom;
                    idOfShortestInRow = widgetId;
                }
            }
        }
        y += heightOfShortestInRow - 1;
    }

    if (!yStart) {
        // No space was found so create some
        var idsToAvoid = [];

        for (var attempts = 0; attempts < widthOfContainer; attempts++) { // As a worse case scenario we have lots of 1px wide colliders
            idsToAvoid.push(idOfShortestInRow);

            heightOfContainer = $ul.height();
            var maxAvailableRoom = heightOfContainer - bottomOfShortestInRow;
            var extraHeightRequired = height - maxAvailableRoom;
            if (extraHeightRequired < 0) { extraHeightRequired = 0;}

            $ul.height(heightOfContainer + extraHeightRequired);

            var result = findSpace(width, height, bottomOfShortestInRow, idsToAvoid);
            if (result.top) {
                // Found a space
                return result;
            }

            // Got a different collider so lets try that next time
            bottomOfShortestInRow = result.bottom;
            idOfShortestInRow = result.id;

            if (!bottomOfShortestInRow) {
                // If this is undefined then its broken (because the widgets are bigger then their contianer which is hardcoded atm and resets on f5)
                break;
            }
        }

        debugger;
        // Something has gone wrong so we just stick it on the bottom left
        $ul.height($ul.height() + height);
        return { 'left': 0, 'top': $ul.height() - height };

    } else {
        // The function is calling itself and we shouldnt recurse any further, just return the data required to continue searching
        return { 'bottom': bottomOfShortestInRow, 'id': idOfShortestInRow };
    }
}


function isOverlapping($obsticles, tAxis, width, height) {
    var t_x, t_y;
    if (typeof (width) == 'undefined') {
        // Existing element passed in
        var $target = $(tAxis);
        tAxis = $target.position();
        t_x = [tAxis.left, tAxis.left + $target.outerWidth()];
        t_y = [tAxis.top, tAxis.top + $target.outerHeight()];
    } else {
        // Coordinates and dimensions passed in
        t_x = [tAxis.left, tAxis.left + width];
        t_y = [tAxis.top, tAxis.top + height];
    }

    var overlap = false;

    $obsticles.each(function () {
        var $this = $(this);
        var thisPos = $this.position();
        var i_x = [thisPos.left, thisPos.left + $this.outerWidth()]
        var i_y = [thisPos.top, thisPos.top + $this.outerHeight()];

        if (t_x[0] < i_x[1] && t_x[1] > i_x[0] &&
             t_y[0] < i_y[1] && t_y[1] > i_y[0]) {
            overlap = this;
            return false;
        }
    });
    return overlap;
}