This is a bit complicated to describe, so please bear with me.
I'm using the HTML5 canvas to extend a diagramming tool (Diagramo). It implements multiple types of line, straight, jagged (right angle) and curved (cubic or quadratic). These lines can be solid, dotted or dashed.
The new feature I am implementing is a "squiggly" line, where instead of following a constant path, the line zigzags back and forth across the desired target path in smooth arcs.
Below is an example of this that is correct. This works in most cases, however, in certain edge cases it does not.
The implementation is to take the curve, use the quadratic or cubic functions to estimate equidistance points along the line, and draw squiggles along these straight lines by placing control points on either side of the straight line (alternating) and drawing multiple cubic curves.
The issues occur when the line is relatively short, and doubles back on itself close to the origin. An example is below, this happens on longer lines too - the critical point is that there is a very small sharp curve immediately after the origin. In this situation the algorithm picks the first point after the sharp curve, in some cases immediately next to the origin, and considers that the first segment.
Each squiggle has a minimum/maximum pixel length of 8px/14px (which I can change, but much below that and it becomes too sharp, and above becomes too wavy) the code tries to find the right sized squiggle for the line segment to fit with the minimum empty space, which is then filled by a straight line.
I'm hoping there is a solution to this that can account for sharply curved lines, if I know all points along a line can I choose control points that alternate either side of the line, perpendicular too it?
Would one option be to consider a point i and the points i-1 and i+1 and use that to determine the orientation of the line, and thus pick control points?
Code follows below
//fragment is either Cubic or Quadratic curve.
paint(fragment){
var length = fragment.getLength();
var points = Util.equidistancePoints(fragment, length < 100 ? (length < 50 ? 3: 5): 11);
points.splice(0, 1); //remove origin as that is the initial point of the delegate.
//points.splice(0, 1);
delegate.paint(context, points);
}
/**
*
* #param {QuadCurve} or {CubicCurbe} curve
* #param {Number} m the number of points
* #return [Point] a set of equidistance points along the polyline of points
* #author Zack
* #href http://math.stackexchange.com/questions/321293/find-coordinates-of-equidistant-points-in-bezier-curve
*/
equidistancePoints: function(curve, m){
var points = curve.getPoints(0.001);
// Get fractional arclengths along polyline
var n = points.length;
var s = 1.0/(n-1);
var dd = [];
var cc = [];
var QQ = [];
function findIndex(dd, d){
var i = 0;
for (var j = 0 ; j < dd.length ; j++){
if (d > dd[j]) {
i = j;
}
else{
return i;
}
}
return i;
};
dd.push(0);
cc.push(0);
for (var i = 0; i < n; i++){
if(i >0) {
cc.push(Util.distance(points[i], points[i - 1]));
}
}
for (var i = 1 ; i < n ; i++) {
dd.push(dd[i-1] + cc[i]);
}
for (var i = 1 ; i < n ; i++) {
dd[i] = dd[i]/dd[n-1];
}
var step = 1.0/(m-1);
for (var r = 0 ; r < m ; r++){
var d = parseFloat(r)*step;
var i = findIndex(dd, d);
var u = (d - dd[i]) / (dd[i+1] - dd[i]);
var t = (i + u)*s;
QQ[r] = curve.getPoint(t);
}
return QQ;
}
SquigglyLineDelegate.prototype = {
constructor: SquigglyLineDelegate,
paint: function(context, points){
var squiggles = 0;
var STEP = 0.1;
var useStart = false;
var bestSquiggles = -1;
var bestA = 0;
var distance = Util.distance(points[0], this.start);
for(var a = SquigglyLineDelegate.MIN_SQUIGGLE_LENGTH; a < SquigglyLineDelegate.MAX_SQUIGGLE_LENGTH; a += STEP){
squiggles = distance / a;
var diff = Math.abs(Math.floor(squiggles) - squiggles);
if(diff < bestSquiggles || bestSquiggles == -1){
bestA = a;
bestSquiggles = diff;
}
}
squiggles = distance / bestA;
for(var i = 0; i < points.length; i++){
context.beginPath();
var point = points[i];
for(var s = 0; s < squiggles-1; s++){
var start = Util.point_on_segment(this.start, point, s * bestA);
var end = Util.point_on_segment(this.start, point, (s + 1) * bestA);
var mid = Util.point_on_segment(this.start, point, (s + 0.5) * bestA);
end.style.lineWidth = 1;
var line1 = new Line(Util.point_on_segment(mid, end, -this.squiggleWidth), Util.point_on_segment(mid, end, this.squiggleWidth));
var mid1 = Util.getMiddle(line1.startPoint, line1.endPoint);
line1.transform(Matrix.translationMatrix(-mid1.x, -mid1.y));
line1.transform(Matrix.rotationMatrix(radians = 90 * (Math.PI/180)));
line1.transform(Matrix.translationMatrix(mid1.x, mid1.y));
var control1 = useStart ? line1.startPoint : line1.endPoint;
var curve = new QuadCurve(start, control1, end);
curve.style = null;
curve.paint(context);
useStart = !useStart;
}
this.start = point;
context.lineTo(point.x, point.y);
context.stroke();
}
}
}
Related
I'm trying to create a little simulation with the help of HTML5 and Javascript using a canvas. My problem however is, I can't really think of a way to control the behavior of my pixels, without making every single pixel an object, which leads to an awful slowdown of my simulation.
Heres the code so far:
var pixels = [];
class Pixel{
constructor(color){
this.color=color;
}
}
window.onload=function(){
canv = document.getElementById("canv");
ctx = canv.getContext("2d");
createMap();
setInterval(game,1000/60);
};
function createMap(){
pixels=[];
for(i = 0; i <= 800; i++){
pixels.push(sub_pixels = []);
for(j = 0; j <= 800; j++){
pixels[i].push(new Pixel("green"));
}
}
pixels[400][400].color="red";
}
function game(){
ctx.fillStyle = "white";
ctx.fillRect(0,0,canv.width,canv.height);
for(i = 0; i <= 800; i++){
for(j = 0; j <= 800; j++){
ctx.fillStyle=pixels[i][j].color;
ctx.fillRect(i,j,1,1);
}
}
for(i = 0; i <= 800; i++){
for(j = 0; j <= 800; j++){
if(pixels[i][j].color == "red"){
direction = Math.floor((Math.random() * 4) + 1);
switch(direction){
case 1:
pixels[i][j-1].color= "red";
break;
case 2:
pixels[i+1][j].color= "red";
break;
case 3:
pixels[i][j+1].color= "red";
break;
case 4:
pixels[i-1][j].color= "red";
break;
}
}
}
}
}
function retPos(){
return Math.floor((Math.random() * 800) + 1);
}
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<script language="javascript" type="text/javascript" src="game.js"></script>
</head>
<body>
<canvas width="800px" height="800px" id="canv"></canvas>
</body>
</html>
So my two big questions are, what better way of controlling those pixels is there? And how can I speed up the pixel generation?
Hope you can help me.
Optimizing pixel manipulation
There are many options to speed up your code
Pixels as 32bit ints
The following will slug most machines with too much work.
// I removed fixed 800 and replaced with const size
for(i = 0; i <= size; i++){
for(j = 0; j <= size; j++){
ctx.fillStyle=pixels[i][j].color;
ctx.fillRect(i,j,1,1);
}
}
Don't write each pixel via a rect. Use the pixel data you can get from the canvas API via createImageData and associated functions. It uses typed arrays that are a little quicker than arrays and can have multiple view on the same content.
You can write all the pixels to the canvas in a single call. Not blindingly fast but a zillion times faster than what you are doing.
const size = 800;
const imageData = ctx.createImageData(size,size);
// get a 32 bit view
const data32 = new Uint32Array(imageData.data.buffer);
// To set a single pixel
data32[x+y*size] = 0xFF0000FF; // set pixel to red
// to set all pixels
data32.fill(0xFF00FF00); // set all to green
To get a pixel at a pixel coord
const pixel = data32[x + y * imageData.width];
See Accessing pixel data for more on using the image data.
The pixel data is not displayed until you put it onto the canvas
ctx.putImageData(imageData,0,0);
That will give you a major improvement.
Better data organization.
When performance is critical you sacrifice memory and simplicity to get more CPU cycles doing what you want and less doing a lot of nothing.
You have red pixels randomly expanding into the scene, you read every pixel and check (via a slow string comparison) if it is red. When you find one you add a random red pixel besides it.
Checking the green pixels is a waste and can be avoided. Expanding red pixels that are completely surrounded by other reds is also pointless. They do nothing.
The only pixels you are interested in are the red pixels that are next to green pixels.
Thus you can create a buffer that holds the location of all active red pixels, An active red has at least one green. Each frame you check all the active reds, spawning new ones if they can, and killing them if they are surrounded in red.
We don't need to store the x,y coordinate of each red, just the memory address so we can use a flat array.
const reds = new Uint32Array(size * size); // max size way over kill but you may need it some time.
You dont want to have to search for reds in your reds array so you need to keep track of how many active reds there are. You want all the active reds to be at the bottom of the array. You need to check each active red only once per frame. If a red is dead than all above it must move down one array index. But you only want to move each red only once per frame.
Bubble array
I dont know what this type of array is called its like a separation tank, dead stuff slowly moves up and live stuff moves down. Or unused items bubble up used items settle to the bottom.
I will show it as functional because it will be easier to understand. but is better implemented as one brute force function
// data32 is the pixel data
const size = 800; // width and height
const red = 0xFF0000FF; // value of a red pixel
const green = 0xFF00FF00; // value of a green pixel
const reds = new Uint32Array(size * size); // max size way over kill but you var count = 0; // total active reds
var head = 0; // index of current red we are processing
var tail = 0; // after a red has been process it is move to the tail
var arrayOfSpawnS = [] // for each neighbor that is green you want
// to select randomly to spawn to. You dont want
// to spend time processing so this is a lookup
// that has all the possible neighbor combinations
for(let i = 0; i < 16; i ++){
let j = 0;
const combo = [];
i & 1 && (combo[j++] = 1); // right
i & 2 && (combo[j++] = -1); // left
i & 4 && (combo[j++] = -size); // top
i & 5 && (combo[j++] = size); // bottom
arrayOfSpawnS.push(combo);
}
function addARed(x,y){ // add a new red
const pixelIndex = x + y * size;
if(data32[pixelIndex] === green) { // check if the red can go there
reds[count++] = pixelIndex; // add the red with the pixel index
data32[pixelIndex] = red; // and set the pixel
}
}
function safeAddRed(pixelIndex) { // you know that some reds are safe at the new pos so a little bit faster
reds[count++] = pixelIndex; // add the red with the pixel index
data32[pixelIndex] = red; // and set the pixel
}
// a frame in the life of a red. Returns false if red is dead
function processARed(indexOfRed) {
// get the pixel index
var pixelIndex = reds[indexOfRed];
// check reds neighbors right left top and bottom
// we fill a bit value with each bit on if there is a green
var n = data32[pixelIndex + 1] === green ? 1 : 0;
n += data32[pixelIndex - 1] === green ? 2 : 0;
n += data32[pixelIndex - size] === green ? 4 : 0;
n += data32[pixelIndex + size] === green ? 8 : 0;
if(n === 0){ // no room to spawn so die
return false;
}
// has room to spawn so pick a random
var nCount = arrayOfSpawnS[n].length;
// if only one spawn point then rather than spawn we move
// this red to the new pos.
if(nCount === 1){
reds[indexOfRed] += arrayOfSpawnS[n][0]; // move to next pos
}else{ // there are several spawn points
safeAddRed(pixelIndex + arrayOfSpawnS[n][(Math.random() * nCount)|0]);
}
// reds frame is done so return still alive to spawn another frame
return true;
}
Now to process all the reds.
This is the heart of the bubble array. head is used to index each active red. tail is the index of where to move the current head if no deaths have been encountered tail is equal to head. If however a dead item is encountered the head move up one while the tail remains pointing to the dead item. This moves all the active items to the bottom.
When head === count all active items have been checked. The value of tail now contains the new count which is set after the iteration.
If you were using an object rather than a Integer, instead of moving the active item down you swap the head and tail items. This effectively creates a pool of available objects that can be used when adding new items. This type of array management incurs not GC or Allocation overhead and is hence very quick when compared to stacks and object pools.
function doAllReds(){
head = tail = 0; // start at the bottom
while(head < count){
if(processARed(head)){ // is red not dead
reds[tail++] = reds[head++]; // move red down to the tail
}else{ // red is dead so this creates a gap in the array
// Move the head up but dont move the tail,
// The tail is only for alive reds
head++;
}
}
// All reads done. The tail is now the new count
count = tail;
}
The Demo.
The demo will show you the speed improvement. I used the functional version and there could be some other tweaks.
You can also consider webWorkers to get event more speed. Web worker run on a separate javascript context and provides true concurrent processing.
For the ultimate speed use WebGL. All the logic can be done via a fragment shader on the GPU. This type of task is very well suited to parallel processing for which the GPU is designed.
Will be back later to clean up this answer (got a little too long)
I have also added a boundary to the pixel array as the reds were spawning off the pixel array.
const size = canvas.width;
canvas.height = canvas.width;
const ctx = canvas.getContext("2d");
const red = 0xFF0000FF;
const green = 0xFF00FF00;
const reds = new Uint32Array(size * size);
const wall = 0xFF000000;
var count = 0;
var head = 0;
var tail = 0;
var arrayOfSpawnS = []
for(let i = 0; i < 16; i ++){
let j = 0;
const combo = [];
i & 1 && (combo[j++] = 1); // right
i & 2 && (combo[j++] = -1); // left
i & 4 && (combo[j++] = -size); // top
i & 5 && (combo[j++] = size); // bottom
arrayOfSpawnS.push(combo);
}
const imageData = ctx.createImageData(size,size);
const data32 = new Uint32Array(imageData.data.buffer);
function createWall(){//need to keep the reds walled up so they dont run free
for(let j = 0; j < size; j ++){
data32[j] = wall;
data32[j * size] = wall;
data32[j * size + size - 1] = wall;
data32[size * (size - 1) +j] = wall;
}
}
function addARed(x,y){
const pixelIndex = x + y * size;
if (data32[pixelIndex] === green) {
reds[count++] = pixelIndex;
data32[pixelIndex] = red;
}
}
function processARed(indexOfRed) {
var pixelIndex = reds[indexOfRed];
var n = data32[pixelIndex + 1] === green ? 1 : 0;
n += data32[pixelIndex - 1] === green ? 2 : 0;
n += data32[pixelIndex - size] === green ? 4 : 0;
n += data32[pixelIndex + size] === green ? 8 : 0;
if(n === 0) { return false }
var nCount = arrayOfSpawnS[n].length;
if (nCount === 1) { reds[indexOfRed] += arrayOfSpawnS[n][0] }
else {
pixelIndex += arrayOfSpawnS[n][(Math.random() * nCount)|0]
reds[count++] = pixelIndex;
data32[pixelIndex] = red;
}
return true;
}
function doAllReds(){
head = tail = 0;
while(head < count) {
if(processARed(head)) { reds[tail++] = reds[head++] }
else { head++ }
}
count = tail;
}
function start(){
data32.fill(green);
createWall();
var startRedCount = (Math.random() * 5 + 1) | 0;
for(let i = 0; i < startRedCount; i ++) { addARed((Math.random() * size-2+1) | 0, (Math.random() * size-2+1) | 0) }
ctx.putImageData(imageData,0,0);
setTimeout(doItTillAllDead,1000);
countSameCount = 0;
}
var countSameCount;
var lastCount;
function doItTillAllDead(){
doAllReds();
ctx.putImageData(imageData,0,0);
if(count === 0 || countSameCount === 100){ // all dead
setTimeout(start,1000);
}else{
countSameCount += count === lastCount ? 1 : 0;
lastCount = count; //
requestAnimationFrame(doItTillAllDead);
}
}
start();
<canvas width="800" height="800" id="canvas"></canvas>
The main cause of your slow down is your assumption that you need to loop over every pixel for every operation. You do not do this, as that would be 640,000 iterations for every operation you need to do.
You also shouldn't be doing any manipulation logic within the render loop. The only thing that should be there is drawing code. So this should be moved out to preferably a separate thread (Web Workers). If unable to use those a setTimeout/Interval call.
So first a couple of small changes:
Make Pixel class contain the pixel's coordinates along with the color:
class Pixel{
constructor(color,x,y){
this.color=color;
this.x = x;
this.y = y;
}
}
Keep an array of pixels that will end up creating new red pixels. And another one to keep track of what pixels have been updated so we know which ones need drawn.
var pixels = [];
var infectedPixesl = [];
var updatedPixels = [];
Now the easiest part of the code to change is the render loop. Since the only thing that it needs to do is draw the pixels it will be only a couple lines.
function render(){
var numUpdatedPixels = updatedPixels.length;
for(let i=0; i<numUpdatedPixels; i++){
let pixel = updatedPixels[i];
ctx.fillStyle = pixel.color;
ctx.fillRect(pixel.x,pixel.y,1,1);
}
//clear out the updatedPixels as they should no longer be considered updated.
updatedPixels = [];
//better method than setTimeout/Interval for drawing
requestAnimationFrame(render);
}
From there we can move on to the logic. We will loop over the infectedPixels array, and with each pixel we decide a random direction and get that pixel. If this selected pixel is red we do nothing and continue on. Otherwise we change it's color and add it to a temporary array affectedPixels. After which we test to see if all the pixels around the original pixel are all red, if so we can remove it from the infectedPixels as there is no need to check it again. Then add all the pixels from affectedPixels onto the infectedPixels as these are now new pixels that need to be checked. And the last step is to also add affectedPixels onto updatedPixels so that the render loop draws the changes.
function update(){
var affectedPixels = [];
//needed as we shouldn't change an array while looping over it
var stillInfectedPixels = [];
var numInfected = infectedPixels.length;
for(let i=0; i<numInfected; i++){
let pixel = infectedPixels[i];
let x = pixel.x;
let y = pixel.y;
//instead of using a switch statement, use the random number as the index
//into a surroundingPixels array
let surroundingPixels = [
(pixels[x] ? pixels[x][y - 1] : null),
(pixels[x + 1] ? pixels[x + 1][y] : null),
(pixels[x] ? pixels[x][y + 1] : null),
(pixels[x - 1] ? pixels[x - 1][y] : null)
].filter(p => p);
//filter used above to remove nulls, in the cases of edge pixels
var rand = Math.floor((Math.random() * surroundingPixels.length));
let selectedPixel = surroundingPixels[rand];
if(selectedPixel.color == "green"){
selectedPixel.color = "red";
affectedPixels.push(selectedPixel);
}
if(!surroundingPixels.every(p=>p.color=="red")){
stillInfectedPixels.push(pixel);
}
}
infectedPixels = stillInfectedPixel.concat( affectedPixels );
updatedPixels.push(...affectedPixels);
}
Demo
var pixels = [],
infectedPixels = [],
updatedPixels = [],
canv, ctx;
window.onload = function() {
canv = document.getElementById("canv");
ctx = canv.getContext("2d");
createMap();
render();
setInterval(() => {
update();
}, 16);
};
function createMap() {
for (let y = 0; y < 800; y++) {
pixels.push([]);
for (x = 0; x < 800; x++) {
pixels[y].push(new Pixel("green",x,y));
}
}
pixels[400][400].color = "red";
updatedPixels = [].concat(...pixels);
infectedPixels.push(pixels[400][400]);
}
class Pixel {
constructor(color, x, y) {
this.color = color;
this.x = x;
this.y = y;
}
}
function update() {
var affectedPixels = [];
var stillInfectedPixels = [];
var numInfected = infectedPixels.length;
for (let i = 0; i < numInfected; i++) {
let pixel = infectedPixels[i];
let x = pixel.x;
let y = pixel.y;
let surroundingPixels = [
(pixels[x] ? pixels[x][y - 1] : null),
(pixels[x + 1] ? pixels[x + 1][y] : null),
(pixels[x] ? pixels[x][y + 1] : null),
(pixels[x - 1] ? pixels[x - 1][y] : null)
].filter(p => p);
var rand = Math.floor((Math.random() * surroundingPixels.length));
let selectedPixel = surroundingPixels[rand];
if (selectedPixel.color == "green") {
selectedPixel.color = "red";
affectedPixels.push(selectedPixel);
}
if (!surroundingPixels.every(p => p.color == "red")) {
stillInfectedPixels.push(pixel);
}
}
infectedPixels = stillInfectedPixels.concat(affectedPixels);
updatedPixels.push(...affectedPixels);
}
function render() {
var numUpdatedPixels = updatedPixels.length;
for (let i = 0; i < numUpdatedPixels; i++) {
let pixel = updatedPixels[i];
ctx.fillStyle = pixel.color;
ctx.fillRect(pixel.x, pixel.y, 1, 1);
}
updatedPixels = [];
requestAnimationFrame(render);
}
<canvas id="canv" width="800" height="800"></canvas>
I am trying to write a script to place 100 circles of varying sizes onto a stage. I've outlined the concise requirements below.
Given the following:
var stage; // contains a "width" and "height" property.
var circle; // the circle class. contains x, y, radius & a unique id property.
var circleArray; // contains 100 circle instances
requirements:
write a function to place 100 circles of varying radius onto the stage.
placements must be random but evenly distributed (no clumping).
placement must be performant - this will be executing on a mobile web browser.
circles must not intersect/overlap other circles.
circle.x >= 0 must be true.
circle.y >= 0 && circle.y <= stage.height must be true.
circles may have any of the following radius sizes (assigned at creation):
150
120
90
80
65
My current attempt is a brute-force method, which does not operate efficiently. If I attempt to insert any more than ~10 circles, the browser hangs. Below is my current implementation, which I am completely OK with throwing away in favor of a more performant / better one.
Here is a live demo (NOTE: there is no actual drawing code, just the logic, but it will still lock up the browser so be warned!!) http://jsbin.com/muhiziduxu/2/edit?js,console
function adjustForOverlap (circleArray) {
// a reference to the circle that is invoking this function.
var _this = this;
// remove this circle from the array we are iterating over.
var arr = circleArray.filter(function (circle){
return circle.id !== _this.id;
});
// while repeat == true, the circle may be overlapping something.
var repeat = true;
while(repeat) {
var hasOverlap = false;
for (var i=0; i<arr.length; i++) {
var other = arr[i];
var dx = _self.x - other.x;
var dy = _self.y - other.y;
var rr = _self.radius + other.radius;
if (dx * dx + dy * dy < rr * rr) {
// if here, then an overlap was detected.
hit = true;
break;
}
}
// if hit is false, the circle didn't overlap anything, so break.
if (hit === false) {
repeat = false;
break;
} else {
// an overlap was detected, so randomize position.
_self.x = Math.random() * (stage.width*2);
_self.y = Math.random() * stage.height;
}
}
}
There are lots of efficient collision detection algorithms. Many of them work by dividing up the space into cells and maintaining a separate data structure with efficient lookup of other objects in the cell. The basic steps are:
Identify a random spot for your new circle
Determine which cells it's in
Look in each of those cells for a collision
If there's a collision, goto 1.
Else, add the new circle to each of the cells it overlaps.
You can use a simple square grid (i.e. a 2-d array) for the cell data structure, or something else like a quadtree. You can also in some cases get a bit of extra speed by trying a cheap-but-coarse collision check first (do the bounding boxes overlap), and if that returns true try the slightly more expensive and exact check.
Update
For quadtrees, check out d3-quadtree, which ought to give you a pretty good implementation, with examples.
For a (very quick, untested) 2-d array implementation:
function Grid(radius, width, height) {
// I'm not sure offhand how to find the optimum grid size.
// Let's use a radius as a starting point
this.gridX = Math.ceil(width / radius);
this.gridY = Math.ceil(height / radius);
// Determine cell size
this.cellWidth = width / this.gridX;
this.cellHeight = height / this.gridY;
// Create the grid structure
this.grid = [];
for (var i = 0; i < gridY; i++) {
// grid row
this.grid[i] = [];
for (var j = 0; j < gridX; j++) {
// Grid cell, holds refs to all circles
this.grid[i][j] = [];
}
}
}
Grid.prototype = {
// Return all cells the circle intersects. Each cell is an array
getCells: function(circle) {
var cells = [];
var grid = this.grid;
// For simplicity, just intersect the bounding boxes
var gridX1Index = Math.floor(
(circle.x - circle.radius) / this.cellWidth
);
var gridX2Index = Math.ceil(
(circle.x + circle.radius) / this.cellWidth
);
var gridY1Index = Math.floor(
(circle.y - circle.radius) / this.cellHeight
);
var gridY2Index = Math.ceil(
(circle.y + circle.radius) / this.cellHeight
);
for (var i = gridY1Index; i < gridY2Index; i++) {
for (var j = gridX1Index; j < gridX2Index; j++) {
// Add cell to list
cells.push(grid[i][j]);
}
}
return cells;
},
add: function(circle) {
this.getCells(circle).forEach(function(cell) {
cell.push(circle);
});
},
hasCollisions: function(circle) {
return this.getCells(circle).some(function(cell) {
return cell.some(function(other) {
return this.collides(circle, other);
}, this);
}, this);
},
collides: function (circle, other) {
if (circle === other) {
return false;
}
var dx = circle.x - other.x;
var dy = circle.y - other.y;
var rr = circle.radius + other.radius;
return (dx * dx + dy * dy < rr * rr);
}
};
var g = new Grid(150, 1000, 800);
g.add({x: 100, y: 100, radius: 50});
g.hasCollisions({x: 100, y:80, radius: 100});
Here's a fully-functional example: http://jsbin.com/cojoxoxufu/1/edit?js,output
Note that this only shows 30 circles. It looks like the problem is often unsolvable with your current radii, width, and height. This is set up to look for up to 500 locations for each circle before giving up and accepting a collision.
This is a box with an irregular shape that I have generated:
And this is the end effect I'd like to achieve (note the smooth edges):
Here's the code for my sharp version:
var path1 = new Path({
segments: [[123, 6], [290, 6], [304, 142], [112, 142]],
strokeColor: 'white',
closed: true,
strokeWidth: 3,
strokeJoin: 'round'
});
Thing is, I'm already using the strokeJoin: 'round' option and the difference is hardly noticeable with a stroke width of 3px. It's a small thing but could turn into a game breaker as there are going to be multiple objects like this and the difference is huge.
Is there any way to achieve that with paper.js without overdoing it?
As markE mentioned, strokeJoin only changes the canvas style of a path's stroke. Paper.js does not come with a corner-rounding function, you'll have to make your own.
Here's a quick function that you can use a starting point. It will negatively offset the points of a polygon by a given distance and add the appropriate handles.
function roundPath(path,radius) {
var segments = path.segments.slice(0);
path.segments = [];
for(var i = 0, l = segments.length; i < l; i++) {
var curPoint = segments[i].point;
var nextPoint = segments[i + 1 == l ? 0 : i + 1].point;
var prevPoint = segments[i - 1 < 0 ? segments.length - 1 : i - 1].point;
var nextDelta = curPoint - nextPoint;
var prevDelta = curPoint - prevPoint;
nextDelta.length = radius;
prevDelta.length = radius;
path.add({
point:curPoint - prevDelta,
handleOut: prevDelta/2
});
path.add({
point:curPoint - nextDelta,
handleIn: nextDelta/2
});
}
path.closed = true;
return path;
}
Here it is in action.
I was looking for an exact implementation, as described here: http://shanfanhuang.com/everything/2015/10/27/rounding-corners
My implementation works as follows:
curPoint is the corner, prevPoint and nextPoint as above
nextNorm and prevNorm are the normalized versions of the points
angle is the angle of the corner, derived from the dot product
delta is the distance from the corner points to where the control points need to be inserted, this is derived from a right triangle formed by the control point, curPoint and the center of the corner arc. The corner is a half angle, and the side opposing that corner is the radius
prevDelta and nextDelta are the new endpoints of the sides, between those an arc is inserted
through is a point halfway on the arc, found by getting the hypotenuse of the above triangle and subtracting the radius.
var segments = path.segments.slice(0);
path.segments = [];
for(var i = 0, l = segments.length; i < l; i++) {
var curPoint = segments[i].point;
var nextPoint = segments[i + 1 == l ? 0 : i + 1].point;
var prevPoint = segments[i - 1 < 0 ? segments.length - 1 : i - 1].point;
var nextNorm = (curPoint - nextPoint).normalize();
var prevNorm = (curPoint - prevPoint).normalize();
var angle = Math.acos(nextNorm.dot(prevNorm));
var delta = radius/Math.tan(angle/2);
var prevDelta = prevNorm.normalize(delta);
var nextDelta = nextNorm.normalize(delta);
var through = curPoint - (prevNorm + nextNorm).normalize(Math.sqrt(delta*delta + radius*radius) - radius);
path.add(curPoint - prevDelta);
path.arcTo(through, curPoint - nextDelta);
}
So, I am trying to create a N-Body Gravity simulation in JavaScript:
http://jsfiddle.net/4M94x/
var Circle = function(c, r, cor, cof) { // Fix CoR & CoF // Had to add code for JSFiddle link :P
this.c = c
this.r = r
this.m = r * r * Math.PI
this.v = new Vector()
this.cor = cor
this.cof = cof
}
The problem's that when you spawn (click) and put 2 balls (accidentally renamed "particles") next to each other they start to generate velocity and faster and faster push eachother.. How do I fix this, btw is my gravity implementation correct?
This is easy to explain: You are implementing Euler forward as solver for the ODE, and in mechanical systems the systematic error of Euler forward increases the energy. Euler backward decreases the energy, so a combination of alternating the explicit and implicit Euler methods would leave the energy a little more constant.
But then you can implement with the same or even less effort the second order symplectic methods which preserve energy and other physical invariants, either the (implicit) midpoint method or the Verlet-(Stoermer-Cromer-...-Newton-)method.
Or even higher order Runge-Kutta, which will also preserve the energy to a higher order, despite not being symplectic.
See Hairer on the Stoermer-Verlet-...-Newton method, postprint or preprint and the "Moving stars around" tutorial text using C++ or Ruby.
A note to the physics: All in all the implementation is very minimal and well readable. But the gravitational force is
g*m1*m2*(p2-p1)/norm(p2-p1)^3
as the negative gradient of
g*m1*m2/norm(p2-p1)
you are only using the square of the norm, where the force would be the negative gradient of the gravitational potential energy
g*m1*m2*ln(norm(p2-p1))
which is right for flatland physics, but not for a 2D section of 3D space.
Working code
with velocity Verlet and energy preservation:
Add a new field a=Vector() to the circle object and replace the kitchen sink which is the update() function with the following collection of dedicated functions
function compute_forces() {
for (var i = 0; i < particles.length; i++) {
var p = particles[i];
p.a.set(0);
for (var j = 0; j < i; j++) {
var p2 = particles[j];
var d = p.c.sub(p2.c);
var norm = Math.sqrt(100.0 + d.lengthSq());
var mag = gravity / (norm * norm * norm);
p.a.set(p.a.sub(d.mul(mag * p2.m)));
p2.a.set(p2.a.add(d.mul(mag * p.m)));
}
}
}
function do_collisions() {
for (var i = 0; i < particles.length; i++) {
var p = particles[i];
for (var j = 0; j < i; j++) {
var p2 = particles[j];
if (checkCCCol(p, p2)) {
resCCCol(p, p2);
}
}
}
}
function do_physics(dt) {
// do velocity Verlet
// with consistent state at interval half points
// x += 0.5*v*dt
for (var i1 = 0; i1 < particles.length; i1++) {
var p1 = particles[i1];
p1.c.set(p1.c.add(p1.v.mul(0.5 * dt)));
}
// a = A(x)
compute_forces();
// v += a*dt
for (var i2 = 0; i2 < particles.length; i2++) {
var p2 = particles[i2];
p2.v.set(p2.v.add(p2.a.mul(dt)));
}
// x += 0.5*v*dt
for (var i3 = 0; i3 < particles.length; i3++) {
var p3 = particles[i3];
p3.c.set(p3.c.add(p3.v.mul(0.5 * dt)));
}
do_collisions();
}
function update() {
for (var k = 0; k < 4; k++) {
do_physics(1.0 / 4);
}
render();
RAF(update);
}
See http://jsfiddle.net/4XVPH/
Altered example with particles coloured based on their mass(hopefully better displaying their interaction), one bug fixed, and some additional comments: http://jsfiddle.net/24mg6ctg/12/
I'm doing a BattleShip game in javascript with iio engine.
I'm trying to play against a computer so I have to put a random position for the ships (I hope you know the game :) ).
I have 5 ships that have to be placed in a grid (10x10). The problem is that the function is pretty slow, and sometimes the page don't get load at all.
I want to know if there are some emprovement for the speed of these function, I'm a little bit newbie :D
function posShips(size){
// var size -> size of the ship
var isOk = false; // flag var to check if the ship is in a right position
var isOk2 = true; // flag var, become false if the cell is already fill with another ship
var i;
var j;
var side; // horizontal or vertical
while(!isOk){
i = iio.getRandomInt(1,11);
j = iio.getRandomInt(1,11);
side = iio.getRandomInt(0,2);
if((side ? j : i)+size-1 < 11){ // Not out of the array
for (var k = 0; k < size; k++) { // Size of the ship
if(side){
if(gridHit[i][j+k].stat == "empty"){ //If is empty put the ship
gridHit[i][j+k].stat = "ship";
gridHit[i][j+k].setFillStyle("red")
}else{ // If not empty
isOk2 = false; //Position is not good, do all the thing again.
for (var a = 0; a < size; a++) { // Reset cell
gridHit[i][j+a].stat = "empty";
}
k = 10;
}
}else{
if(gridHit[i+k][j].stat == "empty"){ //If is empty put the ship
gridHit[i+k][j].stat = "ship";
gridHit[i+k][j].setFillStyle("red")
}else{ // If not empty
isOk2 = false; //Position is not good, do all the thing again.
for (var a = 0; a < size; a++) { // Reset cell
gridHit[i+a][j].stat = "empty";
}
k = 10;
}
}
};
if(isOk2)
isOk = true;
}
}
}
Don't pick ship positions that will fall outside the grid. Pick the direction first, and then limit the x and y initial positions based on size. e.g. if the size is 3, there's no point going above 7 for the initial value of the varying coordinate.
Don't change the array while you're searching. Do the search first, and only afterwards update the array. This avoids any "cleanup" operation.
Wherever possible, eliminate repeated deep object references. If accessing grid[y][x] repeatedly for differing x, take a reference to grid[y] first, and then use that for the subsequent accesses.
Break out of loops early, there's no point continuing to test a position if a previous one already failed.
Place your big ships first - it's easier to fit small ships into the gaps left between the big ones.
See http://jsfiddle.net/alnitak/Rp9Ke/ for my implementation, with the equivalent of your function being this:
this.place = function(size) {
// faster array access
var g = this.grid;
// initial direction, and vector
var dir = rand(2); // 0 - y, 1 - x
var dx = dir ? 1 : 0;
var dy = dir ? 0 : 1; // or 1 - dx
LOOP: while (true) {
// initial position
var x = dir ? rand(10 - size) : rand(10);
var y = dir ? rand(10) : rand(10 - size);
// test points
var n = size, tx = x, ty = y;
while (n--) {
if (g[ty][tx]) continue LOOP;
tx += dx;
ty += dy;
}
// fill points
n = size;
while (n--) {
g[y][x] = size;
x += dx;
y += dy;
}
break;
}
};