Am adding a second answer, as this is a radical departure from the first answer, and attempts to resolve the more central issue with the 2D Bin Packing algorithm presented in the question. With that particular algorithm, the splitNode routine generates down and right nodes available for fitting blocks, but does not take into account the possibility that as the available nodes accumulate, that the union of adjoining nodes can accommodate larger blocks...
For example, in the proposed algorithm below, given an 800x600 initial heap, placing a 500x300 block will result in the heap containing two heapBlocks of (0,300)-(800,600) and (500,0)-(800,600). These two heapBlocks will overlap in the area of (500,300)-(800,600) to ensure that the maximal heapBlock areas are represented when searching for a location to fit a block. Whereas in the 2D Bin Packing algorithm, there is no intersecting area in down or right, but rather, favors the potential overlapping space to one or the other node...
The algorithm below attempts to remedy this shortcoming by implementing an array of available heapBlocks that represent the largest available blocks, even if these heapBlocks overlap each other. The drawback is that this introduces an O(n^2) algorithm (unionAll) to manage the heap, on top of the O(n) loop (fit) of walking through the blocks to fit. Thus, this algorithm might approach O(n^3) in performance, although this might be a worse case scenario...
Packer = function(w, h) {
this.init(w, h);
};
Packer.prototype = {
init: function(w, h) {
this._root = { x: 0, y: 0, w: w, h: h }
},
intersect: function(block0, block1) {
//
// Returns the intersecting block of
// block0 and block1.
//
let ix0 = Math.max(block0.x0, block1.x0);
let ix1 = Math.min(block0.x1, block1.x1);
let iy0 = Math.max(block0.y0, block1.y0);
let iy1 = Math.min(block0.y1, block1.y1);
if (ix0 <= ix1 && iy0 <= iy1) {
return {x0: ix0, y0: iy0, x1: ix1, y1: iy1};
} else {
return null;
}
},
chunkContains: function(heapBlock0, heapBlock1) {
//
// Determine whether heapBlock0 totally encompasses (ie, contains) heapBlock1.
//
return heapBlock0.x0 <= heapBlock1.x0 && heapBlock0.y0 <= heapBlock1.y0 && heapBlock1.x1 <= heapBlock0.x1 && heapBlock1.y1 <= heapBlock0.y1;
},
expand: function(heapBlock0, heapBlock1) {
//
// Extend heapBlock0 and heapBlock1 if they are
// adjoining or overlapping.
//
if (heapBlock0.x0 <= heapBlock1.x0 && heapBlock1.x1 <= heapBlock0.x1 && heapBlock1.y0 <= heapBlock0.y1) {
heapBlock1.y0 = Math.min(heapBlock0.y0, heapBlock1.y0);
heapBlock1.y1 = Math.max(heapBlock0.y1, heapBlock1.y1);
}
if (heapBlock0.y0 <= heapBlock1.y0 && heapBlock1.y1 <= heapBlock0.y1 && heapBlock1.x0 <= heapBlock0.x1) {
heapBlock1.x0 = Math.min(heapBlock0.x0, heapBlock1.x0);
heapBlock1.x1 = Math.max(heapBlock0.x1, heapBlock1.x1);
}
},
unionMax: function(heapBlock0, heapBlock1) {
//
// Given two heap blocks, determine whether...
//
if (heapBlock0 && heapBlock1) {
// ...heapBlock0 and heapBlock1 intersect, and if so...
let i = this.intersect(heapBlock0, heapBlock1);
if (i) {
if (this.chunkContains(heapBlock0, heapBlock1)) {
// ...if heapBlock1 is contained by heapBlock0...
heapBlock1 = null;
} else if (this.chunkContains(heapBlock1, heapBlock0)) {
// ...or if heapBlock0 is contained by heapBlock1...
heapBlock0 = null;
} else {
// ...otherwise, let's expand both heapBlock0 and
// heapBlock1 to encompass as much of the intersected
// space as possible. In this instance, both heapBlock0
// and heapBlock1 will overlap.
this.expand(heapBlock0, heapBlock1);
this.expand(heapBlock1, heapBlock0);
}
}
}
},
unionAll: function() {
//
// Loop through the entire heap, looking to eliminate duplicative
// heapBlocks, and to extend adjoining or intersecting heapBlocks,
// despite this introducing overlapping heapBlocks.
//
for (let i = 0; i < this.heap.length; i++) {
for (let j = 0; j < this.heap.length; j++) {
if (i !== j) {
this.unionMax(this.heap[i],this.heap[j]);
if (this.heap[i] && this.heap[j]) {
if (this.chunkContains(this.heap[j], this.heap[i])) {
this.heap[i] = null;
} else if (this.chunkContains(this.heap[i], this.heap[j])) {
this.heap[j] = null;
}
}
}
}
}
// Eliminate the duplicative (ie, nulled) heapBlocks.
let onlyBlocks = [];
for (let i = 0; i < this.heap.length; i++) {
if (this.heap[i]) {
onlyBlocks.push(this.heap[i]);
}
}
this.heap = onlyBlocks;
},
fit: function(blocks) {
//
// Loop through all the blocks, looking for a heapBlock
// that it can fit into.
//
this.heap = [{x0:0,y0:0,x1:this._root.w, y1: this._root.h}];
var n, node, block;
for (n = 0; n < blocks.length; n++) {
block = blocks[n];
block.rotate = false;
if (this.findInHeap(block)) {
this.adjustHeap(block);
} else {
// If the block didn't fit in its current orientation,
// rotate its dimensions and look again.
block.w = block.h + (block.h = block.w, 0);
block.rotate = true;
if (this.findInHeap(block)) {
this.adjustHeap(block);
}
}
}
},
findInHeap: function(block) {
//
// Find a heapBlock that can contain the block.
//
for (let i = 0; i < this.heap.length; i++) {
let heapBlock = this.heap[i];
if (heapBlock && block.w <= heapBlock.x1 - heapBlock.x0 && block.h <= heapBlock.y1 - heapBlock.y0) {
block.x0 = heapBlock.x0;
block.y0 = heapBlock.y0;
block.x1 = heapBlock.x0 + block.w;
block.y1 = heapBlock.y0 + block.h;
return true;
}
}
return false;
},
adjustHeap: function(block) {
//
// Find all heap entries that intersect with block,
// and adjust the heap by breaking up the heapBlock
// into the possible 4 blocks that remain after
// removing the intersecting portion.
//
let n = this.heap.length;
for (let i = 0; i < n; i++) {
let heapBlock = this.heap[i];
let overlap = this.intersect(heapBlock, block);
if (overlap) {
// Top
if (overlap.y1 !== heapBlock.y1) {
this.heap.push({
x0: heapBlock.x0,
y0: overlap.y1,
x1: heapBlock.x1,
y1: heapBlock.y1
});
}
// Right
if (overlap.x1 !== heapBlock.x1) {
this.heap.push({
x0: overlap.x1,
y0: heapBlock.y0,
x1: heapBlock.x1,
y1: heapBlock.y1
});
}
// Bottom
if (heapBlock.y0 !== overlap.y0) {
this.heap.push({
x0: heapBlock.x0,
y0: heapBlock.y0,
x1: heapBlock.x1,
y1: overlap.y0
});
}
// Left
if (heapBlock.x0 != overlap.x0) {
this.heap.push({
x0: heapBlock.x0,
y0: heapBlock.y0,
x1: overlap.x0,
y1: heapBlock.y1
});
}
this.heap[i] = null;
}
}
this.unionAll();
}
}
The fit algorithm will leave the heap and the incoming blocks array with the results. For example...
p = new Packer(2400,1200);
blocks = [{w:2100,h:600},{w:2100,h:600},{w:150,h:200},{w:740,h:200},{w:500,h:100}];
p.fit(blocks);
...will leave p.heap and blocks as follows...
The final HEAP
[{"x0":2100,"y0":940,"x1":2400,"y1":1200},
{"x0":2300,"y0":500,"x1":2400,"y1":1200},
{"x0":2250,"y0":0,"x1":2300,"y1":200}]
The final BLOCKS
[{"w":2100,"h":600,"rotate":false,"x0":0,"y0":0,"x1":2100,"y1":600},
{"w":2100,"h":600,"rotate":false,"x0":0,"y0":600,"x1":2100,"y1":1200},
{"w":150,"h":200,"rotate":false,"x0":2100,"y0":0,"x1":2250,"y1":200},
{"w":200,"h":740,"rotate":true,"x0":2100,"y0":200,"x1":2300,"y1":940},
{"w":100,"h":500,"rotate":true,"x0":2300,"y0":0,"x1":2400,"y1":500}]
Note that this algorithm is not optimized. Ie, it does not sort the incoming blocks (ie, by width, height, or area, etc), nor does it sort the heap after performing a unionAll which reduces the heap to the list of maximum sized heapBlocks. (Ie, after each call to unionAll, the opportunity exists to sort the heap by width, height, or area, etc so that when searching the heap for the next available block to place, if the heap is sorted largest to smallest, the algorithm will place the block in the largest available heapBlock, or if sorted smallest to largest, the block will be placed in the heapBlock that's just big enough...) In any event, will leave these types of optimizations as an exercise.
Also, please view this algorithm with some skepticism, and test appropriately.
