How can I draw arc's in angles of an arbitrary triangle? - javascript

I have realized a javascript program, which can draw an arbitrary triangle, and calculate the angles and sides length.
Here is a program, which I try to realize: https://www.mathsisfun.com/proof180deg.html
Sadly I can't draw the arc's in angles of triangle!
Maybe by means of the HTML canvas arc() Method will be realized. E.g. like:
ctx.arc(x, y, 50, start , end);
The x-y position is known. I'm looking for "start" and "end" of angles.
Thanks in advance.

Math.atan2
You can use Math.atan2 to get the direction of a line.
for example
// line from x1,y1 to x2,y2
var nx1 = x2 - x1;
var ny1 = y2 - y1;
var angle = Math.atan2(ny1,nx1);
So the you get the angle of the two lines from a corner. The angles are in the range -Math.PI to Math.PI so you need to move the first angle ahead of the second if it is lower or it will take the long way around.
There is also the problem of the triangle orientation, it can be clockwise or anticlockwise. If the wrong way the angles will be on the outside. You can use the cross product of the two lines to find the directio. If the wrong way then just swap the two angles.
Demo function
Use the mouse to move one of the points.
const ctx = canvas.getContext("2d");
// 2 lines start at x1,y1, then join at x2,y2, and then out to x3,y3
function drawLinesAndAngle(x1,y1,x2,y2,x3,y3){
// get vectors from x2,y2 to the other points
var nx1 = x1 - x2;
var ny1 = y1 - y2;
var nx2 = x3 - x2;
var ny2 = y3 - y2;
var lineAngle1 = Math.atan2(ny1,nx1);
var lineAngle2 = Math.atan2(ny2,nx2);
// use cross product to find correct direction.
if(nx1 * ny2 - ny1 * nx2 < 0){ // wrong way around swap direction
const t = lineAngle2;
lineAngle2 = lineAngle1;
lineAngle1 = t;
}
// if angle 1 is behind then move ahead
if(lineAngle1 < lineAngle2){
lineAngle1 += Math.PI * 2;
}
// render the arc
ctx.fillStyle = "red";
ctx.beginPath();
ctx.moveTo(x2,y2);
ctx.arc(x2,y2,35,lineAngle1, lineAngle2);
ctx.fill();
// render outside arc
ctx.fillStyle = "blue";
ctx.beginPath();
ctx.moveTo(x2,y2);
ctx.arc(x2,y2,7,lineAngle2, lineAngle1);
ctx.fill();
// get the mid point
const mx = -Math.cos((lineAngle1 + lineAngle2) / 2) * 50 + x2;
const my = -Math.sin((lineAngle1 + lineAngle2) / 2) * 50 + y2;
// render the angle
ctx.fillStyle = "black";
ctx.font = "16px arial";
ctx.textAlign = "center";
ctx.textBaseline = "middle";
ctx.fillText(
(360-(lineAngle1 - lineAngle2) * (180 /Math.PI)).toFixed(0), // convert to deg
mx,
my,
)
}
// short cut vars
var w = canvas.width;
var h = canvas.height;
var cw = w / 2; // center
var ch = h / 2;
// main update function
function update(timer){
ctx.setTransform(1,0,0,1,0,0); // reset transform
ctx.globalAlpha = 1; // reset alpha
if(w !== innerWidth || h !== innerHeight){
cw = (w = canvas.width = innerWidth) / 2;
ch = (h = canvas.height = innerHeight) / 2;
}else{
ctx.clearRect(0,0,w,h);
}
// start line
const x = Math.cos(timer / 5000) * Math.min(cw,ch) * 0.95 + cw;
const y = Math.sin(timer / 5000) * Math.min(cw,ch) * 0.95 + ch;
// fill triangle
ctx.fillStyle = "#FD8";
ctx.beginPath();
ctx.lineTo(x,y);
ctx.lineTo(cw,ch);
ctx.lineTo(mouse.x,mouse.y);
ctx.closePath();
ctx.fill();
drawLinesAndAngle(x,y,cw,ch,mouse.x,mouse.y);
drawLinesAndAngle(cw,ch,mouse.x,mouse.y,x,y);
drawLinesAndAngle(mouse.x,mouse.y,x,y,cw,ch);
// render the lines
ctx.strokeStyle = "black";
ctx.lineWidth = 3;
ctx.lineJoin = "round";
ctx.beginPath();
ctx.lineTo(x,y);
ctx.lineTo(cw,ch);
ctx.lineTo(mouse.x,mouse.y);
ctx.closePath();
ctx.stroke();
requestAnimationFrame(update);
}
requestAnimationFrame(update);
const mouse = {x : 0, y : 0, button : false, drag : false, dragStart : false, dragEnd : false, dragStartX : 0, dragStartY : 0}
function mouseEvents(e){
mouse.x = e.pageX;
mouse.y = e.pageY;
mouse.button = e.type === "mousedown" ? true : e.type === "mouseup" ? false : mouse.button;
}
["down","up","move"].forEach(name => document.addEventListener("mouse"+name,mouseEvents));
canvas { position : absolute; top : 0px; left : 0px; }
<canvas id="canvas"></canvas>

Related

Why does this function that checks if a line intersects a circle sometimes gives false positives?

I found this function on Stackoverflow some time ago and only now am I realizing that it sometimes seems to give false-positives. Here it is:
function lineIntersectsCircle(p1X, p1Y, p2X, p2Y, cX, cY, r) {
let xDelta = p1X - p2X;
let yDelta = p1Y - p2Y;
let distance = Math.sqrt(xDelta * xDelta + yDelta * yDelta)
let a = (cY - p1Y) * (p2X - p1X);
let b = (cX - p1X) * (p2Y - p1Y);
return Math.abs(a - b) / distance <= r;
}
Here's a full code demo reproduction showing the issue here:
let ctx = document.querySelector("canvas").getContext("2d");
function drawCircle(xCenter, yCenter, radius) {
ctx.beginPath();
ctx.arc(xCenter, yCenter, radius, 0, 2 * Math.PI);
ctx.fill();
}
function drawLine(x1, y1, x2, y2) {
ctx.beginPath();
ctx.moveTo(x1, y1);
ctx.lineTo(x2, y2);
ctx.stroke();
}
function lineIntersectsCircle(p1X, p1Y, p2X, p2Y, cX, cY, r) {
let xDelta = p1X - p2X;
let yDelta = p1Y - p2Y;
let distance = Math.sqrt(xDelta * xDelta + yDelta * yDelta)
let a = (cY - p1Y) * (p2X - p1X);
let b = (cX - p1X) * (p2Y - p1Y);
return Math.abs(a - b) / distance <= r;
}
let circleX = 250;
let circleY = 250;
let circleR = 50;
let lineX1 = 50;
let lineY1 = 350;
let lineX2 = 185;
let lineY2 = 250;
draw = () => {
ctx.fillStyle = "#b2c7ef";
ctx.fillRect(0, 0, 800, 800);
ctx.fillStyle = "#ffffff";
drawCircle(circleX, circleY, circleR);
drawLine(lineX1, lineY1, lineX2, lineY2);
}
console.log(lineIntersectsCircle(lineX1, lineY1, lineX2, lineY2, circleX, circleY, circleR))
draw();
canvas { display: flex; margin: 0 auto; }
<canvas width="400" height="400"></canvas>
As you can see, the line doesn't intersect the circle, yet it console logs a true statement. Does anyone know why this would be? If this function is incorrect, what is the proper function for only determining if a line and circle intersect? I do not need the intersection points, only whether or not they intersect at all.
Mathematically, a line is different from a line segment; a line is infinitely long.
You use the formula for finding the distance between a point (centre of the circle) and a line. While the formula uses a line defined by two points, it is not terminated by those points, so that doesn't apply to a line segment.
If you extend that line segment out, you can see that it intersects with the circle.
Three steps to determine whether a line segment intersects with a circle:
transform the coordinates to make (xCenter, yCenter) of the circle as the zero point, and switch the X,Y coordinates (because the Y axis of the canvas points downward, which makes linear functions incorrect);
find the point nearest to the circle in the (infinite) line, if the point is not inside the line segment, get one of the end points which is closer to the point;
if the point is inside the circle, and the 2 end points are not both inside the circle, there is at least one intersection.
let ctx = document.querySelector("canvas").getContext("2d");
function drawCircle(xCenter, yCenter, radius) {
ctx.beginPath();
ctx.arc(xCenter, yCenter, radius, 0, 2 * Math.PI);
ctx.fill();
}
function drawLine(x1, y1, x2, y2) {
ctx.beginPath();
ctx.moveTo(x1, y1);
ctx.lineTo(x2, y2);
ctx.stroke();
}
function lineIntersectsCircle(p1X, p1Y, p2X, p2Y, cX, cY, r) {
// to calculate the new position based on the new zero point at the circle center,
//where X, Y coordinates have to be switched because in Canvas Y coordinate increases downwards
let newp1y = p1X - cX, newp1x = p1Y - cY, newp2y = p2X - cX, newp2x = p2Y - cY;
// when the 2 end points are all inside the circle, there is no intersection
if((newp1x*newp1x + newp1y*newp1y < r*r) && (newp2x*newp2x + newp2y*newp2y < r*r)) {
return false;
}
// slope of the line and the slope of the perpendicular line from the circle center
let slopeL = (newp2y - newp1y) / (newp2x - newp1x), slopeC;
if(slopeL != 0){
slopeC = -1/slopeL;
}
else{
slopeC = 65535; // for a vertical line, this slope number is big enough
}
// calculate the nearest point at the straight line from the circle center
let closeX = (newp1y - slopeL*newp1x)/(slopeC - slopeL);
let closeY = closeX * slopeC;
// in this condition, the nearest point is not inside the line segment, so the end point
// which is closer to this point will be picked as the real nearest point to the circle center
if((closeX - newp1x)*(closeX - newp2x) >=0 && (closeY - newp1y)*(closeY - newp2y) >=0){
if((closeX - newp1x)*(closeX - newp2x) > 0){
if(Math.abs(closeX - newp1x) > Math.abs(closeX - newp2x)){
closeX = newp2x;
closeY = newp2y;
}
else{
closeX = newp1x;
closeY = newp1y;
}
}
else {
if(Math.abs(closeY - newp1y) > Math.abs(closeY - newp2y)){
closeX = newp2x;
closeY = newp2y;
}
else{
closeX = newp1x;
closeY = newp1y;
}
}
}
//check if the picked nearest point is inside the circle
return (closeX*closeX + closeY*closeY) < r*r;
}
let circleX = 250;
let circleY = 250;
let circleR = 50;
let lineX1 = 50;
let lineY1 = 350;
let lineX2 = 185;
let lineY2 = 250;
draw = () => {
ctx.fillStyle = "#b2c7ef";
ctx.fillRect(0, 0, 800, 800);
ctx.fillStyle = "#ffffff";
drawCircle(circleX, circleY, circleR);
drawLine(lineX1, lineY1, lineX2, lineY2);
}
console.log(lineIntersectsCircle(lineX1, lineY1, lineX2, lineY2, circleX, circleY, circleR))
draw();
canvas { display: flex; margin: 0 auto; }
<canvas width="400" height="400"></canvas>

Using a line to divide a canvas into two new canvases

I'm looking to allow users to slice an existing canvas into two canvases in whatever direction they would like.
I know how to allow the user to draw a line and I also know how to copy the image data of one canvas onto two new ones, but how can I copy only the relevant color data on either side of the user-drawn line to its respective canvas?
For example, in the following demo I'd like the canvas to be "cut" where the white line is:
const canvas = document.querySelector("canvas"),
ctx = canvas.getContext("2d");
const red = "rgb(104, 0, 0)",
lb = "rgb(126, 139, 185)",
db = "rgb(20, 64, 87)";
var width,
height,
centerX,
centerY,
smallerDimen;
var canvasData,
inCoords;
function sizeCanvas() {
width = canvas.width = window.innerWidth;
height = canvas.height = window.innerHeight;
centerX = width / 2;
centerY = height / 2;
smallerDimen = Math.min(width, height);
}
function drawNormalState() {
// Color the bg
ctx.fillStyle = db;
ctx.fillRect(0, 0, width, height);
// Color the circle
ctx.arc(centerX, centerY, smallerDimen / 4, 0, Math.PI * 2, true);
ctx.fillStyle = red;
ctx.fill();
ctx.lineWidth = 3;
ctx.strokeStyle = lb;
ctx.stroke();
// Color the triangle
ctx.beginPath();
ctx.moveTo(centerX + smallerDimen / 17, centerY - smallerDimen / 10);
ctx.lineTo(centerX + smallerDimen / 17, centerY + smallerDimen / 10);
ctx.lineTo(centerX - smallerDimen / 9, centerY);
ctx.fillStyle = lb;
ctx.fill();
ctx.closePath();
screenshot();
ctx.beginPath();
ctx.strokeStyle = "rgb(255, 255, 255)";
ctx.moveTo(width - 20, 0);
ctx.lineTo(20, height);
ctx.stroke();
ctx.closePath();
}
function screenshot() {
canvasData = ctx.getImageData(0, 0, width, height).data;
}
function init() {
sizeCanvas();
drawNormalState();
}
init();
body {
margin: 0;
}
<canvas></canvas>
TL;DR the demo.
The best way I've found to do this is to 1) calculate "end points" for the line at the edge of (or outside) the canvas' bounds, 2) create two* polygons using the end points of the line generated in step 1 and the canvas' four corners, and 3) divide up the original canvas' image data into two new canvases based on the polygons we create.
* We actually create one, but the "second" is the remaining part of the original canvas.
1) Calculate the end points
You can use a very cheap algorithm to calculate some end points given a start coordinate, x and y difference (i.e. slope), and the bounds for the canvas. I used the following:
function getEndPoints(startX, startY, xDiff, yDiff, maxX, maxY) {
let currX = startX,
currY = startY;
while(currX > 0 && currY > 0 && currX < maxX && currY < maxY) {
currX += xDiff;
currY += yDiff;
}
let points = {
firstPoint: [currX, currY]
};
currX = startX;
currY = startY;
while(currX > 0 && currY > 0 && currX < maxX && currY < maxY) {
currX -= xDiff;
currY -= yDiff;
}
points.secondPoint = [currX, currY];
return points;
}
where
let xDiff = firstPoint.x - secondPoint.x,
yDiff = firstPoint.y - secondPoint.y;
2) Create two polygons
To create the polygons, I make use of Paul Bourke's Javascript line intersection:
function intersect(point1, point2, point3, point4) {
let x1 = point1[0],
y1 = point1[1],
x2 = point2[0],
y2 = point2[1],
x3 = point3[0],
y3 = point3[1],
x4 = point4[0],
y4 = point4[1];
// Check if none of the lines are of length 0
if((x1 === x2 && y1 === y2) || (x3 === x4 && y3 === y4)) {
return false;
}
let denominator = ((y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1));
// Lines are parallel
if(denominator === 0) {
return false;;
}
let ua = ((x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3)) / denominator;
let ub = ((x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3)) / denominator;
// is the intersection along the segments
if(ua < 0 || ua > 1 || ub < 0 || ub > 1) {
return false;
}
// Return a object with the x and y coordinates of the intersection
let x = x1 + ua * (x2 - x1);
let y = y1 + ua * (y2 - y1);
return [x, y];
}
Along with some of my own logic:
let origin = [0, 0],
xBound = [width, 0],
xyBound = [width, height],
yBound = [0, height];
let polygon = [origin];
// Work clockwise from 0,0, adding points to our polygon as appropriate
// Check intersect with top bound
let topIntersect = intersect(origin, xBound, points.firstPoint, points.secondPoint);
if(topIntersect) {
polygon.push(topIntersect);
}
if(!topIntersect) {
polygon.push(xBound);
}
// Check intersect with right
let rightIntersect = intersect(xBound, xyBound, points.firstPoint, points.secondPoint);
if(rightIntersect) {
polygon.push(rightIntersect);
}
if((!topIntersect && !rightIntersect)
|| (topIntersect && rightIntersect)) {
polygon.push(xyBound);
}
// Check intersect with bottom
let bottomIntersect = intersect(xyBound, yBound, points.firstPoint, points.secondPoint);
if(bottomIntersect) {
polygon.push(bottomIntersect);
}
if((topIntersect && bottomIntersect)
|| (topIntersect && rightIntersect)) {
polygon.push(yBound);
}
// Check intersect with left
let leftIntersect = intersect(yBound, origin, points.firstPoint, points.secondPoint);
if(leftIntersect) {
polygon.push(leftIntersect);
}
3) Divide up the original canvas' image data
Now that we have our polygon, all that's left is putting this data into new canvases. The easiest way to do this is to use canvas' ctx.drawImage and ctx.globalCompositeOperation.
// Use or create 2 new canvases with the split original canvas
let newCanvas1 = document.querySelector("#newCanvas1");
if(newCanvas1 == null) {
newCanvas1 = document.createElement("canvas");
newCanvas1.id = "newCanvas1";
newCanvas1.width = width;
newCanvas1.height = height;
document.body.appendChild(newCanvas1);
}
let newCtx1 = newCanvas1.getContext("2d");
newCtx1.globalCompositeOperation = 'source-over';
newCtx1.drawImage(canvas, 0, 0);
newCtx1.globalCompositeOperation = 'destination-in';
newCtx1.beginPath();
newCtx1.moveTo(polygon[0][0], polygon[0][1]);
for(let item = 1; item < polygon.length; item++) {
newCtx1.lineTo(polygon[item][0], polygon[item][1]);
}
newCtx1.closePath();
newCtx1.fill();
let newCanvas2 = document.querySelector("#newCanvas2");
if(newCanvas2 == null) {
newCanvas2 = document.createElement("canvas");
newCanvas2.id = "newCanvas2";
newCanvas2.width = width;
newCanvas2.height = height;
document.body.appendChild(newCanvas2);
}
let newCtx2 = newCanvas2.getContext("2d");
newCtx2.globalCompositeOperation = 'source-over';
newCtx2.drawImage(canvas, 0, 0);
newCtx2.globalCompositeOperation = 'destination-out';
newCtx2.beginPath();
newCtx2.moveTo(polygon[0][0], polygon[0][1]);
for(let item = 1; item < polygon.length; item++) {
newCtx2.lineTo(polygon[item][0], polygon[item][1]);
}
newCtx2.closePath();
newCtx2.fill();
All of that put together gives us this demo!

angled direction sine wave

I have been able to draw the sin wave in horizontal direction as shows the image(image link: https://i.stack.imgur.com/RTpDY.png) and in the vertical direction.
now I need to draw it in an angled 45° direction
could any one help me pleese!
the script code:
var c =document.getElementById("c");
var ctx=c.getContext('2d');
var x=0,y=250,vx=0.05,vy=0.05,a=1;
for(var i=0; i<501;i++){
x += a;
y = Math.floor(500 * (0.5 - 0.15 * Math.sin(vy)));
vy += vx;
// this.ctx.clearRect(0, 0, 500,500);
this.ctx.beginPath();
this.ctx.arc(x, y, 2, 0, Math.PI * 2, true);
this.ctx.closePath();
this.ctx.fillStyle = 'red';
this.ctx.fill();
console.log("x:"+x+"y:"+y+"vy:"+vy);
}
Draw a sin wave along a line
The following will draw a sin wave aligned to a line. The line can be in any direction.
The standard settings
The wave length will be in pixels. For a sin wave to make a complete cycle you need to rotate its input angle by Math.PI * 2 so you will need to convert it to value matching pixel wavelength.
const waveLen = 400; // pixels
The phase of the sin wave is at what part of the wave it starts at, as the wave length is in pixels, the phase is also in pixels, and represents the distance along the wave that denotes the starting angle.
const phase = 200; // mid way
The amplitude of the wave is how far above and below the center line the wave max and min points are. This is again in pixels
const amplitude = 100;
A wave also has an offset, though in this case not really important I will added it as well. In pixels as well
const offset = 0;
The line that marks the center of the wave has a start and end coordinate
const x1 = 20;
const y1 = 20;
const x2 = 400;
const y2 = 400;
And some context settings
const lineWidth = 3;
const lineCap = "round";
const lineJoin = "round";
const strokeStyle = "blue";
Example code
And so to the code that does the rendering, I have expanded the code with comments so you can read what is going on. Below that is a more useable version.
const ctx = canvas.getContext("2d");
canvas.width = innerWidth;
canvas.height = innerHeight;
window.addEventListener("resize", () => {
canvas.width = innerWidth;
canvas.height = innerHeight;
y2 = x2 = innerWidth; // at 45 deg
drawSinWave();
})
const waveLen = 120; // pixels
const phase = 50; // mid way
const amplitude = 25;
const offset = 0;
const x1 = 20;
const y1 = 20;
var x2 = 400; // as vars to let it change to fit resize
var y2 = 400;
function drawSinWave() {
ctx.lineWidth = 3;
ctx.lineCap = "round";
ctx.lineJoin = "round";
ctx.strokeStyle = "blue";
// get the vector form of the line
const vx = x2 - x1;
const vy = y2 - y1;
// Get the length of the line in pixels
const dist = Math.sqrt(vx * vx + vy * vy);
// Make the vector one pixel long to move along the line
const px = vx / dist;
const py = vy / dist;
// We also need a vector to move out from the line (at 90 deg to the ine)
// So rotate the pixel vector 90deg CW
const ax = -py; // a for amplitude vector
const ay = px;
// Begin the path
ctx.beginPath();
// Now loop along every pixel in the line
// We go past the end a bit as floating point errors can cause it to end
// a pixels too early
for (var i = 0; i <= dist + 0.5; i++) {
// fix i if past end
if (i > dist) {
i = dist
} // Carefull dont mess with this ot it will block the page
// Use the distance to get the current angle of the wave
// based on the wave length and phase
const ang = ((i + phase) / waveLen) * Math.PI * 2;
// and at this position get sin
const val = Math.sin(ang);
// Scale to match the amplitude and move to offset
// as the distance from the center of the line
const amp = val * amplitude + offset;
// Get line ceneter at distance i using the pixel vector
var x = x1 + px * i;
var y = y1 + py * i;
// Use the amp vector to move away from the line at 90 degree
x += ax * amp;
y += ay * amp;
// Now add the point
ctx.lineTo(x, y);
}
ctx.stroke();
}
drawSinWave();
canvas {
position: absolute;
top: 0px;
left: 0px;
}
<canvas id=canvas width=4 00 height=4 00></canvas>
As a more useable function with a few shortcuts
const ctx = canvas.getContext("2d");
canvas.width = innerWidth;
canvas.height = innerHeight;
window.addEventListener("resize", () => {
canvas.width = innerWidth;
canvas.height = innerHeight;
waveExample.y2 = waveExample.x2 = innerWidth; // at 45 deg
drawSinWave(waveExample);
})
const waveExample = {
waveLen: 100, // pixels
phase: 50, // mid way
amplitude: 35,
offset: 0,
x1: 20,
y1: 20,
x2: 400, // as vars to let it change to fit resize
y2: 400,
lineWidth : 5,
lineCap : "round",
lineJoin : "round",
strokeStyle : "Red",
}
function drawSinWave(wave) {
ctx.lineWidth = wave.lineWidth;
ctx.lineCap = wave.lineCap;
ctx.lineJoin = wave.lineJoin;
ctx.strokeStyle = wave.strokeStyle;
var vx = wave.x2 - wave.x1;
var vy = wave.y2 - wave.y1;
const dist = Math.sqrt(vx * vx + vy * vy);
vx /= dist;
vy /= dist;
ctx.beginPath();
for (var i = 0; i <= dist + 0.5; i++) {
if (i > dist) { i = dist }
const pos = Math.sin(((i + wave.phase) / wave.waveLen) * Math.PI * 2) * wave.amplitude + wave.offset;
ctx.lineTo(
wave.x1 + vx * i - vy * pos,
wave.y1 + vy * i + vx * pos
);
}
ctx.stroke();
}
drawSinWave(waveExample);
canvas {
position: absolute;
top: 0px;
left: 0px;
}
<canvas id=canvas width=4 00 height=4 00></canvas>
The easiest solution is rotating the canvas:
ctx.rotate(45*Math.PI/180);
Although I'm presuming you need the canvas orientation fixed and you need to mathematically alter the way you draw? In which case here's a whole bunch of math about how to plot sine waves at a rotated counterclockwise:
http://mathman.biz/html/rotatingsine.html

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

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>

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