Performance concerns when storing data in large arrays with Javascript - javascript

I have a browser-based visualization app where there is a graph of data points, stored as an array of objects:
data = [
{x: 0.4612451, y: 1.0511} ,
... etc
]
This graph is being visualized with d3 and drawn on a canvas (see that question for an interesting discussion). It is interactive and the scales can change a lot, meaning the data has to be redrawn, and the array needs to be iterated through quite frequently, especially when animating zooms.
From the back of my head and reading other Javascript posts, I have a vague idea that optimizing dereferences in Javascript can lead to big performance improvements. Firefox is the only browser on which my app runs really slow (compared to IE9, Chrome, and Safari) and it needs to be improved. Hence, I'd like to get a firm, authoritative answer the following:
How much slower is this:
// data is an array of 2000 objects with {x, y} attributes
var n = data.length;
for (var i=0; i < n; i++) {
var d = data[i];
// Draw a circle at scaled values on canvas
var cx = xs(d.x);
var cy = ys(d.y);
canvas.moveTo(cx, cy);
canvas.arc(cx, cy, 2.5, 0, twopi);
}
compared to this:
// data_x and data_y are length 2000 arrays preprocessed once from data
var n = data_x.length;
for (var i=0; i < n; i++) {
// Draw a circle at scaled values on canvas
var cx = xs(data_x[i]);
var cy = ys(data_y[i]);
canvas.moveTo(cx, cy);
canvas.arc(cx, cy, 2.5, 0, twopi);
}
xs and ys are d3 scale objects, they are functions that compute the scaled positions. I mentioned the above that the above code may need to run up to 60 frames per second and can lag like balls on Firefox. As far as I can see, the only differences are array dereferences vs object accessing. Which one runs faster and is the difference significant?

It's pretty unlikely that any of these loop optimizations will make any difference. 2000 times through a loop like this is not much at all.
I tend to suspect the possibility of a slow implementation of canvas.arc() in Firefox. You could test this by substituting a canvas.lineTo() call which I know is fast in Firefox since I use it in my PolyGonzo maps. The "All 3199 Counties" view on the test map on that page draws 3357 polygons (some counties have more than one polygon) with a total of 33,557 points, and it loops through a similar canvas loop for every one of those points.

Thanks to the suggestion for JsPerf, I implemented a quick test. I would be grateful for anyone else to add their results here.
http://jsperf.com/canvas-dots-testing: results as of 3/27/13:
I have observed the following so far:
Whether arrays or objects is better seems to depend on the browser, and OS. For example Chrome was the same speed on Linux but objects were faster in Windows. But for many they are almost identical.
Firefox is just the tortoise of the bunch and this also helps confirm Michael Geary's hypothesis that its canvas.arc() is just super slow.

Related

Japavascript and P5.js - Optimizing a 4D projection code

I know that "how to optimize this code?" kind of question is generally not welcomed in stack overflow. But I think this is only the way i could phrase my question. I wrote a code that projects a 4 dimensional points onto a 3 dimensional space. I then draw the 3d points using the p5.js library.
Here is my code: https://jsfiddle.net/dfq8ykLw/
Now my question here is, how am I supposed to make this run faster, and optimize the code? Since I am supposed to draw few thousand points (sometimes more) per frame, and calculate the rotation for each of those points, my code tend to run incredibly slowly (mac devices can run this a little faster for some reason).
I tried drawing points instead of vertices, which ended up running even slower.
Are there any suggestion of how to improve the performance? Or an advice of what kind of library to use for drawing 3 dimensional shapes?
Just to explain, my program stores the points as nested array, just like [[Point object, Point object, ...], ...].
Each array in the data works as a face, with each Point object being the vertices.
I first rotate each of these points by applying 6 rotations (for axis xy, xz, xw, yz, yw and zw), then draw them by projecting them onto the 3d space.
Any help is appreciated, as I am terribly stuck!
in source code
Begin shape drawing. However in WEBGL mode, application
performance will likely drop as a result of too many calls to
beginShape() / endShape(). As a high performance alternative,
...
_main.default.RendererGL.prototype.beginShape
So we may want to avoid too many beginShape calls.
Idem call it on cube instead of face
beginShape()
data.forEach((hyperobject, i) => {
// face
for (var p in hyperobject){
hyperobject[p].rotate(angles[0], angles[1], angles[2], angles[3], angles[4], angles[5])
hyperobject[p].draw()
}
if (i % 6 === 0) {
endShape(CLOSE);
beginShape()
}
})
endShape()
However there are some ugly drawn line, because default mode is TRIANGLE_FAN
_main.default.RendererGL.prototype.beginShape = function(mode) {
this.immediateMode.shapeMode =
mode !== undefined ? mode : constants.TRIANGLE_FAN;
So we may specify TRIANGLES instead:
function draw(){
//noLoop()
background(0);
// translate(250, 250);
for (var a in angles){
angles[a] += angleSpeeds[a];
}
beginShape(TRIANGLES)
data.forEach((hyperobject, i) => {
// face
const [a, b, c, d] = hyperobject.map(a => {
a.rotate(angles[0], angles[1], angles[2], angles[3], angles[4], angles[5])
return a
})
//first triangle
a.draw()
b.draw()
c.draw()
a.draw()
b.draw()
d.draw()
if (i % 6 === 0) {
endShape()
beginShape(TRIANGLES)
}
})
endShape()
}
Note that you could factorize the rotation
const [axy, axz, axw, ayz, ayw, azw] = angles
const f = x => [Math.cos(x), Math.sin(x)]
const [Ca, Sa] = f(axy)
const [Cb, Sb] = f(axz)
const [Cc, Sc] = f(axw)
const [Cd, Sd] = f(ayz)
const [Ce, Se] = f(ayw)
const [Cf, Sf] = f(azw)
const R = [
[Ca*Cb*Cc, -Cb*Cc*Sa, -Cc*Sb, -Sc],
[Ca*(-Cb*Sc*Se-Ce*Sb*Sd)+Cd*Ce*Sa, -Sa*(-Cb*Sc*Se-Ce*Sb*Sd)+Ca*Cd*Ce, -Cb*Ce*Sd+Sb*Sc*Se, -Cc*Se],
[Ca*(Sb*(Sd*Se*Sf+Cd*Cf)-Cb*Ce*Sc*Sf)+Sa*(-Cd*Se*Sf+Cf*Sd), -Sa*(Sb*(Sd*Se*Sf+Cd*Cf)-Cb*Ce*Sc*Sf)+Ca*(-Cd*Se*Sf+Cf*Sd), Cb*(Sd*Se*Sf+Cd*Cf)+Ce*Sb*Sc*Sf, -Cc*Ce*Sf],
[Ca*(Sb*(-Cf*Sd*Se+Cd*Sf)+Cb*Ce*Cf*Sc)+Sa*(Cd*Cf*Se+Sd*Sf),-Sa*(Sb*(-Cf*Sd*Se+Cd*Sf)+Cb*Ce*Cf*Sc)+Ca*(Cd*Cf*Se+Sd*Sf), Cb*(-Cf*Sd*Se+Cd*Sf)-Ce*Cf*Sb*Sc, Cc*Ce*Cf]
]
Point.prototype.rotate = function (R) {
const X = [this.origx, this.origy, this.origz, this.origw]
const [x,y,z,w] = prod(R, X)
Object.assign(this, { x, y, z, w })
}
but this is not the bottleneck, (like 1ms to 50ms for drawing), so keeping your matrix decomposition may be preferable.
I can't put the code snippet here since webgl not secure
https://jsfiddle.net/gk4Lvptm/
first see this (and all sub links) for inspiration:
how should i handle (morphing) 4D objects in opengl?
especially the 4D rotations and reper4D links.
Use 5x5 4D homogenuous transform matrices
this will convert all your transformations into single matrix * vector operation without any goniometrics (repeated for each vertex) so it should be much faster. Even allows to stack operations and much more.
You can port to GLSL
You can move much of the computations (transformations included) into shaders. I know GLSL suports only 4x4 matrices but You can compute mat5 * vec5 by using mat4 and vec4 too... You just add the missing stuff into separate variable and use dot product for the missing col/row
Use of VAO/VBO
This can improve speed a lot as you would not need to pass any data to GPU during rendering anymore... However you would need to do the projection on GPU side (which is doable as unlike cross-section the projection is easy to implement).

EaselJS with 200+ vector shapes : performance and aesthetics

I'm having a huge perf issue when using EaselJS vs Canvas native method : 2.2 s vs 0.01 s (although EaselJS do map canvas native methods...).
I wrote a canvas app which draws a tree*. In order to animate the growth af the tree, it seems cleaner and handier to tween an EaselJS graphics object than writing a custom drawing function.
*(actually it'll look more like a virginia creeper)
1) I must have done something wrong, as the perf with EaselJS are awfull.
The significant piece of the code :
var g=new createjs.Graphics();
g.bs(branchTexture);
for (var i=0; i < arbre.length; i++) {
var step=arbre[i];
for (var t=0; t < step.length; t++){
var d=step[t];
var c=d[5];
var s=new createjs.Shape(g);
s.graphics.setStrokeStyle(7*(Math.pow(.65,d[7]-1)),'round').mt(c[0],c[1]).qt(c[2],c[3],c[4],c[5]);
}
mainStage.addChild(s);
}
}
mainStage.update();
Here's a jsfiddle showing the comparison :
http://jsfiddle.net/xxsL683x/29/
I tried removing texture, simplifying moveTo() operations, but the result si still very slow. Caching doesn't apply, as it's the first rendering pass.
What have I done wrong ?
2) Additionally, I need to find a way to orient the filling pattern in the direction of the growth, so I think i'll get rid of the vector shapes and interpolate some bitmap between two "growth states". If anyone has a better idea, i would be glad to read it.
(But it would be nice to have an answer to the first question though, it's probably not the last time I'll be attempting to tween complex objects.)
3) Another reason for getting rid of EaselJS is that the antialiasing doesn't apply. Why ? Also has to be investigated...
Hope this question will help others to avoid some errors, if I've done some, or at least lead to a better understanding of the way easeljs handles vector shapes.
PS : The tree do have leaves ;)... but I pulled them out for obvious clarity reasons.
I've update your Fiddle, it's now much faster. The problem is that you're creating a new Shape in each loop, which is pretty slow.
for (var t=0; t < step.length; t++){
// loop
g.setStrokeStyle(7*(Math.pow(.65,d[7]-1)),'round').mt(c[0],c[1]).qt(c[2],c[3],c[4],c[5]);
}
// then just create a Shape after all your graphic commands are built
var s = new createjs.Shape(g);
mainStage.addChild(s);
http://jsfiddle.net/xxsL683x/31/

render a tile map using javascript

I'm looking for a logical understanding with sample implementation ideas on taking a tilemap such as this:
http://thorsummoner.github.io/old-html-tabletop-test/pallete/tilesets/fullmap/scbw_tiles.png
And rendering in a logical way such as this:
http://thorsummoner.github.io/old-html-tabletop-test/
I see all of the tiles are there, but I don't understand how they are placed in a way that forms shapes.
My understanding of rendering tiles so far is simple, and very manual. Loop through map array, where there are numbers (1, 2, 3, whatever), render that specified tile.
var mapArray = [
[0, 0, 0, 0 ,0],
[0, 1, 0, 0 ,0],
[0, 0, 0, 0 ,0],
[0, 0, 0, 0 ,0],
[0, 0, 1, 1 ,0]
];
function drawMap() {
background = new createjs.Container();
for (var y = 0; y < mapArray.length; y++) {
for (var x = 0; x < mapArray[y].length; x++) {
if (parseInt(mapArray[y][x]) == 0) {
var tile = new createjs.Bitmap('images/tile.png');
}
if (parseInt(mapArray[y][x]) == 1) {
var tile = new createjs.Bitmap('images/tile2.png');
}
tile.x = x * 28;
tile.y = y * 28;
background.addChild(tile);
}
}
stage.addChild(background);
}
Gets me:
But this means I have to manually figure out where each tile goes in the array so that logical shapes are made (rock formations, grass patches, etc)
Clearly, the guy who made the github code above used a different method. Any guidance on understanding the logic (with simply pseudo code) would be very helpful
There isn't any logic there.
If you inspect the page's source, you'll see that the last script tag, in the body, has a huge array of tile coordinates.
There is no magic in that example which demonstrates an "intelligent" system for figuring out how to form shapes.
Now, that said, there are such things... ...but they're not remotely simple.
What is more simple, and more manageable, is a map-editor.
Tile Editors
out of the box:
There are lots of ways of doing this... There are free or cheap programs which will allow you to paint tiles, and will then spit out XML or JSON or CSV or whatever the given program supports/exports.
Tiled ( http://mapeditor.org ) is one such example.
There are others, but Tiled is the first I could think of, is free, and is actually quite decent.
pros:
The immediate upside is that you get an app that lets you load image tiles, and paint them into maps.
These apps might even support adding collision-layers and entity-layers (put an enemy at [2,1], a power-up at [3,5] and a "hurt-player" trigger, over the lava).
cons:
...the downside is that you need to know exactly how these files are formatted, so that you can read them into your game engines.
Now, the outputs of these systems are relatively-standardized... so that you can plug that map data into different game engines (what's the point, otherwise?), and while game-engines don't all use tile files that are exactly the same, most good tile-editors allow for export into several formats (some will let you define your own format).
...so that said, the alternative (or really, the same solution, just hand-crafted), would be to create your own tile-editor.
DIY
You could create it in Canvas, just as easily as creating the engine to paint the tiles.
The key difference is that you have your map of tiles (like the tilemap .png from StarCr... erm... the "found-art" from the example, there).
Instead of looping through an array, finding the coordinates of the tile and painting them at the world-coordinates which match that index, what you would do is choose a tile from the map (like choosing a colour in MS Paint), and then wherever you click (or drag), figure out which array point that relates to, and set that index to be equal to that tile.
pros:
The sky is the limit; you can make whatever you want, make it fit any file-format you want to use, and make it handle any crazy stuff you want to throw at it...
cons:
...this of course, means you have to make it, yourself, and define the file-format you want to use, and write the logic to handle all of those zany ideas...
basic implementation
While I'd normally try to make this tidy, and JS-paradigm friendly, that would result in a LOT of code, here.
So I'll try to denote where it should probably be broken up into separate modules.
// assuming images are already loaded properly
// and have fired onload events, which you've listened for
// so that there are no surprises, when your engine tries to
// paint something that isn't there, yet
// this should all be wrapped in a module that deals with
// loading tile-maps, selecting the tile to "paint" with,
// and generating the data-format for the tile, for you to put into the array
// (or accepting plug-in data-formatters, to do so)
var selected_tile = null,
selected_tile_map = get_tile_map(), // this would be an image with your tiles
tile_width = 64, // in image-pixels, not canvas/screen-pixels
tile_height = 64, // in image-pixels, not canvas/screen-pixels
num_tiles_x = selected_tile_map.width / tile_width,
num_tiles_y = selected_tile_map.height / tile_height,
select_tile_num_from_map = function (map_px_X, map_px_Y) {
// there are *lots* of ways to do this, but keeping it simple
var tile_y = Math.floor(map_px_Y / tile_height), // 4 = floor(280/64)
tile_x = Math.floor(map_px_X / tile_width ),
tile_num = tile_y * num_tiles_x + tile_x;
// 23 = 4 down * 5 per row + 3 over
return tile_num;
};
// won't go into event-handling and coordinate-normalization
selected_tile_map.onclick = function (evt) {
// these are the coordinates of the click,
//as they relate to the actual image at full scale
map_x, map_y;
selected_tile = select_tile_num_from_map(map_x, map_y);
};
Now you have a simple system for figuring out which tile was clicked.
Again, there are lots of ways of building this, and you can make it more OO,
and make a proper "tile" data-structure, that you expect to read and use throughout your engine.
Right now, I'm just returning the zero-based number of the tile, reading left to right, top to bottom.
If there are 5 tiles per row, and someone picks the first tile of the second row, that's tile #5.
Then, for "painting", you just need to listen to a canvas click, figure out what the X and Y were,
figure out where in the world that is, and what array spot that's equal to.
From there, you just dump in the value of selected_tile, and that's about it.
// this might be one long array, like I did with the tile-map and the number of the tile
// or it might be an array of arrays: each inner-array would be a "row",
// and the outer array would keep track of how many rows down you are,
// from the top of the world
var world_map = [],
selected_coordinate = 0,
world_tile_width = 64, // these might be in *canvas* pixels, or "world" pixels
world_tile_height = 64, // this is so you can scale the size of tiles,
// or zoom in and out of the map, etc
world_width = 320,
world_height = 320,
num_world_tiles_x = world_width / world_tile_width,
num_world_tiles_y = world_height / world_tile_height,
get_map_coordinates_from_click = function (world_x, world_y) {
var coord_x = Math.floor(world_px_x / num_world_tiles_x),
coord_y = Math.floor(world_px_y / num_world_tiles_y),
array_coord = coord_y * num_world_tiles_x + coord_x;
return array_coord;
},
set_map_tile = function (index, tile) {
world_map[index] = tile;
};
canvas.onclick = function (evt) {
// convert screen x/y to canvas, and canvas to world
world_px_x, world_px_y;
selected_coordinate = get_map_coordinates_from_click(world_px_x, world_px_y);
set_map_tile(selected_coordinate, selected_tile);
};
As you can see, the procedure for doing one is pretty much the same as the procedure for doing the other (because it is -- given an x and y in one coordinate-set, convert it to another scale/set).
The procedure for drawing the tiles, then, is nearly the exact opposite.
Given the world-index and tile-number, work in reverse to find the world-x/y and tilemap-x/y.
You can see that part in your example code, as well.
This tile-painting is the traditional way of making 2d maps, whether we're talking about StarCraft, Zelda, or Mario Bros.
Not all of them had the luxury of having a "paint with tiles" editor (some were by hand in text-files, or even spreadsheets, to get the spacing right), but if you load up StarCraft or even WarCraft III (which is 3D), and go into their editors, a tile-painter is exactly what you get, and is exactly how Blizzard made those maps.
additions
With the basic premise out of the way, you now have other "maps" which are also required:
you'd need a collision-map to know which of those tiles you could/couldn't walk on, an entity-map, to show where there are doors, or power-ups or minerals, or enemy-spawns, or event-triggers for cutscenes...
Not all of these need to operate in the same coordinate-space as the world map, but it might help.
Also, you might want a more intelligent "world".
The ability to use multiple tile-maps in one level, for instance...
And a drop-down in a tile-editor to swap tile-maps.
...a way to save out both tile-information (not just X/Y, but also other info about a tile), and to save out the finished "map" array, filled with tiles.
Even just copying JSON, and pasting it into its own file...
Procedural Generation
The other way of doing this, the way you suggested earlier ("knowing how to connect rocks, grass, etc") is called Procedural Generation.
This is a LOT harder and a LOT more involved.
Games like Diablo use this, so that you're in a different randomly-generated environment, every time you play. Warframe is an FPS which uses procedural generation to do the same thing.
premise:
Basically, you start with tiles, and instead of just a tile being an image, a tile has to be an object that has an image and a position, but ALSO has a list of things that are likely to be around it.
When you put down a patch of grass, that grass will then have a likelihood of generating more grass beside it.
The grass might say that there's a 10% chance of water, a 20% chance of rocks, a 30% chance of dirt, and a 40% chance of more grass, in any of the four directions around it.
Of course, it's really not that simple (or it could be, if you're wrong).
While that's the idea, the tricky part of procedural generation is actually in making sure everything works without breaking.
constraints
You couldn't, for example have the cliff wall, in that example, appear on the inside of the high-ground. It can only appear where there's high ground above and to the right, and low-ground below and to the left (and the StarCraft editor did this automatically, as you painted). Ramps can only connect tiles that make sense. You can't wall off doors, or wrap the world in a river/lake that prevents you from moving (or worse, prevents you from finishing a level).
pros
Really great for longevity, if you can get all of your pathfinding and constraints to work -- not only for pseudo-randomly generating the terrain and layout, but also enemy-placement, loot-placement, et cetera.
People are still playing Diablo II, nearly 14 years later.
cons
Really difficult to get right, when you're a one-man team (who doesn't happen to be a mathematician/data-scientist in their spare time).
Really bad for guaranteeing that maps are fun/balanced/competitive...
StarCraft could never have used 100% random-generation for fair gameplay.
Procedural-generation can be used as a "seed".
You can hit the "randomize" button, see what you get, and then tweak and fix from there, but there'll be so much fixing for "balance", or so many game-rules written to constrain the propagation, that you'll end up spending more time fixing the generator than just painting a map, yourself.
There are some tutorials out there, and learning genetic-algorithms, pathfinding, et cetera, are all great skills to have... ...buuuut, for purposes of learning to make 2D top-down tile-games, are way-overkill, and rather, are something to look into after you get a game/engine or two under your belt.

JavaScript "pixel"-perfect collision detection for rotating sprites using math (probably linear algebra)

I'm making a 2D game in JavaScript. For it, I need to be able to "perfectly" check collision between two sprites which have x/y positions (corresponding to their centre), a rotation in radians, and of course known width/height.
After spending many weeks of work (yeah, I'm not even exaggerating), I finally came up with a working solution, which unfortunately turned out to be about 10,000x too slow and impossible to optimize in any meaningful manner. I have entirely abandoned the idea of actually drawing and reading pixels from a canvas. That's just not going to cut it, but please don't make me explain in detail why. This needs to be done with math and an "imaginated" 2D world/grid, and from talking to numerous people, the basic idea became obvious. However, the practical implementation is not. Here's what I do and want to do:
What I already have done
In the beginning of the program, each sprite is pixel-looked through in its default upright position and a 1-dimensional array is filled up with data corresponding to the alpha channel of the image: solid pixels get represented by a 1, and transparent ones by 0. See figure 3.
The idea behind that is that those 1s and 0s no longer represent "pixels", but "little math orbs positioned in perfect distances to each other", which can be rotated without "losing" or "adding" data, as happens with pixels if you rotate images in anything but 90 degrees at a time.
I naturally do the quick "bounding box" check first to see if I should bother calculating accurately. This is done. The problem is the fine/"for-sure" check...
What I cannot figure out
Now that I need to figure out whether the sprites collide for sure, I need to construct a math expression of some sort using "linear algebra" (which I do not know) to determine if these "rectangles of data points", positioned and rotated correctly, both have a "1" in an overlapping position.
Although the theory is very simple, the practical code needed to accomplish this is simply beyond my capabilities. I've stared at the code for many hours, asking numerous people (and had massive problems explaining my problem clearly) and really put in an effort. Now I finally want to give up. I would very, very much appreciate getting this done with. I can't even give up and "cheat" by using a library, because nothing I find even comes close to solving this problem from what I can tell. They are all impossible for me to understand, and seem to have entirely different assumptions/requirements in mind. Whatever I'm doing always seems to be some special case. It's annoying.
This is the pseudo code for the relevant part of the program:
function doThisAtTheStartOfTheProgram()
{
makeQuickVectorFromImageAlpha(sprite1);
makeQuickVectorFromImageAlpha(sprite2);
}
function detectCollision(sprite1, sprite2)
{
// This easy, outer check works. Please ignore it as it is unrelated to the problem.
if (bounding_box_match)
{
/*
This part is the entire problem.
I must do a math-based check to see if they really collide.
These are the relevant variables as I have named them:
sprite1.x
sprite1.y
sprite1.rotation // in radians
sprite1.width
sprite1.height
sprite1.diagonal // might not be needed, but is provided
sprite2.x
sprite2.y
sprite2.rotation // in radians
sprite2.width
sprite2.height
sprite2.diagonal // might not be needed, but is provided
sprite1.vectorForCollisionDetection
sprite2.vectorForCollisionDetection
Can you please help me construct the math expression, or the series of math expressions, needed to do this check?
To clarify, using the variables above, I need to check if the two sprites (which can rotate around their centre, have any position and any dimensions) are colliding. A collision happens when at least one "unit" (an imagined sphere) of BOTH sprites are on the same unit in our imaginated 2D world (starting from 0,0 in the top-left).
*/
if (accurate_check_goes_here)
return true;
}
return false;
}
In other words, "accurate_check_goes_here" is what I wonder what it should be. It doesn't need to be a single expression, of course, and I would very much prefer seeing it done in "steps" (with comments!) so that I have a chance of understanding it, but please don't see this as "spoon feeding". I fully admit I suck at math and this is beyond my capabilities. It's just a fact. I want to move on and work on the stuff I can actually solve on my own.
To clarify: the 1D arrays are 1D and not 2D due to performance. As it turns out, speed matters very much in JS World.
Although this is a non-profit project, entirely made for private satisfaction, I just don't have the time and energy to order and sit down with some math book and learn about that from the ground up. I take no pride in lacking the math skills which would help me a lot, but at this point, I need to get this game done or I'll go crazy. This particular problem has prevented me from getting any other work done for far too long.
I hope I have explained the problem well. However, one of the most frustrating feelings is when people send well-meaning replies that unfortunately show that the person helping has not read the question. I'm not pre-insulting you all -- I just wish that won't happen this time! Sorry if my description is poor. I really tried my best to be perfectly clear.
Okay, so I need "reputation" to be able to post the illustrations I spent time to create to illustrate my problem. So instead I link to them:
Illustrations
(censored by Stackoverflow)
(censored by Stackoverflow)
OK. This site won't let me even link to the images. Only one. Then I'll pick the most important one, but it would've helped a lot if I could link to the others...
First you need to understand that detecting such collisions cannot be done with a single/simple equation. Because the shapes of the sprites matter and these are described by an array of Width x Height = Area bits. So the worst-case complexity of the algorithm must be at least O(Area).
Here is how I would do it:
Represent the sprites in two ways:
1) a bitmap indicating where pixels are opaque,
2) a list of the coordinates of the opaque pixels. [Optional, for speedup, in case of hollow sprites.]
Choose the sprite with the shortest pixel list. Find the rigid transform (translation + rotation) that transforms the local coordinates of this sprite into the local coordinates of the other sprite (this is where linear algebra comes into play - the rotation is the difference of the angles, the translation is the vector between upper-left corners - see http://planning.cs.uiuc.edu/node99.html).
Now scan the opaque pixel list, transforming the local coordinates of the pixels to the local coordinates of the other sprite. Check if you fall on an opaque pixel by looking up the bitmap representation.
This takes at worst O(Opaque Area) coordinate transforms + pixel tests, which is optimal.
If you sprites are zoomed-in (big pixels), as a first approximation you can ignore the zooming. If you need more accuracy, you can think of sampling a few points per pixel. Exact computation will involve a square/square collision intersection algorithm (with rotation), more complex and costly. See http://en.wikipedia.org/wiki/Sutherland%E2%80%93Hodgman_algorithm.
Here is an exact solution that will work regardless the size of the pixels (zoomed or not).
Use both a bitmap representation (1 opacity bit per pixel) and a decomposition into squares or rectangles (rectangles are optional, just an optimization; single pixels are ok).
Process all rectangles of the (source) sprite in turn. By means of rotation/translation, map the rectangles to the coordinate space of the other sprite (target). You will obtain a rotated rectangle overlaid on a grid of pixels.
Now you will perform a filling of this rectangle with a scanline algorithm: first split the rectangle in three (two triangles and one parallelogram), using horizontal lines through the rectangle vertexes. For the three shapes independently, find all horizontal between-pixel lines that cross them (this is simply done by looking at the ranges of Y values). For every such horizontal line, compute the two intersections points. Then find all pixel corners that fall between the two intersections (range of X values). For any pixel having a corner inside the rectangle, lookup the corresponding bit in the (target) sprite bitmap.
No too difficult to program, no complicated data structure. The computational effort is roughly proportional to the number of target pixels covered by every source rectangle.
Although you have already stated that you don't feel rendering to the canvas and checking that data is a viable solution, I'd like to present an idea which may or may not have already occurred to you and which ought to be reasonably efficient.
This solution relies on the fact that rendering any pixel to the canvas with half-opacity twice will result in a pixel of full opacity. The steps follow:
Size the test canvas so that both sprites will fit on it (this will also clear the canvas, so you don't have to create a new element each time you need to test for collision).
Transform the sprite data such that any pixel that has any opacity or color is set to be black at 50% opacity.
Render the sprites at the appropriate distance and relative position to one another.
Loop through the resulting canvas data. If any pixels have an opacity of 100%, then a collision has been detected. Return true.
Else, return false.
Wash, rinse, repeat.
This method should run reasonably fast. Now, for optimization--the bottleneck here will likely be the final opacity check (although rendering the images to the canvas could be slow, as might be clearing/resizing it):
reduce the resolution of the opacity detection in the final step, by changing the increment in your loop through the pixels of the final data.
Loop from middle up and down, rather than from the top to bottom (and return as soon as you find any single collision). This way you have a higher chance of encountering any collisions earlier in the loop, thus reducing its length.
I don't know what your limitations are and why you can't render to canvas, since you have declined to comment on that, but hopefully this method will be of some use to you. If it isn't, perhaps it might come in handy to future users.
Please see if the following idea works for you. Here I create a linear array of points corresponding to pixels set in each of the two sprites. I then rotate/translate these points, to give me two sets of coordinates for individual pixels. Finally, I check the pixels against each other to see if any pair are within a distance of 1 - which is "collision".
You can obviously add some segmentation of your sprite (only test "boundary pixels"), test for bounding boxes, and do other things to speed this up - but it's actually pretty fast (once you take all the console.log() statements out that are just there to confirm things are behaving…). Note that I test for dx - if that is too large, there is no need to compute the entire distance. Also, I don't need the square root for knowing whether the distance is less than 1.
I am not sure whether the use of new array() inside the pixLocs function will cause a problem with memory leaks. Something to look at if you run this function 30 times per second...
<html>
<script type="text/javascript">
var s1 = {
'pix': new Array(0,0,1,1,0,0,1,0,0,1,1,0),
'x': 1,
'y': 2,
'width': 4,
'height': 3,
'rotation': 45};
var s2 = {
'pix': new Array(1,0,1,0,1,0,1,0,1,0,1,0),
'x': 0,
'y': 1,
'width': 4,
'height': 3,
'rotation': 90};
pixLocs(s1);
console.log("now rotating the second sprite...");
pixLocs(s2);
console.log("collision detector says " + collision(s1, s2));
function pixLocs(s) {
var i;
var x, y;
var l1, l2;
var ca, sa;
var pi;
s.locx = new Array();
s.locy = new Array();
pi = Math.acos(0.0) * 2;
var l = new Array();
ca = Math.cos(s.rotation * pi / 180.0);
sa = Math.sin(s.rotation * pi / 180.0);
i = 0;
for(x = 0; x < s.width; ++x) {
for(y = 0; y < s.height; ++y) {
// offset to center of sprite
if(s.pix[i++]==1) {
l1 = x - (s.width - 1) * 0.5;
l2 = y - (s.height - 1) * 0.5;
// rotate:
r1 = ca * l1 - sa * l2;
r2 = sa * l1 + ca * l2;
// add position:
p1 = r1 + s.x;
p2 = r2 + s.y;
console.log("rotated pixel [ " + x + "," + y + " ] is at ( " + p1 + "," + p2 + " ) " );
s.locx.push(p1);
s.locy.push(p2);
}
else console.log("no pixel at [" + x + "," + y + "]");
}
}
}
function collision(s1, s2) {
var i, j;
var dx, dy;
for (i = 0; i < s1.locx.length; i++) {
for (j = 0; j < s2.locx.length; j++) {
dx = Math.abs(s1.locx[i] - s2.locx[j]);
if(dx < 1) {
dy = Math.abs(s1.locy[i] - s2.locy[j]);
if (dx*dx + dy+dy < 1) return 1;
}
}
}
return 0;
}
</script>
</html>

How does 2D drawing frameworks such as Pixi.js make canvas drawing faster?

I found a bunnymark for Javascript canvas here.
Now of course, I understand their default renderer is using webGL but I am only interested in the native 2D context performance for now. I disabled webGL on firefox and after spawning 16500 bunnies, the counter showed a FPS of 25. I decided to wrote my own little very simple rendering loop to see how much overhead Pixi added. To my surprise, I only got a FPS of 20.
My roughly equivalent JSFiddle.
So I decided to take a look into their source here and it doesn't appear to be that the magic is in their rendering code:
do
{
transform = displayObject.worldTransform;
...
if(displayObject instanceof PIXI.Sprite)
{
var frame = displayObject.texture.frame;
if(frame)
{
context.globalAlpha = displayObject.worldAlpha;
context.setTransform(transform[0], transform[3], transform[1], transform[4], transform[2], transform[5]);
context.drawImage(displayObject.texture.baseTexture.source,
frame.x,
frame.y,
frame.width,
frame.height,
(displayObject.anchor.x) * -frame.width,
(displayObject.anchor.y) * -frame.height,
frame.width,
frame.height);
}
}
Curiously, it seems they are using a linked list for their rendering loop and a profile on both app shows that while my version allocates the same amount of cpu time per frame, their implementation shows cpu usage in spikes.
My knowledge ends here unfortunately and I am curious if anyone can shed some light on whats going on.
I think, in my opinion, that it boils down to how "compilable" (cache-able) the code is. Chrome and Firefox uses two different JavaScript "compilers"/engines as we know which optimizes and caching code differently.
Canvas operations
Using transform versus direct coordinates should not have an impact as setting a transform merely updates the matrix which is in any case is used with what-ever is in it.
The type of position values can affect performance though, float versus integer values, but as both your fiddle and PIXI seem to use floats only this is not the key here.
So here I don't think canvas is the cause of the difference.
Variable and property caching
(I got unintentionally too focused on the prototypal aspect in the first version of this answer. The essence I was trying to get at was mainly object traversing, so here the following text is re-worded a bit -)
PIXI uses object properties as the fiddle but these custom objects in PIXI are smaller in size so the traversing of the object tree takes less time compared to what it takes to traverse a larger object such as canvas or image (a property such as width would also be at the end of this object).
It's a well known classic optimization trick to cache variables due to this very reason (traverse time). The effect is less today as the engines has become smarter, especially V8 in Chrome which seem to be able to predict/cache this better internally, while in Firefox it seem to still have a some impact not to cache these variables in code.
Does it matter performance-wise? For short operations very little, but drawing 16,500 bunnies onto canvas is demanding and do gain a benefit from doing this (in FF) so any micro-optimization do actually count in situations such as this.
Demos
I prototyped the "renderer" to get even closer to PIXI as well as caching the object properties. This gave a performance burst in Firefox:
http://jsfiddle.net/AbdiasSoftware/2Dbys/8/
I used a slow computer (to scale the impact) which ran your fiddle at about 5 FPS. After caching the values it ran at 6-7 fps which is more than 20% increase on this computer showing it do have an effect. On a computer with a larger CPU instruction cache and so forth the effect may be less, but it's there as this is related to the FF engine itself (disclaimer: I am not claiming this to be a scientific test however, only a pointer :-) ).
/// cache object properties
var lastTime = 0,
w = canvas.width,
h = canvas.height,
iw = image.width,
ih = image.height;
This next version caches these variables as properties on an object (itself) to show that also this improves performance compared to using large global objects directly - result about the same as above:
http://jsfiddle.net/AbdiasSoftware/2Dbys/9/
var RENDER = function () {
this.width = canvas.width;
this.height = canvas.height;
this.imageWidth = image.width;
this.imageHeight = image.height;
}
In conclusion
I am certain based on the results and previous experience that PIXI can run the code faster due to using custom small-sized objects rather than getting the properties directly from large objects (elements) such as canvas and image.
The FF engine seem not yet to be as "smart" as the V8 engine in regard to object traversing of tree and branches so caching variables do have an impact in FF which comes to display when the demand is high (such as when drawing 16,500 bunnies per "frame").
One difference I noticed between your version and Pixi's is this:
You render image at certain coordinates by passing x/y straight to drawImage function:
drawImage(img, x, y, ...);
..whereas Pixi translates entire canvas context, and then draws image at 0/0 (of already shifted context):
setTransform(1, 0, 0, 1, x, y);
drawImage(img, 0, 0, ...);
They also pass more arguments to drawImage; arguments that control "destination rectangle" — dx, dy, dw, dh.
I suspected this is where speed difference hides. However, changing your test to use same "technique" doesn't really make things better.
But there's something else...
I clocked bunnies to 5000, disabled WebGL, and Pixi actually performs worse than the custom fiddle version.
I get ~27 FPS on Pixi:
and ~32-35 FPS on Fiddle:
This is all on Chrome 33.0.1712.4 dev, Mac OS X.
I'd suspect that this is some canvas compositing issue. Canvas is transparent by default, so the page background needs to be combined with the canvas contents...
I found this in their source...
// update the background color
if (this.view.style.backgroundColor != stage.backgroundColorString &&
!this.transparent) {
this.view.style.backgroundColor = stage.backgroundColorString;
}
Maybe they set the canvas to be opaque for this demo (the fiddle doesn't really work for me, seems like most of the bunnys jump out with an extremely large dt most of the time)?
I don't think it's an object property access timing / compilability thing: The point is valid, but I don't think it can explain that much of a difference.

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