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HTML5 Canvas rotate gradient around centre with best fit

I want to make a gradient that covers the whole canvas whatever the angle of it.
So I used a method found on a Stack Overflow post which is finally incorrect. The solution is almost right but, in fact, the canvas is not totally covered by the gradient.
It is this answer: https://stackoverflow.com/a/45628098/5594331
(You have to look at the last point named "Example of best fit.")
In my code example below, the yellow part should not be visible because it should be covered by the black and white gradient. This is mostly the code written in Blindman67's answer with some adjustments to highlight the problem.
I have drawn in green the control points of the gradient. With the right calculations, these should be stretched to the edges of the canvas at any angle.
var ctx = canvas.getContext("2d");
var w = canvas.width;
var h = canvas.height;
function bestFitGradient(angle){
var dist = Math.sqrt(w * w + h * h) / 2; // get the diagonal length
var diagAngle = Math.asin((h / 2) / dist); // get the diagonal angle
// Do the symmetry on the angle (move to first quad
var a1 = ((angle % (Math.PI *2))+ Math.PI*4) % (Math.PI * 2);
if(a1 > Math.PI){ a1 -= Math.PI }
if(a1 > Math.PI / 2 && a1 <= Math.PI){ a1 = (Math.PI / 2) - (a1 - (Math.PI / 2)) }
// get angles from center to edges for along and right of gradient
var ang1 = Math.PI/2 - diagAngle - Math.abs(a1);
var ang2 = Math.abs(diagAngle - Math.abs(a1));
// get distance from center to horizontal and vertical edges
var dist1 = Math.cos(ang1) * h;
var dist2 = Math.cos(ang2) * w;
// get the max distance
var scale = Math.max(dist2, dist1) / 2;
// get the vector to the start and end of gradient
var dx = Math.cos(angle) * scale;
var dy = Math.sin(angle) * scale;
var x0 = w / 2 + dx;
var y0 = h / 2 + dy;
var x1 = w / 2 - dx;
var y1 = h / 2 - dy;
// create the gradient
const g = ctx.createLinearGradient(x0, y0, x1, y1);
// add colours
g.addColorStop(0, "yellow");
g.addColorStop(0, "white");
g.addColorStop(.5, "black");
g.addColorStop(1, "white");
g.addColorStop(1, "yellow");
return {
g: g,
x0: x0,
y0: y0,
x1: x1,
y1: y1
};
}
function update(timer){
var r = bestFitGradient(timer / 1000);
// draw gradient
ctx.fillStyle = r.g;
ctx.fillRect(0,0,w,h);
// draw points
ctx.lineWidth = 3;
ctx.fillStyle = '#00FF00';
ctx.strokeStyle = '#FF0000';
ctx.beginPath();
ctx.arc(r.x0, r.y0, 5, 0, 2 * Math.PI, false);
ctx.stroke();
ctx.fill();
ctx.beginPath();
ctx.arc(r.x1, r.y1, 5, 0, 2 * Math.PI, false);
ctx.stroke();
ctx.fill();
requestAnimationFrame(update);
}
requestAnimationFrame(update);
canvas {
border : 2px solid red;
}
<canvas id="canvas" width="300" height="200"></canvas>

In this fiddle there is a function that calculates the distance between a rotated line and a point:
function distanceToPoint(px, py, angle) {
const cx = width / 2;
const cy = height / 2;
return Math.abs((Math.cos(angle) * (px - cx)) - (Math.sin(angle) * (py - cy)));
}
Which is then used to find the maximum distance between the line and the corner points (only two points are considered, because the distances to the other two points are mirrored):
const dist = Math.max(
distanceToPoint(0, 0, angle),
distanceToPoint(0, height, angle)
);
Which can be used to calculate offset points for the end of the gradient:
const ox = Math.cos(angle) * dist;
const oy = Math.sin(angle) * dist;
const gradient = context.createLinearGradient(
width / 2 + ox,
height / 2 + oy,
width / 2 - ox,
height / 2 - oy
)

Rotate a line in 3rd dimension on HTML5 canvas

I can easily draw/rotate a line of given length around z-axis, y-axis or x-axis.
const ctx = document.getElementById("drawing").getContext("2d");
ctx.scale(1, -1); ctx.translate(0, -ctx.canvas.height); // flip canvas
const length = 50;
let t = 0;
//x = r sin(q) cos(f)
//y = r sin(q) sin(f)
//z = r cos(q)
function rotate_around_zaxis() {
const x1=50; const y1=50;
const line_angle = 20 * Math.PI/180;
const angle = 0;
ctx.beginPath();
ctx.moveTo(x1, y1);
ctx.lineTo(x1 + length * Math.sin(line_angle) * Math.cos(angle + t),
y1 + length * Math.sin(line_angle) * Math.sin(angle + t));
ctx.stroke();
}
function rotate_around_yaxis() {
const x1=150; const y1=50;
const line_angle = 20 * Math.PI/180;
const angle = 0;
ctx.beginPath();
ctx.moveTo(x1, y1);
ctx.lineTo(x1 + length * Math.sin(line_angle) * Math.cos(angle + t),
y1 + length /*Math.sin(angle + t)*/ * Math.cos(line_angle) );
ctx.stroke();
}
function rotate_around_xaxis() {
const x1=250; const y1=50;
const line_angle = 20 * Math.PI/180;
const angle = 0;
ctx.beginPath();
ctx.moveTo(x1, y1);
ctx.lineTo(x1 + length /**Math.sin(angle + t)*/ * Math.cos(line_angle),
y1 + length * Math.sin(line_angle) * Math.sin(angle + t));
ctx.stroke();
}
function line(x1, y1, x2, y2) {
ctx.beginPath(); ctx.moveTo(x1, y1); ctx.lineTo(x2, y2); ctx.stroke();
}
function animate() {
ctx.clearRect(0,0,300,100);
line(0, 50, 100, 50);line(50, 0, 50, 100);rotate_around_zaxis();
line(105, 50, 200, 50);line(150, 0, 150, 100);rotate_around_yaxis();
line(205, 50, 300, 50);line(250, 0, 250, 100);rotate_around_xaxis();
t+=Math.PI/180;
requestAnimationFrame(animate);
}
requestAnimationFrame(animate);
<canvas id="drawing" width=300 height=100></canvas>
However I can only do this around straight up/down y-axis degree or straight x-axis. I can not figure out rotation around an arbitrary line in space. In other words I don't know how to move it to any point in 3d space between x,y and z/.
I couldn't grasp rotation matrices. Rotation calculation on many places is given like this.
x' = x * cos(angle) - y * sin(angle);
y' = x * sin(angle) + y * cos(angle);
I don't understand where this equation fits in what I am trying to do.
I want to be able to rotate the line in cone like shape around any axis. How do I achieve this?

Well, theoretically, if the first example works, then to get the second one, you can apply the first one, and then just translate everything -60°
let newX2 = Math.cos(-60 / Math.PI/180) * x2
let newY2 = Math.sin(-60 / Math.PI/180) * y2
same for x1 and y1

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;
...

How to draw an arrowhead with proper coordinates in the canvas

I have drawn the curved line using below lines of code, I need to draw an arrowhead.For this I need to draw 2 lines wth some angle and rotate it some some angle. It is very confusing to draw. I am following the post present in the link provided for arrowhead.
.html
<canvas id = "canvas" width = "100px" height = "120px"></canvas>
.ts
arrow({ x: 10, y: 10 }, { x: 100, y: 140 }, 15); //function called on reload.
function arrow(p1, p2, size) {
var angle = Math.atan2((p2.y - p1.y), (p2.x - p1.x));
//curve line
ctx.strokeStyle = 'white';
ctx.beginPath();
ctx.lineWidth=3;
ctx.moveTo(40,0);
ctx.bezierCurveTo(30, 0, -70, 75, 100, 150);
ctx.lineTo(100,120)
ctx.stroke();
//to draw a triangle ??
}

I tried look a like
arrow({ x: 10, y: 10 }, { x: 100, y: 140 }, 15); //function called on reload.
function arrow(p1, p2, size) {
var angle = Math.atan2((p2.y - p1.y), (p2.x - p1.x));
var canvas = document.getElementById("canvas");
var ctx = canvas.getContext("2d");
//curve line
ctx.fillStyle = "";
ctx.fillRect(0,0,200,200);
ctx.strokeStyle = 'white';
ctx.beginPath();
ctx.lineWidth=3;
ctx.moveTo(40,20);
ctx.bezierCurveTo(30,40, -0,110, 100, 149.5);
ctx.moveTo(100,150.6);
ctx.lineTo(82,133);
ctx.stroke();
ctx.moveTo(100,149.7);
ctx.lineTo(76,146);
ctx.stroke();
//to draw a triangle ??
}
<canvas id = "canvas" width = "150px" height = "300px"></canvas>

You need some mathematics for this. This javascript method will draw a simple arrow head at the end of a line using canvas. It doesn't matter from which angle you come into the "arrow head".
//..come to the end of the line at some point
ctx.lineTo(tox, toy);
//draw the arrow head
ctx.lineTo(tox - headlen * Math.cos(angle + Math.PI / 5), toy - headlen * Math.sin(angle + Math.PI / 5));
ctx.moveTo(tox, toy);
ctx.lineTo(tox - headlen * Math.cos(angle - Math.PI / 5), toy - headlen * Math.sin(angle - Math.PI / 5));

smoother lineWidth changes in canvas lineTo

so i'm trying to create a drawing tool in HTML5 canvas where the weight of the stroke increases the faster you move the mouse and decreases the slower you move. I'm using ctx.lineTo() but on my first attempt noticed that if i move too quickly the change in thickness is registered as obvious square increments ( rather than a smooth increase in weight )
so i changed the ctx.lineJoin and ctx.lineCap to "round" and it got a little better
but this is still not as smooth as i'd like. i'm shooting for something like this
any advice on how to make the change in weight a bit smoother would be great! here's a working demo: http://jsfiddle.net/0fhag522/1/
and here' a preview of my "dot" object ( the pen ) and my draw function:
var dot = {
start: false,
weight: 1,
open: function(x,y){
ctx.lineJoin = "round";
ctx.lineCap = "round";
ctx.beginPath();
ctx.moveTo(x,y);
},
connect: function(x,y){
ctx.lineWidth = this.weight;
ctx.lineTo(x,y);
ctx.stroke();
ctx.closePath();
ctx.beginPath();
ctx.moveTo(x,y);
},
close: function(){
ctx.closePath();
}
}
function draw(){
if(down){
if(!dot.start){
dot.close();
prevx = mx; prevy = my;
dot.open(mx,my);
dot.start=true;
}
else {
var dx = (prevx>mx) ? prevx-mx : mx-prevx;
var dy = (prevy>my) ? prevy-my : my-prevy;
dot.weight = Math.abs(dx-dy)/2;
dot.connect( mx,my );
prevx = mx; prevy = my;
}
}
}

Here is a simple function to create growing lines with a round line cap:
/*
* this function returns a Path2D object
* the path represents a growing line between two given points
*/
function createGrowingLine (x1, y1, x2, y2, startWidth, endWidth) {
// calculate direction vector of point 1 and 2
const directionVectorX = x2 - x1,
directionVectorY = y2 - y1;
// calculate angle of perpendicular vector
const perpendicularVectorAngle = Math.atan2(directionVectorY, directionVectorX) + Math.PI/2;
// construct shape
const path = new Path2D();
path.arc(x1, y1, startWidth/2, perpendicularVectorAngle, perpendicularVectorAngle + Math.PI);
path.arc(x2, y2, endWidth/2, perpendicularVectorAngle + Math.PI, perpendicularVectorAngle);
path.closePath();
return path;
}
const ctx = myCanvas.getContext('2d');
// create a growing line between P1(10, 10) and P2(250, 100)
// with a start line width of 10 and an end line width of 50
let line1 = createGrowingLine(10, 10, 250, 100, 10, 50);
ctx.fillStyle = 'green';
// draw growing line
ctx.fill(line1);
<canvas width="300" height="150" id="myCanvas"></canvas>
Explanation:
The function createGrowingLine constructs a shape between two given points by:
calculating the direction vector of the two points
calculating the angle in radians of the perpendicular vector
creating a semi circle path from the calculated angle to the calculated angle + 180 degree with the center and radius of the start point
creating another semi circle path from the calculated angle + 180 degree to the calculated angle with the center and radius of the end point
closing the path by connecting the start point of the first circle with the end point of the second circle
In case you do not want to have the rounded line cap use the following function:
/*
* this function returns a Path2D object
* the path represents a growing line between two given points
*/
function createGrowingLine (x1, y1, x2, y2, startWidth, endWidth) {
const startRadius = startWidth/2;
const endRadius = endWidth/2;
// calculate direction vector of point 1 and 2
let directionVectorX = x2 - x1,
directionVectorY = y2 - y1;
// calculate vector length
const directionVectorLength = Math.hypot(directionVectorX, directionVectorY);
// normalize direction vector (and therefore also the perpendicular vector)
directionVectorX = 1/directionVectorLength * directionVectorX;
directionVectorY = 1/directionVectorLength * directionVectorY;
// construct perpendicular vector
const perpendicularVectorX = -directionVectorY,
perpendicularVectorY = directionVectorX;
// construct shape
const path = new Path2D();
path.moveTo(x1 + perpendicularVectorX * startRadius, y1 + perpendicularVectorY * startRadius);
path.lineTo(x1 - perpendicularVectorX * startRadius, y1 - perpendicularVectorY * startRadius);
path.lineTo(x2 - perpendicularVectorX * endRadius, y2 - perpendicularVectorY * endRadius);
path.lineTo(x2 + perpendicularVectorX * endRadius, y2 + perpendicularVectorY * endRadius);
path.closePath();
return path;
}
const ctx = myCanvas.getContext('2d');
// create a growing line between P1(10, 10) and P2(250, 100)
// with a start line width of 10 and an end line width of 50
let line1 = createGrowingLine(10, 10, 250, 100, 10, 50);
ctx.fillStyle = 'green';
// draw growing line
ctx.fill(line1);
<canvas width="300" height="150" id="myCanvas"></canvas>

Since canvas does not have a variable width line you must draw closed paths between your line points.
However, this leaves a visible butt-joint.
To smooth the butt-joint, you can draw a circle at each joint.
Here is example code and a Demo:
var canvas = document.getElementById("canvas");
var ctx = canvas.getContext("2d");
var cw = canvas.width;
var ch = canvas.height;
var $canvas = $("#canvas");
var canvasOffset = $canvas.offset();
var offsetX = canvasOffset.left;
var offsetY = canvasOffset.top;
var scrollX = $canvas.scrollLeft();
var scrollY = $canvas.scrollTop();
var isDown = false;
var startX;
var startY;
var PI = Math.PI;
var halfPI = PI / 2;
var points = [];
$("#canvas").mousedown(function(e) {
handleMouseDown(e);
});
function handleMouseDown(e) {
e.preventDefault();
e.stopPropagation();
mx = parseInt(e.clientX - offsetX);
my = parseInt(e.clientY - offsetY);
var pointsLength = points.length;
if (pointsLength == 0) {
points.push({
x: mx,
y: my,
width: Math.random() * 5 + 2
});
} else {
var p0 = points[pointsLength - 1];
var p1 = {
x: mx,
y: my,
width: Math.random() * 5 + 2
};
addAngle(p0, p1);
p0.angle = p1.angle;
addEndcap(p0);
addEndcap(p1);
points.push(p1);
extendLine(p0, p1);
}
}
function addAngle(p0, p1) {
var dx = p1.x - p0.x;
var dy = p1.y - p0.y;
p1.angle = Math.atan2(dy, dx);
}
function addEndcap(p) {
p.x0 = p.x + p.width * Math.cos(p.angle - halfPI);
p.y0 = p.y + p.width * Math.sin(p.angle - halfPI);
p.x1 = p.x + p.width * Math.cos(p.angle + halfPI);
p.y1 = p.y + p.width * Math.sin(p.angle + halfPI);
}
function extendLine(p0, p1) {
ctx.beginPath();
ctx.moveTo(p0.x0, p0.y0);
ctx.lineTo(p0.x1, p0.y1);
ctx.lineTo(p1.x1, p1.y1);
ctx.lineTo(p1.x0, p1.y0);
ctx.closePath();
ctx.fillStyle = 'blue';
ctx.fill();
// draw a circle to cover the butt-joint
ctx.beginPath();
ctx.moveTo(p1.x, p1.y);
ctx.arc(p1.x, p1.y, p1.width, 0, Math.PI * 2);
ctx.closePath();
ctx.fill();
}
body{ background-color: ivory; }
#canvas{border:1px solid red;}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<h4>Click to add line segments.</h4>
<canvas id="canvas" width=300 height=300></canvas>