javascript - 在二维区域内为对象寻找空间的算法

Question

我正在构建一个网站，该网站使用 jQuery 允许用户将小部件添加到页面，将它们四处拖动并调整它们的大小(页面是固定宽度和无限高度。)我遇到的问题是添加时页面的新小部件我必须为其找到可用空间(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。原因是它们设计用于将所有对象打包到容器中，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，这简化了计算下一行/列中适合的位置。当用户可以随意移动/调整小部件时，这些算法将无法正常工作。

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，我意识到它行不通。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？它是我正在寻找的打包算法还是其他更好的算法？

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了放置小部件，那么您可以跳过大部分网格。

这是一个例子:(在这个例子中放置的小部件是 20x20，页面宽度是 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. 我们尝试在 0x0 处放置一个小部件，但它不适合，因为在该坐标处有一个 50x50 的小部件。
2. 然后我们将当前扫描的 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，但这没有为放置的小部件留出足够的空间，因此我们增加 y 坐标并将 x 重置回 0。
5. 我们从之前的尝试中得知，前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，发现我们可以在 51x31 处放置一个小部件

这是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
}

这是一个更长、更不优雅的版本，它还可以调整容器的高度(我现在只是把它拼凑在一起，但稍后会清理它并进行编辑)

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;
}