Develop Reference

Apply noise on circle according to mouseX and mouseY

I have created a blob with small points. I want my blob to show noise on its surface according to mouseX and mouseY. I want it to show high noise in the quadrant in which the mouse lies. I want it to be wavy. Below is my code.
var ctx = document.querySelector("canvas").getContext("2d");
var cx = 200;
var cy = 200;
var radius = 50;
var amp = 2;
var mouseX = 0;
var mouseY = 0;
document.querySelector("canvas").addEventListener("mousemove", function (e) {
mouseX = e.clientX;
mouseY = e.clientY;
});
function drawTheBlob() {
ctx.fillStyle = "#000";
ctx.fillRect(0, 0, 400, 400);
ctx.beginPath();
ctx.strokeStyle = "#fff";
for (var a = 0; a < 360; a ++) {
var angle = a * Math.PI/180;
var x = cx + radius * Math.cos(angle) + Math.random() * amp;
var y = cy + radius * Math.sin(angle) + Math.random() * amp;
ctx.lineTo(x, y);
}
ctx.stroke();
ctx.closePath();
requestAnimationFrame(drawTheBlob);
}
drawTheBlob();
<canvas width="400" height="400"></canvas>

Adds a sin wave on the circle. Use ctx.arc to draw the flat part of the circle for speed as drawing many circles with lines will be slow. See code for comments on what is done.
var ctx = document.querySelector("canvas").getContext("2d");
ctx.lineWidth = 3;
ctx.lineJoin = "round";
var cx = 100;
var cy = 100;
var radius = 50;
var mouseX = 0;
var mouseY = 0;
const quadWidth = Math.PI / 2; // area of effect PI/2 is 90 degree
const steps = radius / quadWidth; // number steps around the circle matches 1 pixel per step,
const noiseAmpMax = 5; // in pixels
const noiseWaveMoveSpeed = 2; // speed of waves on circle in radians per second
const noiseWaveFreq = 16; // how many waves per 360 deg
document.querySelector("canvas").addEventListener("mousemove", function(e) {
mouseX = e.clientX;
mouseY = e.clientY;
});
function drawTheBlob(time) { // time is passed from the requestAnimationFrame call
var amp = 0; // amplitude of noise
var wavePos = ((time / 1000) * Math.PI) * noiseWaveMoveSpeed;
var mouseDir = Math.atan2(mouseY - cy, mouseX - cx);
ctx.fillStyle = "#000";
ctx.fillRect(0, 0, 400, 400);
ctx.beginPath();
ctx.strokeStyle = "#fff";
ctx.fillStyle = "red";
// draw arc for parts that have no noise as it is a log quicker
ctx.arc(cx, cy, radius, mouseDir + quadWidth / 2, mouseDir + Math.PI * 2 - quadWidth / 2);
for (var a = 0; a < 1; a += 1 / steps) {
var angle = (mouseDir - quadWidth / 2) + a * quadWidth;
var angDist = Math.abs(angle - mouseDir); // find angular distance from mouse
// as a positive value, it does not mater
// what the sign is
if (angDist < quadWidth / 2) { // is angle distance within the range of effect
// normalise the distance (make it 0 to 1)
amp = 1 - angDist / (quadWidth / 2);
} else {
amp = 0; // no noise
}
// amp will be zero if away from mouse direction and 0 to 1 the closer to
// mouse angle it gets.
// add a sin wave to the radius and scale it by amp
var dist = radius + Math.sin(wavePos + noiseWaveFreq * angle) * noiseAmpMax * amp;
var x = cx + dist * Math.cos(angle);
var y = cy + dist * Math.sin(angle);
ctx.lineTo(x, y);
}
ctx.closePath(); // use close path to close the gap (only needed if you need to draw a line from the end to the start. It is not needed to match beginPath
ctx.fill();
ctx.stroke();
requestAnimationFrame(drawTheBlob);
}
requestAnimationFrame(drawTheBlob); // start this way so that you get the time argument
<canvas width="200" height="200"></canvas>
How it works.
Mouse direction
First we need the direction from the circle to the mouse. To do that we use the function Math.atan2 It takes the vector from the circle to the mouse and returns the direction in radians. The function is a little weird as it takes y first, then x.
var mouseDir = Math.atan2(mouseY - cy, mouseX - cx);
Draw arc to save CPU time
Now that we have the direction to the mouse we can draw the parts of the circle that has no noise using arc .
ctx.arc(cx, cy, radius, mouseDir + quadWidth / 2, mouseDir + Math.PI * 2 - quadWidth / 2);
The variable quadWidth is angular size of the noise bit so from the mouseDir we add half that angular width and draw the arc around to mouseDir plus 360deg take half the quadWidth.
Quick word on Radians
Almost all programming languages use radians to define angles, 360deg is equal to 2 * PI or 2 * 3.1415, which can be hard to get your head around, but there is good reason to use radians. For now just remember that a full circle in radians is 2 * Math.PI = 360deg, Math.PI = 180deg, Math.PI / 2 = 90deg, Math.PI / 4 = 45Deg and Math.PI / 180 = 1deg. You dont have to remember the digits just Math.PI is half a circle.
quadWidth from above is a constant defined as const quadWidth = Math.PI / 2; which is 90deg.
The for loop
The for loop only draws the (Math.PI / 2) 90deg section around the mouseDir, from 45 deg left to 45 right. or whatever you set quadWidth to.
for (var a = 0; a < 1; a += 1 / steps) {
I loop from 0 to 1 the number of steps that give a reasonably smooth curve. We can find what part of the noisy arc we are drawing by multiplying the value a *
quadWidth and adding that to the mouseDir - quadWidth / 2. This means that we start at mouseDir - 45deg and move clock wise to mouseDir + 45deg
var angle = (mouseDir - quadWidth / 2) + a * quadWidth;
Next i find how far that angle is from the mouseDir (could optimize it here a bit here but this way is a little more flexible, if you want to draw more noise on the other part of the arc)
var angDist = Math.abs(angle - mouseDir);
If that number is less than quadWidth / 2 convert the value to the range 0 to 1 where 0 is at the angle furthest from the mouse direction and 1 closest.
if (angDist < quadWidth / 2) {
amp = 1 - angDist / (quadWidth / 2);
} else {
amp = 0;
}
The sin wave
Now we calculate the radius of the circle at the current angle and add a sin wave to it. First the radius then the sin wave multiplied by the amp calculated in the last step. Where amp is zero none of the sin wave is added, where amp is 1 (in the direction of the mouse) the full sin wave is added.
var dist = radius + Math.sin(wavePos + noiseWaveFreq * angle) * noiseAmpMax * amp
The values wavePos, noiseWaveFreq, and noiseAmpMax control the animation of the sin wave. Play around with these values to get a feel of what they do, wavePos is calculated based on the time at the start of the function.
With dist we can calculate the x,y position for the next line of the circle
var x = cx + dist * Math.cos(angle);
var y = cy + dist * Math.sin(angle);
ctx.lineTo(x, y);
Experiment
I added some constants
const quadWidth = Math.PI / 2; // area of effect PI/2 is 90 degree
const steps = radius / quadWidth; // number steps around the circle matches 1 pixel per step,
const noiseAmpMax = 5; // in pixels
const noiseWaveMoveSpeed = 2; // speed of waves on circle in radians per second
const noiseWaveFreq = 16; // how many waves per 360 deg
To get a understanding what they do experiment and change the numbers to see what happens.

Raphael.js has weird behavior on drag

I have circle with a line from the center to the edge of the circle. The user can click on and drag the line and get the degrees from wherever they set the line. I'm using the code from the answer here and have adjusted the code accordingly.
Everything works fine, but the farther down the page the element affected by raphael is, the farther outside of the circle the mouse has to be in order to drag the line. jsfiddle
var canvas = Raphael('pivot', 0, 0, 320, 320);
var clock = canvas.circle(200, 150, 100).attr("stroke-width", 2);
canvas.circle(200, 150, 3).attr("fill", "#000");
var angleplus = 360,
rad = Math.PI / 180,
cx = 200,
cy = 150,
r = 90,
startangle = -90,
angle = 90,
x, y, endangle;
for (i = 1; i < 5; i++) {
endangle = startangle + angle;
x = cx + r * Math.sin(endangle * rad);
y = cy - r * Math.cos(endangle * rad);
canvas.text(x, y, endangle);
startangle = endangle;
}
var hand = canvas.path("M200 50L200 150").attr("stroke-width", 5);
hand.drag( move, start, end );
function move (dx,dy,x,y) {
var pt = this.node.ownerSVGElement.createSVGPoint();
pt.x = x;
pt.y = y;
var angle = ( 90 + Math.atan2(pt.y - clock.attr('cy') - 5, pt.x - clock.attr('cx') - 5 ) * 180 / Math.PI + 360) % 360;
this.rotate(angle, 200,150);
this.angle = angle;
}
function start() {
};
function end() {
alert(parseInt(this.angle));
}
I'm wondering why this happens and if it's even fixable?

Here is an updated original one, a bit added and another bit of redundancy removed, and I've added an extra fiddle to the original answer to reflect it.
The key bits I've added are...
var cpt = clock.node.ownerSVGElement.createSVGPoint();
cpt.x = clock.attr('cx');
cpt.y = clock.attr('cy');
cpt = cpt.matrixTransform(clock.node.getScreenCTM());
The centre of the clock has now moved, so using cx of the circle alone, doesn't really make sense relative to the mouse event. We need to take into account any offset and transforms on the screen to the clock.
We can get this with getScreenCTM (get the matrix from element to the screen), and we can use that matrix with the original cx, cy to figure out where it is on the screen.
Then later, instead of cx, cy, we use the new adjusted coordinates cpt.x/y
var angle = ( 90 + Math.atan2(y - cpt.y - 5, x - cpt.x - 5 ) * 180 / Math.PI + 360)
jsfiddle - drag any hand

Create equilateral triangle in the middle of canvas?

I want to draw an equilateral triangle in the middle of canvas. I tried this:
ctx.moveTo(canvas.width/2, canvas.height/2-50);
ctx.lineTo(canvas.width/2-50, canvas.height/2+50);
ctx.lineTo(canvas.width/2+50, canvas.height/2+50);
ctx.fill();
But the triangle looks a bit too tall.
How can I draw an equilateral triangle in the middle of canvas?
Someone told me you have to find the ratio of the height of an equilateral triangle to the side of an equilateral triangle.
h:s
What are the two numbers?

The equation for the three corner points is
x = r*cos(angle) + x_center
y = r*sin(angle) + y_center
where for angle = 0, (1./3)*(2*pi), and (2./3)*(2*pi); and where r is the radius of the circle in which the triangle is inscribed.

You have to do it with the height of the triangle
var h = side * (Math.sqrt(3)/2);
or
var h = side * Math.cos(Math.PI/6);
So the ratio h:s is equal to:
sqrt( 3 ) / 2 : 1 = cos( π / 6 ) : 1 ≈ 0.866025
See : http://jsfiddle.net/rWSKh/2/

A simple version where X and Y are the points you want to top of the triangle to be:
var height = 100 * (Math.sqrt(3)/2);
context.beginPath();
context.moveTo(X, Y);
context.lineTo(X+50, Y+height);
context.lineTo(X-50, Y+height);
context.lineTo(X, Y);
context.fill();
context.closePath();
This makes an equilateral triange with all sides = 100. Replace 100 with how long you want your side lengths to be.
After you find the midpoint of the canvas, if you want that to be your triangle's midpoint as well you can set X = midpoint's X and Y = midpoint's Y - 50 (for a 100 length triangle).

The side lengths will not be equal given those coordinates.
The horizontal line constructed on the bottom has a length of 100, but the other sides are actually the hypotenuse of a 50x100 triangle ( approx. 112).

I can get you started with drawing an equilateral triangle but I don't have the time to get it centered.
jsFiddle
var ax=0;
var ay=0;
var bx=0;
var by=150;
var dx=bx-ax
var dy=by-ay;
var dangle = Math.atan2(dy, dx) - Math.PI / 3;
var sideDist = Math.sqrt(dx * dx + dy * dy);
var cx = Math.cos(dangle) * sideDist + ax;
var cy = Math.sin(dangle) * sideDist + ay;
var canvas = document.getElementById('equ');
var ctx = canvas.getContext('2d');
ctx.beginPath();
ctx.moveTo(ax,ay);
ctx.lineTo(bx,by);
ctx.lineTo(cx,cy);
ctx.fill();

my code for drawing triangle also depending on direction (for lines). code is for Raphael lib.
drawTriangle(x2 - x1, y2 - y1, x2, y2);
function drawTriangle(dx, dy, midX, midY) {
var diff = 0;
var cos = 0.866;
var sin = 0.500;
var length = Math.sqrt(dx * dx + dy * dy) * 0.8;
dx = 8 * (dx / length);
dy = 8 * (dy / length);
var pX1 = (midX + diff) - (dx * cos + dy * -sin);
var pY1 = midY - (dx * sin + dy * cos);
var pX2 = (midX + diff) - (dx * cos + dy * sin);
var pY2 = midY - (dx * -sin + dy * cos);
return [
"M", midX + diff, midY,
"L", pX1, pY1,
"L", pX2, pY2,
"L", midX + diff, midY
].join(",");
}

Drawing a spiral on an HTML canvas using JavaScript

I have searched and haven't found anything really on how to draw spirals in canvas using JavaScript.
I thought it might be possible to do it with the bezier curve and if that didn't work use lineTo(), but that seemed a lot harder.
Also, to do that I'm guessing I would have to use trigonometry and graphing with polar coordinates and its been a while since I did that. If that is the case could you point me in the right direction on the math.

The Archimedean spiral is expressed as r=a+b(angle). Convert that into x, y coordinate, it will be expressed as x=(a+b*angle)*cos(angle), y=(a+b*angle)*sin(angle). Then you can put angle in a for loop and do something like this:
for (i=0; i< 720; i++) {
angle = 0.1 * i;
x=(1+angle)*Math.cos(angle);
y=(1+angle)*Math.sin(angle);
context.lineTo(x, y);
}
Note the above assumes a = 1 and b = 1.
Here is a jsfiddle link: http://jsfiddle.net/jingshaochen/xJc7M/

This is a slightly-changed, javascript-ified version of a Java spiral I once borrowed from here
It uses lineTo() and its not all that hard.
<!DOCTYPE HTML>
<html><body>
<canvas id="myCanvas" width="300" height="300" style="border:1px solid #c3c3c3;"></canvas>
<script type="text/javascript">
var c=document.getElementById("myCanvas");
var cxt=c.getContext("2d");
var centerX = 150;
var centerY = 150;
cxt.moveTo(centerX, centerY);
var STEPS_PER_ROTATION = 60;
var increment = 2*Math.PI/STEPS_PER_ROTATION;
var theta = increment;
while( theta < 40*Math.PI) {
var newX = centerX + theta * Math.cos(theta);
var newY = centerY + theta * Math.sin(theta);
cxt.lineTo(newX, newY);
theta = theta + increment;
}
cxt.stroke();
</script></body></html>

Here's a function I wrote for drawing Archimedean spirals:
CanvasRenderingContext2D.prototype.drawArchimedeanSpiral =
CanvasRenderingContext2D.prototype.drawArchimedeanSpiral ||
function(centerX, centerY, stepCount, loopCount,
innerDistance, loopSpacing, rotation)
{
this.beginPath();
var stepSize = 2 * Math.PI / stepCount,
endAngle = 2 * Math.PI * loopCount,
finished = false;
for (var angle = 0; !finished; angle += stepSize) {
// Ensure that the spiral finishes at the correct place,
// avoiding any drift introduced by cumulative errors from
// repeatedly adding floating point numbers.
if (angle > endAngle) {
angle = endAngle;
finished = true;
}
var scalar = innerDistance + loopSpacing * angle,
rotatedAngle = angle + rotation,
x = centerX + scalar * Math.cos(rotatedAngle),
y = centerY + scalar * Math.sin(rotatedAngle);
this.lineTo(x, y);
}
this.stroke();
}

there is a fine free tool that will help if you have illustrator
ai2canvas
it will create all the curves to javascript in html canvas tag for you!
(if you are looking for archmedes spiral than you will first have to get it from coreldraw and copy that to illustrator, because the default spiral tool enlarges the angle with each point)

this is example of drawing spiral using function below:
spiral(ctx, {
start: {//starting point of spiral
x: 200,
y: 200
},
angle: 30 * (Math.PI / 180), //angle from starting point
direction: false,
radius: 100, //radius from starting point in direction of angle
number: 3 // number of circles
});
spiral drawing code:
spiral = function(ctx,obj) {
var center, eAngle, increment, newX, newY, progress, sAngle, tempTheta, theta;
sAngle = Math.PI + obj.angle;
eAngle = sAngle + Math.PI * 2 * obj.number;
center = {
x: obj.start.x + Math.cos(obj.angle) * obj.radius,
y: obj.start.y + Math.sin(obj.angle) * obj.radius
};
increment = 2 * Math.PI / 60/*steps per rotation*/;
theta = sAngle;
ctx.beginPath();
ctx.moveTo(center.x, center.y);
while (theta <= eAngle + increment) {
progress = (theta - sAngle) / (eAngle - sAngle);
tempTheta = obj.direction ? theta : -1 * (theta - 2 * obj.angle);
newX = obj.radius * Math.cos(tempTheta) * progress;
newY = obj.radius * Math.sin(tempTheta) * progress;
theta += increment;
ctx.lineTo(center.x + newX, center.y + newY);
}
ctx.stroke();
};

The following code approximates a spiral as a collection of quarters of a circle each with a slightly larger radius. It might look worse than an Archimedes spiral for small turning numbers but it should run faster.
function drawSpiral(ctx, centerx, centery, innerRadius, outerRadius, turns=2, startAngle=0){
ctx.save();
ctx.translate(centerx, centery);
ctx.rotate(startAngle);
let r = innerRadius;
let turns_ = Math.floor(turns*4)/4;
let dr = (outerRadius - innerRadius)/turns_/4;
let cx = 0, cy = 0;
let directionx = 0, directiony = -1;
ctx.beginPath();
let angle=0;
for(; angle < turns_*2*Math.PI; angle += Math.PI/2){
//draw a quarter arc around the center point (x, cy)
ctx.arc( cx, cy, r, angle, angle + Math.PI/2);
//move the center point and increase the radius so we can draw a bigger arc
cx += directionx*dr;
cy += directiony*dr;
r+= dr;
//rotate direction vector by 90 degrees
[directionx, directiony] = [ - directiony, directionx ];
}
//draw the remainder of the last quarter turn
ctx.arc( cx, cy, r, angle, angle + 2*Math.PI*( turns - turns_ ))
ctx.stroke();
ctx.restore();
}
Result:

Circle coordinates to array in Javascript

What's the best way to add the coordinates of a circle to an array in JavaScript? So far I've only been able to do a half circle, but I need a formula that returns the whole circle to two different arrays: xValues and yValues. (I'm trying to get the coordinates so I can animate an object along a path.)
Here's what I have so far:
circle: function(radius, steps, centerX, centerY){
var xValues = [centerX];
var yValues = [centerY];
for (var i = 1; i < steps; i++) {
xValues[i] = (centerX + radius * Math.cos(Math.PI * i / steps-Math.PI/2));
yValues[i] = (centerY + radius * Math.sin(Math.PI * i / steps-Math.PI/2));
}
}

Your loop should be set up like this instead:
for (var i = 0; i < steps; i++) {
xValues[i] = (centerX + radius * Math.cos(2 * Math.PI * i / steps));
yValues[i] = (centerY + radius * Math.sin(2 * Math.PI * i / steps));
}
Start your loop at 0
Step through the entire 2 * PI range, not just PI.
You shouldn't have the var xValues = [centerX]; var yValues = [centerY]; -- the center of the circle is not a part of it.

Bresenham's algorithm is way faster. You hear of it in relation to drawing straight lines, but there's a form of the algorithm for circles.
Whether you use that or continue with the trig calculations (which are blazingly fast these days) - you only need to draw 1/8th of the circle. By swapping x,y you can get another 1/8th, and then the negative of x, of y, and of both - swapped and unswapped - gives you points for all the rest of the circle. A speedup of 8x!

Change:
Math.PI * i / steps
to:
2*Math.PI * i / steps
A full circle is 2pi radians, and you are only going to pi radians.

You need to use a partial function to input the radians into cos and sin; therefore take the values you're getting for a quarter or half of the circle, and reflect them over the center points' axis to get your full circle.
That said JavaScript's sin and cos aren't quite as picky, so you must have halved your radian or something; I'd write it as:
function circle(radius, steps, centerX, centerY){
var xValues = [centerX];
var yValues = [centerY];
var table="<tr><th>Step</th><th>X</th><th>Y</th></tr>";
var ctx = document.getElementById("canvas").getContext("2d");
ctx.fillStyle = "red"
ctx.beginPath();
for (var i = 0; i <= steps; i++) {
var radian = (2*Math.PI) * (i/steps);
xValues[i+1] = centerX + radius * Math.cos(radian);
yValues[i+1] = centerY + radius * Math.sin(radian);
if(0==i){ctx.moveTo(xValues[i+1],yValues[i+1]);}else{ctx.lineTo(xValues[i+1],yValues[i+1]);}
table += "<tr><td>" + i + "</td><td>" + xValues[i+1] + "</td><td>" + yValues[i+1] + "</td></tr>";
}
ctx.fill();
return table;
}
document.body.innerHTML="<canvas id=\"canvas\" width=\"300\" height=\"300\"></canvas><table id=\"table\"/>";
document.getElementById("table").innerHTML+=circle(150,15,150,150);
I assumed that for whatever reason you wanted xValues[0] and yValues[0] to be centerX and centerY. I can't figure out why you'd want that, as they're values passed into the function already.

If you already have half a circle, just mirror the points to get the other half
make sure you do this in the right order.
more speficically, for the other half you simply replace the "+ sin(...)" with a "- sin(...)"

I was able to solve it on my own by multiplying the number of steps by 2:
circle: function(radius, steps, centerX, centerY){
var xValues = [centerX];
var yValues = [centerY];
for (var i = 1; i < steps; i++) {
xValues[i] = (centerX + radius * Math.cos(Math.PI * i / steps*2-Math.PI/2));
yValues[i] = (centerY + radius * Math.sin(Math.PI * i / steps*2-Math.PI/2));
}
}