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How to draw triangle pointers inside of circle

I realize this is a simple Trigonometry question, but my high school is failing me right now.
Given an angle, that I have converted into radians to get the first point. How do I figure the next two points of the triangle to draw on the canvas, so as to make a small triangle always point outwards to the circle. So lets say Ive drawn a circle of a given radius already. Now I want a function to plot a triangle that sits on the edge of the circle inside of it, that points outwards no matter the angle. (follows the edge, so to speak)
function drawPointerTriangle(ctx, angle){
var radians = angle * (Math.PI/180)
var startX = this.radius + this.radius/1.34 * Math.cos(radians)
var startY = this.radius - this.radius/1.34 * Math.sin(radians)
// This gives me my starting point on the outer edge of the circle, plotted at the angle I need
ctx.moveTo(startX, startY);
// HOW DO I THEN CALCULATE x1,y1 and x2, y2. So that no matter what angle I enter into this function, the arrow/triangle always points outwards to the circle.
ctx.lineTo(x1, y1);
ctx.lineTo(x2, y2);
}
Example

You don't say what type of triangle you want to draw so I suppose that it is an equilateral triangle.
Take a look at this image (credit here)
I will call 3 points p1, p2, p3 from top right to bottom right, counterclockwise.
You can easily calculate the coordinate of three points of the triangle in the coordinate system with the origin is coincident with the triangle's centroid.
Given a point belongs to the edge of the circle and the point p1 that we just calculated, we can calculate parameters of the translation from our main coordinate system to the triangle's coordinate system. Then, we just have to translate the coordinate of two other points back to our main coordinate system. That is (x1,y1) and (x2,y2).
You can take a look at the demo below that is based on your code.
const w = 300;
const h = 300;
function calculateTrianglePoints(angle, width) {
let r = width / Math.sqrt(3);
let firstPoint = [
r * Math.cos(angle),
r * Math.sin(angle),
]
let secondPoint = [
r * Math.cos(angle + 2 * Math.PI / 3),
r * Math.sin(angle + 2 * Math.PI / 3),
]
let thirdPoint = [
r * Math.cos(angle + 4 * Math.PI / 3),
r * Math.sin(angle + 4 * Math.PI / 3),
]
return [firstPoint, secondPoint, thirdPoint]
}
const radius = 100
const triangleWidth = 20;
function drawPointerTriangle(ctx, angle) {
var radians = angle * (Math.PI / 180)
var startX = radius * Math.cos(radians)
var startY = radius * Math.sin(radians)
var [pt0, pt1, pt2] = calculateTrianglePoints(radians, triangleWidth);
var delta = [
startX - pt0[0],
startY - pt0[1],
]
pt1[0] = pt1[0] + delta[0]
pt1[1] = pt1[1] + delta[1]
pt2[0] = pt2[0] + delta[0]
pt2[1] = pt2[1] + delta[1]
ctx.beginPath();
// This gives me my starting point on the outer edge of the circle, plotted at the angle I need
ctx.moveTo(startX, startY);
[x1, y1] = pt1;
[x2, y2] = pt2;
// HOW DO I THEN CALCULATE x1,y1 and x2, y2. So that no matter what angle I enter into this function, the arrow/triangle always points outwards to the circle.
ctx.lineTo(x1, y1);
ctx.lineTo(x2, y2);
ctx.closePath();
ctx.fillStyle = '#FF0000';
ctx.fill();
}
function drawCircle(ctx, radius) {
ctx.beginPath();
ctx.arc(0, 0, radius, 0, 2 * Math.PI);
ctx.closePath();
ctx.fillStyle = '#000';
ctx.fill();
}
function clear(ctx) {
ctx.fillStyle = '#fff';
ctx.fillRect(-w / 2, -h / 2, w, h);
}
function normalizeAngle(pointCoordinate, angle) {
const [x, y] = pointCoordinate;
if (x > 0 && y > 0) return angle;
else if (x > 0 && y < 0) return 360 + angle;
else if (x < 0 && y < 0) return 180 - angle;
else if (x < 0 && y > 0) return 180 - angle;
}
function getAngleFromPoint(point) {
const [x, y] = point;
if (x == 0 && y == 0) return 0;
else if (x == 0) return 90 * (y > 0 ? 1 : -1);
else if (y == 0) return 180 * (x >= 0 ? 0: 1);
const radians = Math.asin(y / Math.sqrt(
x ** 2 + y ** 2
))
return normalizeAngle(point, radians / (Math.PI / 180))
}
document.addEventListener('DOMContentLoaded', function() {
const canvas = document.querySelector('canvas');
const angleText = document.querySelector('.angle');
const ctx = canvas.getContext('2d');
ctx.translate(w / 2, h / 2);
drawCircle(ctx, radius);
drawPointerTriangle(ctx, 0);
canvas.addEventListener('mousemove', _.throttle(function(ev) {
let mouseCoordinate = [
ev.clientX - w / 2,
ev.clientY - h / 2
]
let degAngle = getAngleFromPoint(mouseCoordinate)
clear(ctx);
drawCircle(ctx, radius);
drawPointerTriangle(ctx, degAngle)
angleText.innerText = Math.floor((360 - degAngle)*100)/100;
}, 15))
})
<script src="https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.9.1/underscore-min.js"></script>
<canvas width=300 height=300></canvas>
<div class="angle">0</div>

reduce the radius, change the angle and call again cos/sin:
function drawPointerTriangle(ctx, angle)
{
var radians = angle * (Math.PI/180);
var radius = this.radius/1.34;
var startX = this.center.x + radius * Math.cos(radians);
var startY = this.center.y + radius * Math.sin(radians);
ctx.moveTo(startX, startY);
radius *= 0.9;
radians += 0.1;
var x1 = this.center.x + radius * Math.cos(radians);
var y1 = this.center.y + radius * Math.sin(radians);
radians -= 0.2;
var x1 = this.center.x + radius * Math.cos(radians);
var y1 = this.center.y + radius * Math.sin(radians);
ctx.lineTo(x1, y1);
ctx.lineTo(x2, y2);
ctx.lineTo(startX, startY);
}
the resulting triangle's size is proportional to the size of the circle.
in case you need an equilateral, fixed size triangle, use this:
//get h by pythagoras
h = sqrt( a^2 - (a/2)^2 );)
//get phi using arcustangens:
phi = atan( a/2, radius-h );
//reduced radius h by pythagoras:
radius = sqrt( (radius-h)^2 + (a/2)^2 );
radians += phi;
...
radians -= 2*phi;
...

JS move point by an angle on circle

I have program where I click three times, each click creating a point on canvas. I then calculate angle between those three points like this:
function find_angle(A, B, C) {
var AB = Math.sqrt(Math.pow(B.x - A.x, 2) + Math.pow(B.y - A.y, 2));
var BC = Math.sqrt(Math.pow(B.x - C.x, 2) + Math.pow(B.y - C.y, 2));
var AC = Math.sqrt(Math.pow(C.x - A.x, 2) + Math.pow(C.y - A.y, 2));
return Math.acos((BC * BC + AB * AB - AC * AC) / (2 * BC * AB));
}
In example picture above, the calculated angle is 93°. I need to move point 3 by -3° so the points make exactly 90°. I have this function for it:
var angleToCorrect = alpha * (Math.PI / 180) - 90 * (Math.PI / 180);
correct_angle(point2, point3, angleToCorrect)
...
function correct_angle(p2, p3, angle) {
var x = p2.x - p3.x;
var y = p2.y - p3.y;
var r = Math.sqrt(x * x + y * y); //circle radius. origin of the circle is point 2
return {
X: p2.x + (Math.cos(angle) * r),
Y: p2.y + (Math.sin(angle) * r)
};
}
Now, this function should return new x and y for point 3 with corrected angle to 90°. Yet the coordinates don't agree with what I expect. Can someone point out what I'm doing wrong?

To calculate the new position it isn't enough to provide just two of the points since the angle is measured between the three.
So inside this function you have to figure out what the current angle of the vector between point 1 and point 2 is. Javascript offers a nifty built-in function for this Math.atan2()
Now that we know the angle (in radians) we need to add the new angle to it. This makes sure we can place point 3 correctly.
function correct_angle(p1, p2, p3, angle)
{
var currentAngle=Math.atan2(p1.y-p2.y, p1.x-p2.x);
currentAngle+=angle;
var x = p2.x - p3.x;
var y = p2.y - p3.y;
var r = Math.sqrt(x * x + y * y);
return {
X: p2.x + (Math.cos(currentAngle) * r),
Y: p2.y + (Math.sin(currentAngle) * r)
};
}
The angle parameter of the function should be the target angle in radians (90 or 1.5707963267949 in your case)
Here's an interactive example:
Point = function(x, y) {
this.x = x;
this.y = y;
}
var pointA = new Point(162, 39);
var pointB = new Point(105, 161);
var pointC = new Point(211, 242);
var context = document.getElementById("canvas").getContext("2d");
function correct() {
var newPoint = correct_angle(pointA, pointB, pointC, 1.5707963267949);
pointC.x = newPoint.X;
pointC.y = newPoint.Y;
draw();
}
function correct_angle(p1, p2, p3, angle) {
var currentAngle = Math.atan2(p1.y - p2.y, p1.x - p2.x);
currentAngle += angle;
var x = p2.x - p3.x;
var y = p2.y - p3.y;
var r = Math.sqrt(x * x + y * y);
return {
X: p2.x + (Math.cos(currentAngle) * r),
Y: p2.y + (Math.sin(currentAngle) * r)
};
}
function draw() {
context.clearRect(0, 0, 400, 300);
context.fillStyle = "red";
context.beginPath();
context.arc(pointA.x, pointA.y, 10, 0, 2 * Math.PI);
context.fill();
context.beginPath();
context.arc(pointB.x, pointB.y, 10, 0, 2 * Math.PI);
context.fill();
context.beginPath();
context.arc(pointC.x, pointC.y, 10, 0, 2 * Math.PI);
context.fill();
}
draw();
<canvas id="canvas" width="400" height="300" style="background-color:#dddddd;"></canvas>
<button onclick="correct()" style="float:left">
correct me
</button>

SVG - Calculate dynamic text coord

I'm currently working on a SVG "pie" which would allow users to have an overview of all categories of the website in a coloured wheel.
For now i'm able to draw the pie with eventlistener on differents shapes.
var svg = document.getElementById('categSVG');
var startAngle = -89.999;
var nbCateg = 6;
var svgMiddleX = svg.width / 2;
var svgMiddleY = svg.height / 2;
var segmentWidth = 100;
function polarToCartesian(centerX, centerY, radius, angleInDegrees) {
var angleInRadians = (angleInDegrees - 90) * Math.PI / 180.0;
return {
x: centerX + (radius * Math.cos(angleInRadians)),
y: centerY + (radius * Math.sin(angleInRadians))
};
}
function describeArc(x, y, radius, startAngle, endAngle) {
var start = polarToCartesian(x, y, radius, endAngle);
var end = polarToCartesian(x, y, radius, startAngle);
var largeArcFlag = endAngle - startAngle <= 180 ? "0" : "1";
var d = [
"M", start.x, start.y,
"A", radius, radius, 0, largeArcFlag, 0, end.x, end.y
];
return d.join(" ");
}
function pathGen(nSegment) {
var newPath;
for (var i = 1; i <= nSegment; i++) {
//Adding path
newPath = document.createElementNS('http://www.w3.org/2000/svg', "path");
newPath.setAttribute("id", "arc" + i);
newPath.setAttribute("stroke", '#' + (Math.random() * 0xFFFFFF << 0).toString(16));
newPath.setAttribute("d", describeArc(150, 150, 100, startAngle, 270));
newPath.setAttribute("stroke-width", segmentWidth);
svg.appendChild(newPath);
startAngle += 360 / nbCateg;
}
}
function init() {
pathGen(nbCateg);
var elem;
for (var i = 1; i <= nbCateg; i++) {
document.getElementById("arc" + i).addEventListener("click", function() {
console.log('I would redirect to ' + this.id); //will change
});
}
}
init();
svg {
height: 1000px;
width: 1000px;
}
path {
fill: none;
}
<svg id="categSVG"></svg>
But i can't find a way to display text (html ID in this case) in the middle of the pie part.
So that's my question, how can I calculate X and Y coords to place a text in the middle of each shape ?
To note that number of parts can vary.
Here's my fiddle
(I'm using random colors for tests)
Thank you.

After many tries, I finally found a solution :
Firstly, I included svg.js :
<script src="https://cdnjs.cloudflare.com/ajax/libs/svg.js/2.6.4/svg.js"></script>
After that, I added this after "svg.appendChild(newPath)" :
bbox = SVG.adopt(newPath).bbox();
x=bbox.cx;
y=bbox.cy;
text.setAttributeNS(null,"x",""+x);
text.setAttributeNS(null,"y",""+y);
text.setAttributeNS(null,"font-size","30");
svg.appendChild(text);
This solution uses a BBOX to calculate center x and y of a path entity, after that you can easily param your text (don't forget to append a Node to set the text).
Hope it will help someone.

How to draw parallel edges (arrows) between vertices with canvas?

I'm working on a flow-network visualization with Javascript.
Vertices are represented as circles and edges are represented as arrows.
Here is my Edge class:
function Edge(u, v) {
this.u = u; // start vertex
this.v = v; // end vertex
this.draw = function() {
var x1 = u.x;
var y1 = u.y;
var x2 = v.x;
var y2 = v.y;
context.beginPath();
context.moveTo(x1, y1);
context.lineTo(x2, y2);
context.stroke();
var dx = x1 - x2;
var dy = y1 - y2;
var length = Math.sqrt(dx * dx + dy * dy);
x1 = x1 - Math.round(dx / ((length / (radius))));
y1 = y1 - Math.round(dy / ((length / (radius))));
x2 = x2 + Math.round(dx / ((length / (radius))));
y2 = y2 + Math.round(dy / ((length / (radius))));
// calculate the angle of the edge
var deg = (Math.atan(dy / dx)) * 180.0 / Math.PI;
if (dx < 0) {
deg += 180.0;
}
if (deg < 0) {
deg += 360.0;
}
// calculate the angle for the two triangle points
var deg1 = ((deg + 25 + 90) % 360) * Math.PI * 2 / 360.0;
var deg2 = ((deg + 335 + 90) % 360) * Math.PI * 2 / 360.0;
// calculate the triangle points
var arrowx = [];
var arrowy = [];
arrowx[0] = x2;
arrowy[0] = y2;
arrowx[1] = Math.round(x2 + 12 * Math.sin(deg1));
arrowy[1] = Math.round(y2 - 12 * Math.cos(deg1));
arrowx[2] = Math.round(x2 + 12 * Math.sin(deg2));
arrowy[2] = Math.round(y2 - 12 * Math.cos(deg2));
context.beginPath();
context.moveTo(arrowx[0], arrowy[0]);
context.lineTo(arrowx[1], arrowy[1]);
context.lineTo(arrowx[2], arrowy[2]);
context.closePath();
context.stroke();
context.fillStyle = "black";
context.fill();
};
}
Given the code
var canvas = document.getElementById('canvas'); // canvas element
var context = canvas.getContext("2d");
context.lineWidth = 1;
context.strokeStyle = "black";
var radius = 20; // vertex radius
var u = {
x: 50,
y: 80
};
var v = {
x: 150,
y: 200
};
var e = new Edge(u, v);
e.draw();
The draw() function will draw an edge between two vertices like this:
If we add the code
var k = new Edge(v, u);
k.draw();
We will get:
but I want to draw edges both directions as following:
(sorry for my bad paint skills)
Of course the vertices and the edge directions are not fixed.
A working example (with drawing vertex fucntion) on JSFiddle:
https://jsfiddle.net/Romansko/0fu01oec/18/

Aligning axis to a line.
It can make everything a little easier if you rotate the rendering to align with the line. Once you do that it is then easy to draw above or below the line as that is just in the y direction and along the line is the x direction.
Thus if you have a line
const line = {
p1 : { x : ? , y : ? },
p2 : { x : ? , y : ? },
};
Convert it to a vector and normalise that vector
// as vector from p1 to p2
var nx = line.p2.x - line.p1.x;
var ny = line.p2.y - line.p1.y;
// then get length
const len = Math.sqrt(nx * nx + ny * ny);
// use the length to normalise the vector
nx /= len;
ny /= len;
The normalised vector represents the new x axis we want to render along, and the y axis is at 90 deg to that. We can use setTransform to set both axis and the origin (0,0) point at the start of the line.
ctx.setTransform(
nx, ny, // the x axis
-ny, nx, // the y axis at 90 deg to the x axis
line.p1.x, line.p1.y // the origin (0,0)
)
Now rendering the line and arrow heads is easy as they are axis aligned
ctx.beginPath();
ctx.lineTo(0,0); // start of line
ctx.lineTo(len,0); // end of line
ctx.stroke();
// add the arrow head
ctx.beginPath();
ctx.lineTo(len,0); // tip of arrow
ctx.lineTo(len - 10, 10);
ctx.lineTo(len - 10, -10);
ctx.fill();
To render two lines offset from the center
var offset = 10;
ctx.beginPath();
ctx.lineTo(0,offset); // start of line
ctx.lineTo(len,offset); // end of line
ctx.moveTo(0,-offset); // start of second line
ctx.lineTo(len,-offset); // end of second line
ctx.stroke();
// add the arrow head
ctx.beginPath();
ctx.lineTo(len,offset); // tip of arrow
ctx.lineTo(len - 10, offset+10);
ctx.lineTo(len - 10, offset-10);
ctx.fill();
offset = -10;
// add second arrow head
ctx.beginPath();
ctx.lineTo(0,offset); // tip of arrow
ctx.lineTo(10, offset+10);
ctx.lineTo(10, offset-10);
ctx.fill();
And you can reset the transform with
ctx.setTransform(1,0,0,1,0,0); // restore default transform

Drawing a smooth curved arc() between two points

I'm trying to draw a smooth curved arc between two points in canvas, I have set up the points as sutch note these are dynamic and can change.
var p1 = {
x=100, y=100
}
var p2 = {
x=255, y=255
}
The curve would look something like this
Here my started code, I can't get my head around the math/logic of this function:
function curveA2B(a,b){
var mindpoint = {
x: (a.x+b.x)/2,
y: (a.y+b.y)/2,
d: Math.sqrt(Math.pow(b.x-a.x,2) + Math.pow(b.y-a.y,2))
};
context.beginPath();
context.arc(
a.x,
a.y,
mindpoint.d/2,
1.5*Math.PI,
0,
false
);
context.arc(
b.x,
b.y,
mindpoint.d/2,
1*Math.PI,
0.5*Math.PI,
true
);
context.context.stroke();
}
The dynamic examples is here: http://jsfiddle.net/CezarisLT/JDdjp/6/

I created a function that would be easily modifiable to many needs called plot_curve that gives you an idea of the breakdown of your problem.
A quick DEMO: http://jsfiddle.net/LVFat/
function plot_curve(x,y,xx,yy, target,color)
{
var startX=x;
var startY=y;
var endX=xx;
var endY=yy;
var diff_x = xx - x;
var diff_y = yy - y;
var bezierX=x; // x1
var bezierY=yy; // y2
console.log("bx:"+bezierX);
console.log("by:"+bezierY);
var cx,cy, t;
for(t=0.0; t<=1; t+=0.01)
{
cx = Math.round( (1-t)*(1-t)*startX + 2*(1-t) * t * bezierX + t*t*endX);
cy = Math.round( (1-t)*(1-t)*startY + 2*(1-t) * t * bezierY + t*t*endY);
// change this part to whatever you are trying to manipulate to the curve
plot_pixel( Math.round(cx), Math.round(cy), target, color);
}
}
example... (works with a divCanvas function I made.. check out jsfiddle link...)
plot_curve(25,25,5,5, ".divCanvas","blue");
if you just want the coords for the curve between the two points, try this:
function plot_curve(x,y,xx,yy)
{
// returns an array of x,y coordinates to graph a perfect curve between 2 points.
var startX=x;
var startY=y;
var endX=xx;
var endY=yy;
var diff_x = xx - x;
var diff_y = yy - y;
var xy = [];
var xy_count = -1;
var bezierX=x; // x1
var bezierY=yy; // y2
var t;
for(t=0.0; t<=1; t+=0.01)
{
xy_count++;
xy[xy_count] = {};
xy[xy_count].x = Math.round( (1-t)*(1-t)*startX + 2*(1-t) * t * bezierX + t*t*endX);
xy[xy_count].y = Math.round( (1-t)*(1-t)*startY + 2*(1-t) * t * bezierY + t*t*endY);
}
return xy; // returns array of coordinates
}

You can use the mid of the two points as two radius settings for the x and y axis.
The following example is simplified but it shows one approach to create smooth curves inside the boxes as in your example.
The boxes will always scale so that the curves goes through the mid point between the two points (alter the end point for example).
DEMO
/// set up some values
var ctx = demo.getContext('2d'),
p1 = {x:100, y:100}, /// point 1
p2 = {x:355, y:255}, /// point 2
mx = (p2.x - p1.x) * 0.5, /// mid-point between point 1 and 2
my = (p2.y - p1.y) * 0.5,
c1 = {x: p1.x, y: p1.y + my}, /// create center point objects
c2 = {x: p2.x, y: p2.y - my},
steps = 0.05; /// curve resolution
/// mark the points and the boxes which represent the center of those
ctx.fillStyle = '#ff6e6e';
ctx.fillRect(p1.x, p1.y, mx, my);
ctx.fillStyle = '#6e93ff';
ctx.fillRect(p1.x + mx, p1.y + my, mx, my);
Then we render the quarter ellipse for each "box":
/// render the smooth curves using 1/4 ellipses
ctx.beginPath();
for(var isFirst = true, /// first point is moveTo, rest lineTo
angle = 1.5 * Math.PI, /// start angle in radians
goal = 2 * Math.PI, /// goal angle
x, y; angle < goal; angle += steps) {
/// calculate x and y using cos/sin
x = c1.x + mx * Math.cos(angle);
y = c1.y + my * Math.sin(angle);
/// move or draw line
(isFirst) ? ctx.moveTo(x, y) : ctx.lineTo(x, y);
isFirst = false;
}
/// second box
for(var isFirst = true,
angle = Math.PI,
goal = 0.5 * Math.PI,
x, y;angle > goal; angle -= steps) {
x = c2.x + mx * Math.cos(angle);
y = c2.y + my * Math.sin(angle);
(isFirst) ? ctx.moveTo(x, y) : ctx.lineTo(x, y);
isFirst = false;
}
ctx.stroke();
I'll leave it to you to put this into re-usable functions. Hope this helps!
If this doesn't cut it I would recommend you to take a look at my cardinal spline implementation.