算法 - 给定所有其他矩形的 x 和 y 轴，找到足够的空间来绘制矩形
Ham*_*iii 4 javascript algorithm axis canvas rectangles
每个矩形都有 x 和 y 坐标、宽度和高度。
屏幕的总宽度为 maxWidth，总高度为 maxHeight。
我有一个包含所有已绘制矩形的数组。
我正在开发一个网络应用程序，用户将使用鼠标在屏幕上绘制矩形。为此，我使用 Javascript 在画布元素上绘制。
挑战在于矩形不得在任何给定点相交。
我试图避免这种情况：
或这个：
这就是我的目标输出应该是这样的：
我基本上需要的是一种算法（最好使用 JavaScript），它可以帮助定位足够的空间来绘制知道矩形的轴、高度和宽度的矩形。
BM67 盒装。
这是我用来打包矩形的方法。我自己编造了创建精灵表。
这个怎么运作。
您维护两个数组，一个保存可用空间的矩形（空间数组），另一个保存您放置的矩形。
您首先向空间数组添加一个矩形，该矩形覆盖要填充的整个区域。这个矩形代表可用空间。
添加矩形以适应时，您可以在可用空间矩形中搜索适合新矩形的矩形。如果您找不到一个更大或大小合理的矩形作为您要添加的矩形，则没有空间。
找到放置矩形的位置后，检查所有可用的空间矩形以查看它们是否与新添加的矩形重叠。如果有任何重叠，则沿顶部、底部、左侧和右侧将其切片，从而产生最多 4 个新的空间矩形。执行此操作时会进行一些优化以减少矩形的数量，但无需优化即可工作。
与其他一些方法相比，它并不那么复杂且相当有效。当空间开始变低时特别好。
例子
下面是它用随机矩形填充画布的演示。它在动画循环中显示该过程，因此速度非常慢。
灰色框是适合的。红色显示当前间隔框。每个框有 2 个像素的边距。有关演示常量，请参阅代码顶部。
单击画布以重新启动。
const boxes = []; // added boxes
const spaceBoxes = []; // free space boxes
const space = 2; // space between boxes
const minW = 4; // min width and height of boxes
const minH = 4;
const maxS = 50; // max width and height
// Demo only
const addCount = 2; // number to add per render cycle
const ctx = canvas.getContext("2d");
canvas.width = canvas.height = 1024;
// create a random integer
const randI = (min, max = min + (min = 0)) => (Math.random() * (max - min) + min) | 0;
// itterates an array
const eachOf = (array, cb) => { var i = 0; const len = array.length; while (i < len && cb(array[i], i++, len) !== true ); };
// resets boxes
function start(){
boxes.length = 0;
spaceBoxes.length = 0;
spaceBoxes.push({
x : space, y : space,
w : canvas.width - space * 2,
h : canvas.height - space * 2,
});
}
// creates a random box without a position
function createBox(){
return { w : randI(minW,maxS), h : randI(minH,maxS) }
}
// cuts box to make space for cutter (cutter is a box)
function cutBox(box,cutter){
var b = [];
// cut left
if(cutter.x - box.x - space > minW){
b.push({
x : box.x, y : box.y,
w : cutter.x - box.x - space,
h : box.h,
})
}
// cut top
if(cutter.y - box.y - space > minH){
b.push({
x : box.x, y : box.y,
w : box.w,
h : cutter.y - box.y - space,
})
}
// cut right
if((box.x + box.w) - (cutter.x + cutter.w + space) > space + minW){
b.push({
x : cutter.x + cutter.w + space,
y : box.y,
w : (box.x + box.w) - (cutter.x + cutter.w + space),
h : box.h,
})
}
// cut bottom
if((box.y + box.h) - (cutter.y + cutter.h + space) > space + minH){
b.push({
x : box.x,
y : cutter.y + cutter.h + space,
w : box.w,
h : (box.y + box.h) - (cutter.y + cutter.h + space),
})
}
return b;
}
// get the index of the spacer box that is closest in size to box
function findBestFitBox(box){
var smallest = Infinity;
var boxFound;
eachOf(spaceBoxes,(sbox,index)=>{
if(sbox.w >= box.w && sbox.h >= box.h){
var area = sbox.w * sbox.h;
if(area < smallest){
smallest = area;
boxFound = index;
}
}
})
return boxFound;
}
// returns an array of boxes that are touching box
// removes the boxes from the spacer array
function getTouching(box){
var b = [];
for(var i = 0; i < spaceBoxes.length; i++){
var sbox = spaceBoxes[i];
if(!(sbox.x > box.x + box.w + space || sbox.x + sbox.w < box.x - space ||
sbox.y > box.y + box.h + space || sbox.y + sbox.h < box.y - space )){
b.push(spaceBoxes.splice(i--,1)[0])
}
}
return b;
}
// Adds a space box to the spacer array.
// Check if it is insid, too small, or can be joined to another befor adding.
// will not add if not needed.
function addSpacerBox(box){
var dontAdd = false;
// is to small?
if(box.w < minW || box.h < minH){ return }
// is same or inside another
eachOf(spaceBoxes,sbox=>{
if(box.x >= sbox.x && box.x + box.w <= sbox.x + sbox.w &&
box.y >= sbox.y && box.y + box.h <= sbox.y + sbox.h ){
dontAdd = true;
return true;
}
})
if(!dontAdd){
var join = false;
// check if it can be joinded with another
eachOf(spaceBoxes,sbox=>{
if(box.x === sbox.x && box.w === sbox.w &&
!(box.y > sbox.y + sbox.h || box.y + box.h < sbox.y)){
join = true;
var y = Math.min(sbox.y,box.y);
var h = Math.max(sbox.y + sbox.h,box.y + box.h);
sbox.y = y;
sbox.h = h-y;
return true;
}
if(box.y === sbox.y && box.h === sbox.h &&
!(box.x > sbox.x + sbox.w || box.x + box.w < sbox.x)){
join = true;
var x = Math.min(sbox.x,box.x);
var w = Math.max(sbox.x + sbox.w,box.x + box.w);
sbox.x = x;
sbox.w = w-x;
return true;
}
})
if(!join){ spaceBoxes.push(box) }// add to spacer array
}
}
// Adds a box by finding a space to fit.
function locateSpace(box){
if(boxes.length === 0){ // first box can go in top left
box.x = space;
box.y = space;
boxes.push(box);
var sb = spaceBoxes.pop();
spaceBoxes.push(...cutBox(sb,box));
}else{
var bf = findBestFitBox(box); // get the best fit space
if(bf !== undefined){
var sb = spaceBoxes.splice(bf,1)[0]; // remove the best fit spacer
box.x = sb.x; // use it to position the box
box.y = sb.y;
spaceBoxes.push(...cutBox(sb,box)); // slice the spacer box and add slices back to spacer array
boxes.push(box); // add the box
var tb = getTouching(box); // find all touching spacer boxes
while(tb.length > 0){ // and slice them if needed
eachOf(cutBox(tb.pop(),box),b => addSpacerBox(b));
}
}
}
}
// draws a box array
function drawBoxes(list,col,col1){
eachOf(list,box=>{
if(col1){
ctx.fillStyle = col1;
ctx.fillRect(box.x+ 1,box.y+1,box.w-2,box.h - 2);
}
ctx.fillStyle = col;
ctx.fillRect(box.x,box.y,box.w,1);
ctx.fillRect(box.x,box.y,1,box.h);
ctx.fillRect(box.x+box.w-1,box.y,1,box.h);
ctx.fillRect(box.x,box.y+ box.h-1,box.w,1);
})
}
// Show the process in action
ctx.clearRect(0,0,canvas.width,canvas.height);
var count = 0;
var handle = setTimeout(doIt,10);
start()
function doIt(){
ctx.clearRect(0,0,canvas.width,canvas.height);
for(var i = 0; i < addCount; i++){
var box = createBox();
locateSpace(box);
}
drawBoxes(boxes,"black","#CCC");
drawBoxes(spaceBoxes,"red");
if(count < 1214 && spaceBoxes.length > 0){
count += 1;
handle = setTimeout(doIt,10);
}
}
canvas.onclick = function(){
clearTimeout(handle);
start();
handle = setTimeout(doIt,10);
count = 0;
}canvas { border : 2px solid black; }<canvas id="canvas"></canvas>更新
改进上述算法。
- 将算法转化为对象
- 通过在纵横比上加权拟合来找到更合适的垫片来提高速度
- 添加
placeBox(box)了添加一个框而不检查它是否合适的功能。它将被放置在它的box.x,box.y坐标
有关用法，请参阅下面的代码示例。
例子
该示例与上面的示例相同，但在拟合框之前添加了随机放置的框。
Demo 显示了盒子和间隔盒，因为它展示了它是如何工作的。单击画布以重新启动。按住 [shift] 键并单击画布重新启动而不显示中间结果。
预先放置的盒子是蓝色的。安装的盒子是灰色的。间距框是红色的，会重叠。
当按住 shift 时，拟合过程在第一个不合适的盒子处停止。红色框将显示可用但未使用的区域。
当显示进度时，该功能将继续添加框而忽略不合适的框直到超出空间。
const minW = 4; // min width and height of boxes
const minH = 4;
const maxS = 50; // max width and height
const space = 2;
const numberBoxesToPlace = 20; // number of boxes to place befor fitting
const fixedBoxColor = "blue";
// Demo only
const addCount = 2; // number to add per render cycle
const ctx = canvas.getContext("2d");
canvas.width = canvas.height = 1024;
// create a random integer randI(n) return random val 0-n randI(n,m) returns random int n-m, and iterator that can break
const randI = (min, max = min + (min = 0)) => (Math.random() * (max - min) + min) | 0;
const eachOf = (array, cb) => { var i = 0; const len = array.length; while (i < len && cb(array[i], i++, len) !== true ); };
// creates a random box. If place is true the box also gets a x,y position and is flaged as fixed
function createBox(place){
if(place){
const box = {
w : randI(minW*4,maxS*4),
h : randI(minH*4,maxS*4),
fixed : true,
}
box.x = randI(space, canvas.width - box.w - space * 2);
box.y = randI(space, canvas.height - box.h - space * 2);
return box;
}
return {
w : randI(minW,maxS),
h : randI(minH,maxS),
}
}
//======================================================================
// BoxArea object using BM67 box packing algorithum
// /sf/ask/3197690961/
// Please leave this and the above two lines with any copies of this code.
//======================================================================
//
// usage
// var area = new BoxArea({
// x: ?, // x,y,width height of area
// y: ?,
// width: ?,
// height : ?.
// space : ?, // optional default = 1 sets the spacing between boxes
// minW : ?, // optional default = 0 sets the in width of expected box. Note this is for optimisation you can add smaller but it may fail
// minH : ?, // optional default = 0 sets the in height of expected box. Note this is for optimisation you can add smaller but it may fail
// });
//
// Add a box at a location. Not checked for fit or overlap
// area.placeBox({x : 100, y : 100, w ; 100, h :100});
//
// Tries to fit a box. If the box does not fit returns false
// if(area.fitBox({x : 100, y : 100, w ; 100, h :100})){ // box added
//
// Resets the BoxArea removing all boxes
// area.reset()
//
// To check if the area is full
// area.isFull(); // returns true if there is no room of any more boxes.
//
// You can check if a box can fit at a specific location with
// area.isBoxTouching({x : 100, y : 100, w ; 100, h :100}, area.boxes)){ // box is touching another box
//
// To get a list of spacer boxes. Note this is a copy of the array, changing it will not effect the functionality of BoxArea
// const spacerArray = area.getSpacers();
//
// Use it to get the max min box size that will fit
//
// const maxWidthThatFits = spacerArray.sort((a,b) => b.w - a.w)[0];
// const minHeightThatFits = spacerArray.sort((a,b) => a.h - b.h)[0];
// const minAreaThatFits = spacerArray.sort((a,b) => (a.w * a.h) - (b.w * b.h))[0];
//
// The following properties are available
// area.boxes // an array of boxes that have been added
// x,y,width,height // the area that boxes are fitted to
const BoxArea = (()=>{
const defaultSettings = {
minW : 0, // min expected size of a box
minH : 0,
space : 1, // spacing between boxes
};
const eachOf = (array, cb) => { var i = 0; const len = array.length; while (i < len && cb(array[i], i++, len) !== true ); };
function BoxArea(settings){
settings = Object.assign({},defaultSettings,settings);
this.width = settings.width;
this.height = settings.height;
this.x = settings.x;
this.y = settings.y;
const space = settings.space;
const minW = settings.minW;
const minH = settings.minH;
const boxes = []; // added boxes
const spaceBoxes = [];
this.boxes = boxes;
// cuts box to make space for cutter (cutter is a box)
function cutBox(box,cutter){
var b = [];
// cut left
if(cutter.x - box.x - space >= minW){
b.push({
x : box.x, y : box.y, h : box.h,
w : cutter.x - box.x - space,
});
}
// cut top
if(cutter.y - box.y - space >= minH){
b.push({
x : box.x, y : box.y, w : box.w,
h : cutter.y - box.y - space,
});
}
// cut right
if((box.x + box.w) - (cutter.x + cutter.w + space) >= space + minW){
b.push({
y : box.y, h : box.h,
x : cutter.x + cutter.w + space,
w : (box.x + box.w) - (cutter.x + cutter.w + space),
});
}
// cut bottom
if((box.y + box.h) - (cutter.y + cutter.h + space) >= space + minH){
b.push({
w : box.w, x : box.x,
y : cutter.y + cutter.h + space,
h : (box.y + box.h) - (cutter.y + cutter.h + space),
});
}
return b;
}
// get the index of the spacer box that is closest in size and aspect to box
function findBestFitBox(box, array = spaceBoxes){
var smallest = Infinity;
var boxFound;
var aspect = box.w / box.h;
eachOf(array, (sbox, index) => {
if(sbox.w >= box.w && sbox.h >= box.h){
var area = ( sbox.w * sbox.h) * (1 + Math.abs(aspect - (sbox.w / sbox.h)));
if(area < smallest){
smallest = area;
boxFound = index;
}
}
})
return boxFound;
}
// Exposed helper function
// returns true if box is touching any boxes in array
// else return false
this.isBoxTouching = function(box, array = []){
for(var i = 0; i < array.length; i++){
var sbox = array[i];
if(!(sbox.x > box.x + box.w + space || sbox.x + sbox.w < box.x - space ||
sbox.y > box.y + box.h + space || sbox.y + sbox.h < box.y - space )){
return true;
}
}
return false;
}
// returns an array of boxes that are touching box
// removes the boxes from the array
function getTouching(box, array = spaceBoxes){
var boxes = [];
for(var i = 0; i < array.length; i++){
var sbox = array[i];
if(!(sbox.x > box.x + box.w + space || sbox.x + sbox.w < box.x - space ||
sbox.y > box.y + box.h + space || sbox.y + sbox.h < box.y - space )){
boxes.push(array.splice(i--,1)[0])
}
}
return boxes;
}
// Adds a space box to the spacer array.
// Check if it is inside, too small, or can be joined to another befor adding.
// will not add if not needed.
function addSpacerBox(box, array = spaceBoxes){
var dontAdd = false;
// is box to0 small?
if(box.w < minW || box.h < minH){ return }
// is box same or inside another box
eachOf(array, sbox => {
if(box.x >= sbox.x && box.x + box.w <= sbox.x + sbox.w &&
box.y >= sbox.y && box.y + box.h <= sbox.y + sbox.h ){
dontAdd = true;
return true; // exits eachOf (like a break statement);
}
})
if(!dontAdd){
var join = false;
// check if it can be joined with another
eachOf(array, sbox => {
if(box.x === sbox.x && box.w === sbox.w &&
!(box.y > sbox.y + sbox.h || box.y + box.h < sbox.y)){
join = true;
var y = Math.min(sbox.y,box.y);
var h = Math.max(sbox.y + sbox.h,box.y + box.h);
sbox.y = y;
sbox.h = h-y;
return true; // exits eachOf (like a break statement);
}
if(box.y === sbox.y && box.h === sbox.h &&
!(box.x > sbox.x + sbox.w || box.x + box.w < sbox.x)){
join = true;
var x = Math.min(sbox.x,box.x);
var w = Math.max(sbox.x + sbox.w,box.x + box.w);
sbox.x = x;
sbox.w = w-x;
return true; // exits eachOf (like a break statement);
}
})
if(!join){ array.push(box) }// add to spacer array
}
}
// Adds a box by finding a space to fit.
// returns true if the box has been added
// returns false if there was no room.
this.fitBox = function(box){
if(boxes.length === 0){ // first box can go in top left
box.x = space;
box.y = space;
boxes.push(box);
var sb = spaceBoxes.pop();
spaceBoxes.push(...cutBox(sb,box));
}else{
var bf = findBestFitBox(box); // get the best fit space
if(bf !== undefined){
var sb = spaceBoxes.splice(bf,1)[0]; // remove the best fit spacer
box.x = sb.x; // use it to position the box
box.y = sb.y;
spaceBoxes.push(...cutBox(sb,box)); // slice the spacer box and add slices back to spacer array
boxes.push(box); // add the box
var tb = getTouching(box); // find all touching spacer boxes
while(tb.length > 0){ // and slice them if needed
eachOf(cutBox(tb.pop(),box),b => addSpacerBox(b));
}
} else {
return false;
}
}
return true;
}
// Adds a box at location box.x, box.y
// does not check if it can fit or for overlap.
this.placeBox = function(box){
boxes.push(box); // add the box
var tb = getTouching(box); // find all touching spacer boxes
while(tb.length > 0){ // and slice them if needed
eachOf(cutBox(tb.pop(),box),b => addSpacerBox(b));
}
}
// returns a copy of the spacer array
this.getSpacers = function(){
return [...spaceBoxes];
}
this.isFull = function(){
return spaceBoxes.length === 0;
}
// resets boxes
this.reset = function(){
boxes.length = 0;
spaceBoxes.length = 0;
spaceBoxes.push({