Me and my group (school project) are trying to create a modular multiplication in a circle, we've had some success with lines inside the circle but I can't figure out what I am missing when it comes to drawing lines between the points that make up the circle.
How I am trying to draw circle:
function drawCircle() {
points = [];
ctx.clearRect(0, 0, canvas.width, canvas.height);
ctx.beginPath();
var step = 2 * Math.PI/points;
ctx.beginPath();
for(var theta=0; theta < 2*Math.PI; theta+=step)
{ var test1 = x + radius*Math.cos(theta);
var test2 = y - radius*Math.sin(theta);
ctx.lineTo(test1,test2);
}
ctx.closePath();
ctx.stroke();
The entire js code:
function draw() {
var canvas = document.getElementById('multiplier');
var ctx = canvas.getContext('2d');
var x = 300; // x coordinate
var y = 300; // y coordinate
var radius = 295; // Arc radius
var point_size = 2;
var number_of_points = 10;
var multiplier = 2;
var points = [];
function drawCircle() {
points = [];
ctx.clearRect(0, 0, canvas.width, canvas.height);
ctx.beginPath();
var step = 2 * Math.PI/points;
ctx.beginPath();
for(var theta=0; theta < 2*Math.PI; theta+=step)
{ var test1 = x + radius*Math.cos(theta);
var test2 = y - radius*Math.sin(theta);
ctx.lineTo(test1,test2);
}
ctx.closePath();
ctx.stroke();
var i;
var angleBetweenPoints = 360 / number_of_points;
for (i = 0; i < number_of_points ; i++) {
drawPoint(i * angleBetweenPoints, 1)
}
for (i = 1; i < points.length; i++ ) {
ctx.beginPath();
ctx.moveTo(points[i].x, points[i].y);
if (i < points.length / multiplier ) {
ctx.lineTo(points[i*multiplier].x, points[i*multiplier].y);
} else {
ctx.lineTo(points[i*multiplier % points.length].x, points[i*multiplier % points.length].y);
}
ctx.stroke();
}
}
function drawPoint(angle,distance){
var pointx = x + radius * Math.cos(-angle*Math.PI/180) * distance;
var pointy = y + radius * Math.sin(-angle*Math.PI/180) * distance;
ctx.beginPath();
ctx.arc(pointx, pointy, point_size, 0, 2 * Math.PI);
ctx.fill();
points.push({x: pointx, y: pointy});
}
if (canvas.getContext) {
drawCircle();
}
// add event listener to point number selection
var pointNumElement = document.getElementById("pointNumber");
pointNumElement.addEventListener('input', function(e){
number_of_points = this.value;
drawCircle();
});
// add event listener to multiplier number selection
var pointNumElement = document.getElementById("multiplierInput");
pointNumElement.addEventListener('input', function(e){
multiplier = this.value;
drawCircle();
});
}
I am trying to achieve a tracing effect where the lines have a faded trail. The way I am trying to do it is simply by drawing the solid background once, and then on further frames draw a transparent background before drawing the new lines, so that you can still see a little of the image before it.
The issue is that I do want the lines to fade out completely after some time, but they seem to leave a permanent after image, even after drawing over them repeatedly.
I've tried setting different globalCompositeOperation(s) and it seemed like I was barking up the wrong tree there.
This code is called once
//initiate trace bg
traceBuffer.getContext("2d").fillStyle = "rgba(0, 30, 50, 1)";
traceBuffer.getContext("2d").fillRect(0, 0, traceBuffer.width, traceBuffer.height);
then inside the setInterval function it calls
//draw transparent background
ctx.fillStyle = "rgba(0, 30, 50, 0.04)";
ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
//set drawing settings
ctx.strokeStyle = "#AAAAAA";
ctx.lineWidth = 4;
for (let i = 0; i < tracer.layer2.length; i++){
ctx.beginPath();
ctx.moveTo(newX, newY);
ctx.lineTo(oldX, oldY);
ctx.stroke();
}
Here's an example: https://i.imgur.com/QTkeIVf.png
On the left is what I am currently getting, and on the right is the edit of what I actually want to happen.
This is how I would do it. I would build a history of the particles moving on the track. The older the position the smaller the value of the alpha value for the fill. Also for a nicer effect I would reduce the size of the circle.
I hope this is what you need.
PS: I would have loved to have your curve. Since I don't have it I've drawn a different one.
const hypotrochoid = document.getElementById("hypotrochoid");
const ctx = hypotrochoid.getContext("2d");
const cw = (hypotrochoid.width = 300);
const ch = (hypotrochoid.height = 300);
const cx = cw / 2,
cy = ch / 2;
ctx.lineWidth = 1;
ctx.strokeStyle = "#d9d9d9";
// variables for the hypotrochoid
let a = 90;
let b = 15;
let h = 50;
// an array where to save the points used to draw the track
let track = [];
//add points to the track array. This will be used to draw the track for the particles
for (var t = 0; t < 2 * Math.PI; t += 0.01) {
let o = {};
o.x = cx + (a - b) * Math.cos(t) + h * Math.cos((a - b) / b * t);
o.y = cy + (a - b) * Math.sin(t) - h * Math.sin((a - b) / b * t);
track.push(o);
}
// a function to draw the track
function drawTrack(ry) {
ctx.beginPath();
ctx.moveTo(ry[0].x, ry[0].y);
for (let t = 1; t < ry.length; t++) {
ctx.lineTo(ry[t].x, ry[t].y);
}
ctx.closePath();
ctx.stroke();
}
// a class of points that are moving on the track
class Point {
constructor(pos) {
this.pos = pos;
this.r = 3;//the radius of the circle
this.history = [];
this.historyLength = 40;
}
update(newPos) {
let old_pos = {};
old_pos.x = this.pos.x;
old_pos.y = this.pos.y;
//save the old position in the history array
this.history.push(old_pos);
//if the length of the track is longer than the max length allowed remove the extra elements
if (this.history.length > this.historyLength) {
this.history.shift();
}
//gry the new position on the track
this.pos = newPos;
}
draw() {
for (let i = 0; i < this.history.length; i++) {
//calculate the alpha value for every element on the history array
let alp = i * 1 / this.history.length;
// set the fill style
ctx.fillStyle = `rgba(0,0,0,${alp})`;
//draw an arc
ctx.beginPath();
ctx.arc(
this.history[i].x,
this.history[i].y,
this.r * alp,
0,
2 * Math.PI
);
ctx.fill();
}
}
}
// 2 points on the track
let p = new Point(track[0]);
let p1 = new Point(track[~~(track.length / 2)]);
let frames = 0;
let n, n1;
function Draw() {
requestAnimationFrame(Draw);
ctx.clearRect(0, 0, cw, ch);
//indexes for the track position
n = frames % track.length;
n1 = (~~(track.length / 2) + frames) % track.length;
//draw the track
drawTrack(track);
// update and draw the first point
p.update(track[n]);
p.draw();
// update and draw the second point
p1.update(track[n1]);
p1.draw();
//increase the frames counter
frames++;
}
Draw();
canvas{border:1px solid}
<canvas id="hypotrochoid"></canvas>
first of all, i am a beginner on js and p5.js. My aim on this program is a smoothly morphing random shape. I was satisfied with the calculateShape()-function and the drawShape()-function, but when it comes to morphing (updateShape()) it gets really ugly. I thought it might be a good idea to save my current array into a temporary array, then loop over the array and add a random number to each x and y of each index and then replace the old x and y at this index. The main problem is, that it is always adding new shapes on the screen instead of changing the values of the vertices of the existing shape. Can anybody of you please give me a hint or point out my mistake(s)? THANK YOU IN ADVANCE!
var c1;
var c2;
var c3;
var centerX;
var centerY;
var fb;
var radius;
var angle;
var shape = [];
var temp;
/*function to calculate the inital shape*/
function calculateShape() {
//calculate coordinates and save into array
for (var i = 0; i < fb; i++) {
var x = cos(angle * i) * radius + random(-77,77);
var y = sin(angle * i) * radius + random(-77,77);
var v = createVector(x, y);
shape.push(v);
}
}
/*function for morphing the shape*/
function updateShape() {
var temp = shape;
for (var i = 0; i < shape.length - 1; i++) {
var x = temp[i].x + random(-1, 1);
var y = temp[i].y + random(-1, 1);
var p = temp[i];
var v = createVector(x, y);
shape.splice(p,1);
shape.push(v);
}
}
/*function for drawing the shape on the screen*/
function createShape(){
beginShape();
curveVertex(shape[shape.length-1].x, shape[shape.length-1].y);
for (var i = 0; i < shape.length; i++){
curveVertex(shape[i].x, shape[i].y);
}
curveVertex(shape[0].x, shape[0].y);
endShape(CLOSE);
}
function setup() {
createCanvas(windowWidth, windowHeight);
smooth();
background(250);
//frameRate(2);
// defining possible colors
c1 = color(0, 196, 181, 235);
c2 = color(50, 227, 232, 235);
c3 = color(248, 49, 62, 255);
var colors = [c1, c2, c3];
//center of the window
centerX = windowWidth/2;
centerY = windowHeight/2;
//defining all variables
fb = 8;
angle = radians(360 / fb);
radius = random(120, 140);
//calling thefunction that initalises the shape
calculateShape();
}
function draw() {
translate(centerX, centerY);
blendMode(BLEND);
fill(c3);
noStroke();
createShape();
updateShape();
}
The main problem is, that it is always adding new shapes on the screen instead of changing the values of the vertices of the existing shape.
Sure, you just need to clear the screen before drawing again. So, reset the background with the background(250) from setup, in draw.
I'm attempting to draw the rotating line in this canvas animation with trailing opacity but it's not working. I've seen this effect with rectangles and arcs but never with a line, so I'm not sure what I need to add.
function radians(degrees) {
return degrees * (Math.PI / 180);
}
var timer = 0;
function sonar() {
var canvas = document.getElementById('sonar');
if (canvas) {
var ctx = canvas.getContext('2d');
var cx = innerWidth / 2,
cy = innerHeight / 2;
canvas.width = innerWidth;
canvas.height = innerHeight;
//ctx.clearRect(0, 0, innerWidth, innerHeight);
ctx.fillStyle = 'rgba(255, 255, 255, 0.5)';
ctx.fillRect(0, 0, innerWidth, innerHeight);
var radii = [cy, cy - 30, innerHeight / 3.33, innerHeight / 6.67];
for (var a = 0; a < 4; a++) {
ctx.beginPath();
ctx.arc(cx, cy, radii[a], radians(0), radians(360), false);
ctx.strokeStyle = 'limegreen';
ctx.stroke();
ctx.closePath();
}
// draw grid lines
for (var i = 0; i < 12; i++) {
var x = cx + cy * Math.cos(radians(i * 30));
var y = cy + cy * Math.sin(radians(i * 30));
ctx.beginPath();
ctx.moveTo(cx, cy);
ctx.lineTo(x, y);
ctx.lineCap = 'round';
ctx.strokeStyle = 'rgba(50, 205, 50, 0.45)';
ctx.stroke();
ctx.closePath();
}
if (timer <= 360) {
timer++;
ctx.beginPath();
ctx.fillstyle = 'limegreen';
ctx.moveTo(cx, cy);
ctx.lineTo(cx + cy * Math.cos(radians(timer)), cy + cy * Math.sin(radians(timer)));
ctx.strokeStyle = 'limegreen';
ctx.stroke();
ctx.closePath();
} else {
timer = 0;
}
requestAnimationFrame(sonar);
}
}
sonar();
jsbin example
Here are two ways to do this: with a gradient and by adding translucent lines.
Sidenote, you should try and only redraw what you need to redraw. I separated the canvases and put one on top of the other so that we don't redraw the grid all the time.
function radians(degrees) {
return degrees * (Math.PI / 180);
}
var timer = 0;
function trail() {
var canvas = document.getElementById('trail');
var ctx = canvas.getContext('2d');
ctx.clearRect(0, 0, innerWidth, innerHeight);
var cx = innerWidth / 2,
cy = innerHeight / 2;
canvas.width = innerWidth;
canvas.height = innerHeight;
if (timer <= 360) {
timer++;
ctx.beginPath();
ctx.fillstyle = 'limegreen';
ctx.moveTo(cx, cy);
ctx.arc(cx,cy,cy,radians(timer-30),radians(timer));
ctx.lineTo(cx + cy * Math.cos(radians(timer)), cy + cy * Math.sin(radians(timer)));
var gradient = ctx.createLinearGradient(
cx+cy*Math.cos(radians(timer)), cy+cy*Math.sin(radians(timer)),
cx+cy*0.9*Math.cos(radians(timer-30)), cy+cy*0.9*Math.sin(radians(timer-30)));
gradient.addColorStop(0,'limegreen');
gradient.addColorStop(1,'transparent');
ctx.strokeStyle='transparent';
ctx.fillStyle = gradient;
ctx.fill();
ctx.beginPath();
var fade = 10;
for(var i =0;i<fade;i++)
{
ctx.moveTo(cx, cy);
ctx.lineTo(cx+cy*Math.cos(radians(180+timer-i*1.3)),cy+cy*Math.sin(radians(180+timer-i*1.3)));
ctx.strokeStyle ="rgba(50,205,50,0.1)";
ctx.lineWidth=5;
ctx.closePath();
ctx.stroke();
}
} else {
timer = 0;
}
requestAnimationFrame(trail);
}
function sonar() {
var canvas = document.getElementById('sonar');
if (canvas) {
var ctx = canvas.getContext('2d');
var cx = innerWidth / 2,
cy = innerHeight / 2;
canvas.width = innerWidth;
canvas.height = innerHeight;
//ctx.clearRect(0, 0, innerWidth, innerHeight);
var radii = [cy, cy - 30, innerHeight / 3.33, innerHeight / 6.67];
for (var a = 0; a < 4; a++) {
ctx.beginPath();
ctx.arc(cx, cy, radii[a], radians(0), radians(360), false);
ctx.strokeStyle = 'limegreen';
ctx.stroke();
ctx.closePath();
}
// draw grid lines
for (var i = 0; i < 12; i++) {
var x = cx + cy * Math.cos(radians(i * 30));
var y = cy + cy * Math.sin(radians(i * 30));
ctx.beginPath();
ctx.moveTo(cx, cy);
ctx.lineTo(x, y);
ctx.lineCap = 'round';
ctx.strokeStyle = 'rgba(50, 205, 50, 0.45)';
ctx.stroke();
ctx.closePath();
}
}
}
sonar();
trail();
canvas{
position: absolute;
}
<canvas id=sonar></canvas>
<canvas id=trail></canvas>
The problem is that to get this effect, you need to draw a triangle with a gradient along an arc, and you can't do that in a canvas. Gradients must be linear or radial.
The other option is to have an inner loop run each time you want to draw the sweeper, and go backwards from your sweeper line, drawing with slightly less opacity each time. But lets say you want your sweep to cover 15 degrees--obviously, if you have a 100% opacity line at d and a 5% opacity line at d - 15, that doesn't do the trick. So start filling in more lines, and more lines...you will have to draw so many lines to make it seem filled your performance would probably suffer.
My suggestion--you shouldn't have to redraw that on every frame. I would just make a PNG that looks like you want it to, and then place it and just rotate it around the center on each frame. No need to redraw it all the time then. That will be much faster than drawing a bunch of lines.
Canvas stack trails.
Below is a quick demo of how to use a stack of canvases to create a trailing effect.
You have a normal on screen canvas (this FX will not effect it) and then a stack of canvases for the trail FX. Each frame you move to the next canvas in the stack, first slightly clearing it then drawing to it what you want to trail. Then you render that canvas and the one just above it to the canvas.
A point to keep in mind is that the trails can also have a hugh range of FX, like blurring (just render each frame stack on itself slightly offset each time you render to it), zoom in and out trails. Trails on top or trails under. You can change the trail distance and much more.
It is overkill but over kill is fun.
The slider above the demo controls the trail length. Also the code need babel because I dont have time to write it for ES5.
Top slider is trail amount.One under that is trail distance. Trail dist does not transition well. Sorry about that.
//==============================================================================
// helper function
function $(query,q1){
if(q1 !== undefined){
if(typeof query === "string"){
var e = document.createElement(query);
if(typeof q1 !== "string"){
for(var i in q1){
e[i] = q1[i];
}
}else{
e.id = q1;
}
return e;
}
return [...query.querySelectorAll(q1)];
}
return [...document.querySelectorAll(query)];
}
function $$(element,e1){
if(e1 !== undefined){
if(typeof element === "string"){
$(element)[0].appendChild(e1);
return e1;
}
element.appendChild(e1);
return e1;
}
document.body.appendChild(element);
return element;
}
function $E(element,types,listener){
if(typeof types === "string"){
types = types.split(",");
}
element = $(element)[0];
types.forEach(t=>{
element.addEventListener(t,listener)
});
return element;
}
function R(I){
if(I === undefined){
return Math.random();
}
return Math.floor(Math.random()*I);
}
//==============================================================================
//==============================================================================
// answer code
// canvas size
const size = 512;
const trailDist = 10; // There is this many canvases so be careful
var trailDistCurrent = 10; // distance between trails
var clearAll = false;
// create a range slider for trail fade
$$($("input",{type:"range",width : size, min:0, max:100, step:0.1, value:50, id:"trail-amount",title:"Trail amount"}));
$("#trail-amount")[0].style.width = size + "px";
$E("#trail-amount","change,mousemove",function(e){fadeAmount = Math.pow(this.value / 100,2);});
// create a range slider trail distance
$$($("input",{type:"range",width : size, min:2, max:trailDist , step:1, value:trailDist , id:"trail-dist",title:"Trail seperation"}));
$("#trail-dist")[0].style.width = size + "px";
$E("#trail-dist","change,mousemove", function(e){
if(this.value !== trailDistCurrent){
trailDistCurrent= this.value;
clearAll = true;
}
});
$$($("br","")) // put canvas under the slider
// Main canvas
var canvas;
$$(canvas = $("canvas",{width:size,height:size})); // Not jquery. Just creates a canvas
// and adds canvas to the document
var ctx = canvas.getContext("2d");
// Trailing canvas
var trailCanvases=[];
var i =0; // create trail canvas
while(i++ < trailDist){trailCanvases.push($("canvas",{width:size,height:size}));}
var ctxT = trailCanvases.map(c=>c.getContext("2d")); // get context
var topCanvas = 0;
var fadeAmount = 0.5;
// Draw a shape
function drawShape(ctx,shape){
ctx.lineWidth = shape.width;
ctx.lineJoin = "round";
ctx.strokeStyle = shape.color;
ctx.setTransform(shape.scale,0,0,shape.scale,shape.x,shape.y);
ctx.rotate(shape.rot);
ctx.beginPath();
var i = 0;
ctx.moveTo(shape.shape[i++],shape.shape[i++]);
while(i < shape.shape.length){
ctx.lineTo(shape.shape[i++],shape.shape[i++]);
}
ctx.stroke();
}
// Create some random shapes
var shapes = (function(){
function createRandomShape(){
var s = [];
var len = Math.floor(Math.random()*5 +4)*2;
while(len--){
s[s.length] = (R() + R()) * 20 * (R() < 0.5 ? -1 : 1);
}
return s;
}
var ss = [];
var i = 10;
while(i--){
ss[ss.length] = createRandomShape();
}
ss[ss.length] = [0,0,300,0]; // create single line
return ss;
})();
// Create some random poits to move the shapes
var points = (function(){
function point(){
return {
color : "hsl("+R(360)+",100%,50%)",
shape : shapes[R(shapes.length)],
width : R(4)+1,
x : R(size),
y : R(size),
scaleMax : R()*0.2 + 1,
scale : 1,
s : 0,
rot : R()*Math.PI * 2,
dr : R()*0.2 -0.1,
dx : R()*2 - 1,
dy : R()*2 - 1,
ds : R() *0.02 + 0.01,
}
}
var line = shapes.pop();
var ss = [];
var i = 5;
while(i--){
ss[ss.length] = point();
}
var s = ss.pop();
s.color = "#0F0";
s.x = s.y = size /2;
s.dx = s.dy = s.ds = 0;
s.scaleMax = 0.5;
s.dr = 0.02;
s.shape = line;
s.width = 6;
ss.push(s);
return ss;
})();
var frameCount = 0; // used to do increamental fades for long trails
function update(){
// to fix the trail distance problem when fade is low and distance high
if(clearAll){
ctxT.forEach(c=>{
c.setTransform(1,0,0,1,0,0);
c.clearRect(0,0,size,size);
});
clearAll = false;
}
frameCount += 1;
// get the next canvas that the shapes are drawn to.
topCanvas += 1;
topCanvas %= trailDistCurrent;
var ctxTop = ctxT[topCanvas];
// clear the main canvas
ctx.setTransform(1,0,0,1,0,0); // reset transforms
// Fade the trail canvas
ctxTop.setTransform(1,0,0,1,0,0);
ctx.clearRect(0,0,size,size); // clear main canvas
// slowly blendout trailing layer
if(fadeAmount < 0.1){ // fading much less than this leaves perminant trails
// so at low levels just reduce how often the fade is done
if(((Math.floor(frameCount/trailDistCurrent)+topCanvas) % Math.ceil(1 / (fadeAmount * 10))) === 0 ){
ctxTop.globalAlpha = 0.1;
ctxTop.globalCompositeOperation = "destination-out";
ctxTop.fillRect(0,0,size,size);
}
}else{
ctxTop.globalAlpha = fadeAmount;
ctxTop.globalCompositeOperation = "destination-out";
ctxTop.fillRect(0,0,size,size);
}
ctxTop.globalCompositeOperation = "source-over";
ctxTop.globalAlpha = 1;
// draw shapes
for(var i = 0; i < points.length; i ++){
var p = points[i];
p.x += p.dx; // move the point
p.y += p.dy;
p.rot += p.dr;
p.s += p.ds;
p.dr += Math.sin(p.s) * 0.001;
p.scale = Math.sin(p.s) * p.scaleMax+1;
p.x = ((p.x % size) + size) % size;
p.y = ((p.y % size) + size) % size;
drawShape(ctxTop,p); // draw trailing layer (middle)
}
// draw the trail the most distance from the current position
ctx.drawImage(trailCanvases[(topCanvas + 1)%trailDistCurrent],0,0);
// do it all again.
requestAnimationFrame(update);
}
update();
I need to generate and store the coordinates of each point of a filled circle of say, radius 10 in Javascript.
It seems like the best way to do this would be to use the midpoint circle algorithm, but I'm not sure how to adapt it to find every point in the circle. The coordinates are going to be stored as objects in an array.
Could someone help me with the implementation?
Personally I think it would probably be faster in this case to test all pixels in the bounding box for their distance to the center. If <= r then the point is in the circle and should be pushed onto your array.
function distance(p1, p2)
{
dx = p2.x - p1.x; dx *= dx;
dy = p2.y - p1.y; dy *= dy;
return Math.sqrt( dx + dy );
}
function getPoints(x, y, r)
{
var ret = [];
for (var j=x-r; j<=x+r; j++)
for (var k=y-r; k<=y+r; k++)
if (distance({x:j,y:k},{x:x,y:y}) <= r) ret.push({x:j,y:k});
return ret;
}
You loop through all the possible points and you run the Point-In-Circle check on them.
Something like the following would suffice...
var result = [];
var d = 10;
var r = d / 2;
var rr = r*r;
for(var y=0; y<d; y++)
for(var x=0; x<d; x++)
if((x-r)*(x-r)+(y-r)*(y-r) < rr)
result.push({"x": x, "y": y});
Modifying the above algorithm to handle other (more complex) shapes/path/polygons would be difficult. For a more generic solution you could use HTML5 CANVAS. You create a canvas, get the 2d context draw all of your shapes/paths/polygons in solid black then iterate through the pixel data and find the pixels with an alpha channel greater than 0 (or 127 if you want to alleviate false positives from anti-aliasing).
var r = 5; // radius of bounding circle
//
// set up a canvas element
//
var canvas = document.createElement("canvas");
canvas.width = r*2;
canvas.height = r*2;
canvas.style.width = (r*2) + "px";
canvas.style.height = (r*2) + "px";
var ctx = canvas.getContext("2d");
ctx.fillStyle = "#000";
//
// draw your shapes/paths/polys here
//
ctx.beginPath();
ctx.arc(r, r, r, 0, Math.PI*2, true);
ctx.closePath();
ctx.fill();
//
// process the pixel data
//
var imageData = ctx.getImageData(0,0,(r*2),(r*2));
var data = imageData.data;
var result = [];
var str = "";
for(var y = 0; y<(r*2); y++) {
for(var x = 0; x<(r*2); x++) {
var pixelOffset = (y * (r*2) + x) * 4;
if(data[pixelOffset+3] > 127) {
result.push({x: x, y: y});
str += "(" + x + ", " + y + ") "; // debug
}
}
}
//
// debug/test output
//
document.body.innerHTML += str;
document.body.appendChild(canvas);
alert(result.length);