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;
...
Need to create simple line of sight from point. Length of this line would be adapt to the size of canvas. If line directed to any object (circle, rectangle etc) it must be interrupted after this. I don't know exactly how to describe this, but behavior should be something like this. It's like laser aim in video-games.
Demo jsfiddle. Target line has red color. I think that line must have dynamic length depending on where I will direct it.
var canvas = document.querySelector("canvas");
canvas.width = 500;
canvas.height = 300;
var ctx = canvas.getContext("2d"),
line = {
x1: 190, y1: 170,
x2: 0, y2: 0,
x3: 0, y3: 0
};
var length = 100;
var circle = {
x: 400,
y: 70
};
window.onmousemove = function(e) {
//get correct mouse pos
var rect = ctx.canvas.getBoundingClientRect(),
x = e.clientX - rect.left,
y = e.clientY - rect.top;
// calc line angle
var dx = x - line.x1,
dy = y - line.y1,
angle = Math.atan2(dy, dx);
//Then render the line using 100 pixel radius:
line.x2 = line.x1 - length * Math.cos(angle);
line.y2 = line.y1 - length * Math.sin(angle);
line.x3 = line.x1 + canvas.width * Math.cos(angle);
line.y3 = line.y1 + canvas.width * Math.sin(angle);
// render
ctx.clearRect(0, 0, canvas.width, canvas.height);
ctx.beginPath();
ctx.moveTo(line.x1, line.y1);
ctx.lineTo(line.x2, line.y2);
ctx.strokeStyle = '#333';
ctx.stroke();
ctx.beginPath();
ctx.moveTo(line.x1, line.y1);
ctx.lineTo(line.x3, line.y3);
ctx.strokeStyle = 'red';
ctx.stroke();
ctx.beginPath();
ctx.arc(circle.x, circle.y, 20, 0, Math.PI * 2, true);
ctx.fillStyle = '#333';
ctx.fill();
}
<canvas></canvas>
Ray casting
The given answer is a good answer but this problem is better suited to a ray casting like solution where we are only interested in the distance to an intercept rather than the actual point of interception. We only need one point per cast ray so not calculating points will reduce the math and hence the CPU load giving more rays and objects per second.
A ray is a point that defines the start and a normalised vector that represents the direction of the ray. Because the ray uses a normalised vector that is a unit length many calculations are simplified because 1 * anything changes nothing.
Also the problem is about looking for the closest intercept so the intercept functions return a distance from the ray's origin. If no intercept is found then Infinity is returned to allow a valid distance comparison to be made. Every number is less than Infinity.
A nice feature of JavaScript is that it allows divide by zero and returns Infinity if that happens, this further reduces the complexity of the solution. Also if the intercept finds a negative intercept that means the object is behind that raycast origin and thus will return infinity as well.
So first let's define our objects by creating functions to make them. They are all ad hoc objects.
The Ray
// Ad Hoc method for ray to set the direction vector
var updateRayDir = function(dir){
this.nx = Math.cos(dir);
this.ny = Math.sin(dir);
return this;
}
// Creates a ray objects from
// x,y start location
// dir the direction in radians
// len the rays length
var createRay = function(x,y,dir,len){
return ({
x : x,
y : y,
len : len,
setDir : updateRayDir, // add function to set direction
}).setDir(dir);
}
A circle
// returns a circle object
// x,y is the center
// radius is the you know what..
// Note r2 is radius squared if you change the radius remember to set r2 as well
var createCircle = function(x , y, radius){
return {
x : x,
y : y,
rayDist : rayDist2Circle, // add ray cast method
radius : radius,
r2 : radius * radius, // ray caster needs square of radius may as well do it here
};
}
A wall
Note I changed the wall code in the demo
// Ad Hoc function to change the wall position
// x1,y1 are the start coords
// x2,y2 are the end coords
changeWallPosition = function(x1, y1, x2, y2){
this.x = x1;
this.y = y1;
this.vx = x2 - x1;
this.vy = y2 - y1;
this.len = Math.hypot(this.vx,this.vy);
this.nx = this.vx / this.len;
this.ny = this.vy / this.len;
return this;
}
// returns a wall object
// x1,y1 are the star coords
// x2,y2 are the end coords
var createWall = function(x1, y1, x2, y2){
return({
x : x1, y : y1,
vx : x2 - x1,
vy : y2 - y1,
rayDist : rayDist2Wall, // add ray cast method
setPos : changeWallPosition,
}).setPos(x1, y1, x2, y2);
}
So those are the objects, they can be static or moving through the circle should have a setRadius function because I have added a property that holds the square of the radius but I will leave that up to you if you use that code.
Now the intercept functions.
Ray Intercepts
The stuff that matters. In the demo these functions are bound to the objects so that the ray casting code need not have to know what type of object it is checking.
Distance to circle.
// Self evident
// returns a distance or infinity if no valid solution
var rayDist2Circle = function(ray){
var vcx, vcy, v;
vcx = ray.x - this.x; // vector from ray to circle
vcy = ray.y - this.y;
v = -2 * (vcx * ray.nx + vcy * ray.ny);
v -= Math.sqrt(v * v - 4 * (vcx * vcx + vcy * vcy - this.r2)); // this.r2 is the radius squared
// If there is no solution then Math.sqrt returns NaN we should return Infinity
// Not interested in intercepts in the negative direction so return infinity
return isNaN(v) || v < 0 ? Infinity : v / 2;
}
Distance to wall
// returns the distance to the wall
// if no valid solution then return Infinity
var rayDist2Wall = function(ray){
var x,y,u;
rWCross = ray.nx * this.ny - ray.ny * this.nx;
if(!rWCross) { return Infinity; } // Not really needed.
x = ray.x - this.x; // vector from ray to wall start
y = ray.y - this.y;
u = (ray.nx * y - ray.ny * x) / rWCross; // unit distance along normalised wall
// does the ray hit the wall segment
if(u < 0 || u > this.len){ return Infinity;} /// no
// as we use the wall normal and ray normal the unit distance is the same as the
u = (this.nx * y - this.ny * x) / rWCross;
return u < 0 ? Infinity : u; // if behind ray return Infinity else the dist
}
That covers the objects. If you need to have a circle that is inside out (you want the inside surface then change the second last line of the circle ray function to v += rather than v -=
The ray casting
Now it is just a matter of iterating all the objects against the ray and keeping the distant to the closest object. Set the ray to that distance and you are done.
// Does a ray cast.
// ray the ray to cast
// objects an array of objects
var castRay = function(ray,objects)
var i,minDist;
minDist = ray.len; // set the min dist to the rays length
i = objects.length; // number of objects to check
while(i > 0){
i -= 1;
minDist = Math.min(objects[i].rayDist(ray),minDist);
}
ray.len = minDist;
}
A demo
And a demo of all the above in action. THere are some minor changes (drawing). The important stuff is the two intercept functions. The demo creates a random scene each time it is resized and cast 16 rays from the mouse position. I can see in your code you know how to get the direction of a line so I made the demo show how to cast multiple rays that you most likely will end up doing
const COLOUR = "BLACK";
const RAY_COLOUR = "RED";
const LINE_WIDTH = 4;
const RAY_LINE_WIDTH = 2;
const OBJ_COUNT = 20; // number of object in the scene;
const NUMBER_RAYS = 16; // number of rays
const RAY_DIR_SPACING = Math.PI / (NUMBER_RAYS / 2);
const RAY_ROTATE_SPEED = Math.PI * 2 / 31000;
if(typeof Math.hypot === "undefined"){ // poly fill for Math.hypot
Math.hypot = function(x, y){
return Math.sqrt(x * x + y * y);
}
}
var ctx, canvas, objects, ray, w, h, mouse, rand, ray, rayMaxLen, screenDiagonal;
// create a canvas and add to the dom
var canvas = document.createElement("canvas");
canvas.width = w = window.innerWidth;
canvas.height = h = window.innerHeight;
canvas.style.position = "absolute";
canvas.style.left = "0px";
canvas.style.top = "0px";
document.body.appendChild(canvas);
// objects to ray cast
objects = [];
// mouse object
mouse = {x :0, y: 0};
//========================================================================
// random helper
rand = function(min, max){
return Math.random() * (max - min) + min;
}
//========================================================================
// Ad Hoc draw line method
// col is the stroke style
// width is the storke width
var drawLine = function(col,width){
ctx.strokeStyle = col;
ctx.lineWidth = width;
ctx.beginPath();
ctx.moveTo(this.x,this.y);
ctx.lineTo(this.x + this.nx * this.len, this.y + this.ny * this.len);
ctx.stroke();
}
//========================================================================
// Ad Hoc draw circle method
// col is the stroke style
// width is the storke width
var drawCircle = function(col,width){
ctx.strokeStyle = col;
ctx.lineWidth = width;
ctx.beginPath();
ctx.arc(this.x , this.y, this.radius, 0 , Math.PI * 2);
ctx.stroke();
}
//========================================================================
// Ad Hoc method for ray to set the direction vector
var updateRayDir = function(dir){
this.nx = Math.cos(dir);
this.ny = Math.sin(dir);
return this;
}
//========================================================================
// Creates a ray objects from
// x,y start location
// dir the direction in radians
// len the rays length
var createRay = function(x,y,dir,len){
return ({
x : x,
y : y,
len : len,
draw : drawLine,
setDir : updateRayDir, // add function to set direction
}).setDir(dir);
}
//========================================================================
// returns a circle object
// x,y is the center
// radius is the you know what..
// Note r2 is radius squared if you change the radius remember to set r2 as well
var createCircle = function(x , y, radius){
return {
x : x,
y : y,
draw : drawCircle, // draw function
rayDist : rayDist2Circle, // add ray cast method
radius : radius,
r2 : radius * radius, // ray caster needs square of radius may as well do it here
};
}
//========================================================================
// Ad Hoc function to change the wall position
// x1,y1 are the start coords
// x2,y2 are the end coords
changeWallPosition = function(x1, y1, len, dir){
this.x = x1;
this.y = y1;
this.len = len;
this.nx = Math.cos(dir);
this.ny = Math.sin(dir);
return this;
}
//========================================================================
// returns a wall object
// x1,y1 are the star coords
// len is the length
// dir is the direction
var createWall = function(x1, y1, len, dir){
return({
x : x1, y : y1,
rayDist : rayDist2Wall, // add ray cast method
draw : drawLine,
setPos : changeWallPosition,
}).setPos(x1, y1, len, dir);
}
//========================================================================
// Self evident
// returns a distance or infinity if no valid solution
var rayDist2Circle = function(ray){
var vcx, vcy, v;
vcx = ray.x - this.x; // vector from ray to circle
vcy = ray.y - this.y;
v = -2 * (vcx * ray.nx + vcy * ray.ny);
v -= Math.sqrt(v * v - 4 * (vcx * vcx + vcy * vcy - this.r2)); // this.r2 is the radius squared
// If there is no solution then Math.sqrt returns NaN we should return Infinity
// Not interested in intercepts in the negative direction so return infinity
return isNaN(v) || v < 0 ? Infinity : v / 2;
}
//========================================================================
// returns the distance to the wall
// if no valid solution then return Infinity
var rayDist2Wall = function(ray){
var x,y,u;
rWCross = ray.nx * this.ny - ray.ny * this.nx;
if(!rWCross) { return Infinity; } // Not really needed.
x = ray.x - this.x; // vector from ray to wall start
y = ray.y - this.y;
u = (ray.nx * y - ray.ny * x) / rWCross; // unit distance along normal of wall
// does the ray hit the wall segment
if(u < 0 || u > this.len){ return Infinity;} /// no
// as we use the wall normal and ray normal the unit distance is the same as the
u = (this.nx * y - this.ny * x) / rWCross;
return u < 0 ? Infinity : u; // if behind ray return Infinity else the dist
}
//========================================================================
// does a ray cast
// ray the ray to cast
// objects an array of objects
var castRay = function(ray,objects){
var i,minDist;
minDist = ray.len; // set the min dist to the rays length
i = objects.length; // number of objects to check
while(i > 0){
i -= 1;
minDist = Math.min(objects[i].rayDist(ray), minDist);
}
ray.len = minDist;
}
//========================================================================
// Draws all objects
// objects an array of objects
var drawObjects = function(objects){
var i = objects.length; // number of objects to check
while(i > 0){
objects[--i].draw(COLOUR, LINE_WIDTH);
}
}
//========================================================================
// called on start and resize
// creats a new scene each time
// fits the canvas to the avalible realestate
function reMakeAll(){
w = canvas.width = window.innerWidth;
h = canvas.height = window.innerHeight;
ctx = canvas.getContext("2d");
screenDiagonal = Math.hypot(window.innerWidth,window.innerHeight);
if(ray === undefined){
ray = createRay(0,0,0,screenDiagonal);
}
objects.length = 0;
var i = OBJ_COUNT;
while( i > 0 ){
if(Math.random() < 0.5){ // half circles half walls
objects.push(createWall(rand(0, w), rand(0, h), rand(screenDiagonal * 0.1, screenDiagonal * 0.2), rand(0, Math.PI * 2)));
}else{
objects.push(createCircle(rand(0, w), rand(0, h), rand(screenDiagonal * 0.02, screenDiagonal * 0.05)));
}
i -= 1;
}
}
//========================================================================
function mouseMoveEvent(event){
mouse.x = event.clientX;
mouse.y = event.clientY;
}
//========================================================================
// updates all that is needed when needed
function updateAll(time){
var i;
ctx.clearRect(0,0,w,h);
ray.x = mouse.x;
ray.y = mouse.y;
drawObjects(objects);
i = 0;
while(i < NUMBER_RAYS){
ray.setDir(i * RAY_DIR_SPACING + time * RAY_ROTATE_SPEED);
ray.len = screenDiagonal;
castRay(ray,objects);
ray.draw(RAY_COLOUR, RAY_LINE_WIDTH);
i ++;
}
requestAnimationFrame(updateAll);
}
// add listeners
window.addEventListener("resize",reMakeAll);
canvas.addEventListener("mousemove",mouseMoveEvent);
// set it all up
reMakeAll();
// start the ball rolling
requestAnimationFrame(updateAll);
An alternative use of above draws a polygon using the end points of the cast rays can be seen at codepen
For this you would need a line to circle intersection algorithm for the balls as well as line to line intersection for the walls.
For the ball you can use this function - I made this to return arrays being empty if no intersection, one point if tangent or two points if secant.
Simply feed it start of line, line of sight end-point as well as the ball's center position and radius. In your case you will probably only need the first point:
function lineIntersectsCircle(x1, y1, x2, y2, cx, cy, r) {
x1 -= cx;
y1 -= cy;
x2 -= cx;
y2 -= cy;
// solve quadrant
var a = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1),
b = 2 * ((x2 - x1) * x1 + (y2 - y1) * y1),
c = x1 * x1 + y1 * y1 - r * r,
d = b * b - 4 * a * c,
dq, p1, p2, t1, t2;
if (d <= 0 || !a) return [];
dq = Math.sqrt(d);
t1 = (-b - dq) / (2 * a);
t2 = (-b + dq) / (2 * a);
// calculate actual intersection points
if (t1 >= 0 && t1 <= 1)
p1 = {
x: x1 + t1 * (x2 - x1) + cx,
y: y1 + t1 * (y2 - y1) + cy
};
if (t2 >= 0 && t2 <= 1)
p2 = {
x: x1 + t2 * (x2 - x1) + cx,
y: y1 + t2 * (y2 - y1) + cy
};
return p1 && p2 ? [p1, p2] : p1 ? [p1] : [p2]
};
Then for the walls you would need a line to line intersection - define one line for each side of the rectangle. If there is line overlap you may get hit for two intersection, just ignore the second.
This will return a single point for the intersection or null if no intersection:
function getLineIntersection(p0x, p0y, p1x, p1y, p2x, p2y, p3x, p3y) {
var d1x = p1x - p0x,
d1y = p1y - p0y,
d2x = p3x - p2x,
d2y = p3y - p2y,
d = d1x * d2y - d2x * d1y,
px, py, s, t;
if (Math.abs(d) < 1e-14) return null;
px = p0x - p2x;
py = p0y - p2y;
s = (d1x * py - d1y * px) / d;
if (s >= 0 && s <= 1) {
t = (d2x * py - d2y * px) / d;
if (t >= 0 && t <= 1) {
return {
x: p0x + (t * d1x),
y: p0y + (t * d1y)
}
}
}
return null
}
Then just iterate with the line through the ball array, if no hit, iterate through the wall array.
Modified fiddle
To utilize these you will have to run the line through these each time it is moved (or per frame update).
Tip: You can make the function recursive so that you can find the intersection point, calculate reflected vector based on the hit angle, then find next intersection for n number of times (or total length the shot can move) using the last intersecting point and new angle as start of next line. This way you can build the path the shot will follow.
var canvas = document.querySelector("canvas");
canvas.width = 500;
canvas.height = 300;
var ctx = canvas.getContext("2d"),
line = {
x1: 190, y1: 170,
x2: 0, y2: 0,
x3: 0, y3: 0
};
var length = 100;
var circle = {
x: 400,
y: 70
};
var wall = {
x1: 440, y1: 0,
x2: 440, y2: 100
};
window.onmousemove = function(e) {
//get correct mouse pos
var rect = ctx.canvas.getBoundingClientRect(),
x = e.clientX - rect.left,
y = e.clientY - rect.top;
// calc line angle
var dx = x - line.x1,
dy = y - line.y1,
angle = Math.atan2(dy, dx);
//Then render the line using length as pixel radius:
line.x2 = line.x1 - length * Math.cos(angle);
line.y2 = line.y1 - length * Math.sin(angle);
line.x3 = line.x1 + canvas.width * Math.cos(angle);
line.y3 = line.y1 + canvas.width * Math.sin(angle);
// does it intersect?
var pts = lineIntersectsCircle(line.x1, line.y1, line.x3, line.y3, circle.x, circle.y, 20);
if (pts.length) {
line.x3 = pts[0].x;
line.y3 = pts[0].y
}
else {
pts = getLineIntersection(line.x1, line.y1, line.x3, line.y3, wall.x1, wall.y1, wall.x2, wall.y2);
if (pts) {
line.x3 = pts.x;
line.y3 = pts.y
}
}
// render
ctx.clearRect(0, 0, canvas.width, canvas.height);
ctx.beginPath();
ctx.moveTo(line.x1, line.y1);
ctx.lineTo(line.x2, line.y2);
ctx.strokeStyle = '#333';
ctx.stroke();
ctx.beginPath();
ctx.moveTo(line.x1, line.y1);
ctx.lineTo(line.x3, line.y3);
ctx.strokeStyle = 'red';
ctx.stroke();
ctx.beginPath();
ctx.arc(circle.x, circle.y, 20, 0, Math.PI * 2, true);
ctx.fillStyle = '#333';
ctx.fill();
// render example wall:
ctx.fillRect(wall.x1, wall.y1, 4, wall.y2-wall.y1);
}
function lineIntersectsCircle(x1, y1, x2, y2, cx, cy, r) {
x1 -= cx;
y1 -= cy;
x2 -= cx;
y2 -= cy;
// solve quadrant
var a = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1),
b = 2 * ((x2 - x1) * x1 + (y2 - y1) * y1),
c = x1 * x1 + y1 * y1 - r * r,
d = b * b - 4 * a * c,
dq, p1, p2, t1, t2;
if (d <= 0 || !a) return [];
dq = Math.sqrt(d);
t1 = (-b - dq) / (2 * a);
t2 = (-b + dq) / (2 * a);
// calculate actual intersection points
if (t1 >= 0 && t1 <= 1)
p1 = {
x: x1 + t1 * (x2 - x1) + cx,
y: y1 + t1 * (y2 - y1) + cy
};
if (t2 >= 0 && t2 <= 1)
p2 = {
x: x1 + t2 * (x2 - x1) + cx,
y: y1 + t2 * (y2 - y1) + cy
};
return p1 && p2 ? [p1, p2] : p1 ? [p1] : [p2]
};
function getLineIntersection(p0x, p0y, p1x, p1y, p2x, p2y, p3x, p3y) {
var d1x = p1x - p0x,
d1y = p1y - p0y,
d2x = p3x - p2x,
d2y = p3y - p2y,
d = d1x * d2y - d2x * d1y,
px, py, s, t;
if (Math.abs(d) < 1e-14) return null;
px = p0x - p2x;
py = p0y - p2y;
s = (d1x * py - d1y * px) / d;
if (s >= 0 && s <= 1) {
t = (d2x * py - d2y * px) / d;
if (t >= 0 && t <= 1) {
return {
x: p0x + (t * d1x),
y: p0y + (t * d1y)
}
}
}
return null
}
<canvas></canvas>
I don't have enough reputation to add this as a comment to Blindman67's solution, so i have to resort to adding this as an answer.
Blindman67's answer is great, but i needed support for polygons as well.
I am no math wizard so there may be a much better solution for polygons than this, but what i did was loop over all pairs of points from a polygon (so all sides of a polygon, really) and treat them as walls based on the code from Blindman67, then check the ray distance in the new rayDist2Polygon:
var rayDist2Polygon = function(ray){
let u,lineU;
const polLength = this.points.length;
const startX = this.x;
const startY = this.y;
// Loop over all lines of the polygon
for (i = 0; i < polLength; i++) {
const nextPoint = i === polLength - 1 ? this.points[0] : this.points[i + 1];
const x1 = startX + this.points[i].x;
const x2 = startX + nextPoint.x;
const y1 = startY + this.points[i].y;
const y2 = startY + nextPoint.y;
this.setupWall(x1, y1, x2, y2);
lineU = rayDist2Wall.bind(this)(ray);
if (!u) {
// If it's the first hit, assign it to `u`
u = lineU;
} else if (lineU < u) {
// If the current hit is smaller than anything we have so far, then this is the closest one, assign it to `u`
u = lineU;
}
}
// Reset positions after running this.setupWall;
this.x = startX;
this.y = startY;
return (!u || u < 0) ? Infinity : u; // if behind ray return Infinity else the dist
}
Then used the same logic to also support squares by converting a square's dimension/shape to points.
You can view it below, or fiddle with it at my codepen.
// Forked from https://stackoverflow.com/a/36566360/16956030
// All credits go to Blindman67
// All i did was add support for Polygons and Squares based on code from
// Blindman67, by treating each side of a polyon/square as a line/wall,
// then loop over each side and get the smallest result in rayDist2Polygon.
// I'm no math wizard and there may be a much better solution for these shapes,
// but this'll do for now.
console.clear();
const COLOUR = "BLACK";
const RAY_COLOUR = "RED";
const LINE_WIDTH = 4;
const RAY_LINE_WIDTH = 2;
const OBJ_COUNT = 20; // number of object in the scene;
const NUMBER_RAYS = 16; // number of rays
const RAY_DIR_SPACING = Math.PI / (NUMBER_RAYS / 2);
const RAY_ROTATE_SPEED = Math.PI * 2 / 31000;
if(typeof Math.hypot === "undefined"){ // poly fill for Math.hypot
Math.hypot = function(x, y){
return Math.sqrt(x * x + y * y);
}
}
var ctx, canvas, objects, ray, w, h, mouse, rand, ray, rayMaxLen, screenDiagonal;
// create a canvas and add to the dom
var canvas = document.createElement("canvas");
canvas.width = w = window.innerWidth;
canvas.height = h = window.innerHeight;
canvas.style.position = "absolute";
canvas.style.left = "0px";
canvas.style.top = "0px";
document.body.appendChild(canvas);
// objects to ray cast
objects = [];
// mouse object
mouse = {x :0, y: 0};
//========================================================================
// random helper
rand = function(min, max){
return Math.random() * (max - min) + min;
}
//========================================================================
// Ad Hoc draw line method
// col is the stroke style
// width is the storke width
var drawLine = function(col,width){
ctx.strokeStyle = col;
ctx.lineWidth = width;
ctx.beginPath();
ctx.moveTo(this.x,this.y);
ctx.lineTo(this.x + this.nx * this.len, this.y + this.ny * this.len);
ctx.stroke();
}
//========================================================================
// Ad Hoc draw circle method
// col is the stroke style
// width is the storke width
var drawCircle = function(col,width){
ctx.strokeStyle = col;
ctx.lineWidth = width;
ctx.beginPath();
ctx.arc(this.x , this.y, this.radius, 0 , Math.PI * 2);
ctx.stroke();
}
//========================================================================
// Ad Hoc draw square method
var drawSquare = function(){
ctx.beginPath();
ctx.rect(this.x, this.y, this.width, this.height);
ctx.stroke();
// Create array of points like a polygon based on the position & dimensions
// from this square, necessary for rayDist2Polygon
this.points = [
{ x: 0, y: 0},
{ x: this.width, y: 0},
{ x: this.width, y: this.height},
{ x: 0, y: this.height}
];
}
//========================================================================
// Ad Hoc draw [poligon] method
var drawPolygon = function(){
ctx.beginPath();
ctx.moveTo(this.x,this.y);
var polLength = this.points.length;
for(var i=0; i < polLength; ++i) {
ctx.lineTo(this.x + this.points[i].x, this.y + this.points[i].y);
}
ctx.closePath();
ctx.stroke();
}
//========================================================================
// Ad Hoc method for ray to set the direction vector
var updateRayDir = function(dir){
this.nx = Math.cos(dir);
this.ny = Math.sin(dir);
return this;
}
//========================================================================
// Creates a ray objects from
// x,y start location
// dir the direction in radians
// len the rays length
var createRay = function(x,y,dir,len){
return ({
x : x,
y : y,
len : len,
draw : drawLine,
setDir : updateRayDir, // add function to set direction
}).setDir(dir);
}
//========================================================================
// returns a circle object
// x,y is the center
// radius is the you know what..
// Note r2 is radius squared if you change the radius remember to set r2 as well
var createCircle = function(x , y, radius){
return {
x : x,
y : y,
draw : drawCircle, // draw function
rayDist : rayDist2Circle, // add ray cast method
radius : radius,
r2 : radius * radius, // ray caster needs square of radius may as well do it here
};
}
// Ad Hoc function to set the wall information
// x1,y1 are the start coords
// x2,y2 are the end coords
setupWallInformation = function(x1, y1, x2, y2){
this.x = x1;
this.y = y1;
this.vx = x2 - x1;
this.vy = y2 - y1;
this.len = Math.hypot(this.vx,this.vy);
this.nx = this.vx / this.len;
this.ny = this.vy / this.len;
return this;
}
//========================================================================
// returns a polygon object
// x,y are the start coords
// In this example the polygon always has the same shape
var createPolygon = function(x , y){
return {
x : x,
y : y,
points: [
{ x: 0, y: 0},
{ x: 100, y: 50},
{ x: 50, y: 100},
{ x: 0, y: 90}
],
draw : drawPolygon, // draw function
setupWall : setupWallInformation,
rayDist : rayDist2Polygon, // add ray cast method
};
}
//========================================================================
// returns a square object
// x,y are the start coords
// In this example the polygon always has the same shape
var createSquare = function(x , y, width, height){
return {
x : x,
y : y,
width: width,
height: height,
draw : drawSquare, // draw function
setupWall : setupWallInformation,
rayDist : rayDist2Polygon, // add ray cast method
};
}
//========================================================================
// Ad Hoc function to change the wall position
// x1,y1 are the start coords
// x2,y2 are the end coords
changeWallPosition = function(x1, y1, len, dir){
this.x = x1;
this.y = y1;
this.len = len;
this.nx = Math.cos(dir);
this.ny = Math.sin(dir);
return this;
}
//========================================================================
// returns a wall object
// x1,y1 are the star coords
// len is the length
// dir is the direction
var createWall = function(x1, y1, len, dir){
return({
x : x1, y : y1,
rayDist : rayDist2Wall, // add ray cast method
draw : drawLine,
setPos : changeWallPosition,
}).setPos(x1, y1, len, dir);
}
//========================================================================
// Self evident
// returns a distance or infinity if no valid solution
var rayDist2Circle = function(ray){
var vcx, vcy, v;
vcx = ray.x - this.x; // vector from ray to circle
vcy = ray.y - this.y;
v = -2 * (vcx * ray.nx + vcy * ray.ny);
v -= Math.sqrt(v * v - 4 * (vcx * vcx + vcy * vcy - this.r2)); // this.r2 is the radius squared
// If there is no solution then Math.sqrt returns NaN we should return Infinity
// Not interested in intercepts in the negative direction so return infinity
return isNaN(v) || v < 0 ? Infinity : v / 2;
}
//========================================================================
// returns the distance to the wall
// if no valid solution then return Infinity
var rayDist2Wall = function(ray){
var x,y,u;
rWCross = ray.nx * this.ny - ray.ny * this.nx;
if(!rWCross) { return Infinity; } // Not really needed.
x = ray.x - this.x; // vector from ray to wall start
y = ray.y - this.y;
u = (ray.nx * y - ray.ny * x) / rWCross; // unit distance along normal of wall
// does the ray hit the wall segment
if(u < 0 || u > this.len){ return Infinity;} /// no
// as we use the wall normal and ray normal the unit distance is the same as the
u = (this.nx * y - this.ny * x) / rWCross;
return u < 0 ? Infinity : u; // if behind ray return Infinity else the dist
}
//========================================================================
// returns the distance to the polygon
// if no valid solution then return Infinity
var rayDist2Polygon = function(ray){
let u,lineU;
const polLength = this.points.length;
const startX = this.x;
const startY = this.y;
// Loop over all lines of the polygon
for (i = 0; i < polLength; i++) {
const nextPoint = i === polLength - 1 ? this.points[0] : this.points[i + 1];
const x1 = startX + this.points[i].x;
const x2 = startX + nextPoint.x;
const y1 = startY + this.points[i].y;
const y2 = startY + nextPoint.y;
this.setupWall(x1, y1, x2, y2);
lineU = rayDist2Wall.bind(this)(ray);
if (!u) {
// If it's the first hit, assign it to `u`
u = lineU;
} else if (lineU < u) {
// If the current hit is smaller than anything we have so far, then this is the closest one, assign it to `u`
u = lineU;
}
}
// Reset positions after running this.setupWall;
this.x = startX;
this.y = startY;
return (!u || u < 0) ? Infinity : u; // if behind ray return Infinity else the dist
}
//========================================================================
// does a ray cast
// ray the ray to cast
// objects an array of objects
var castRay = function(ray,objects){
var i,minDist;
minDist = ray.len; // set the min dist to the rays length
i = objects.length; // number of objects to check
while(i > 0){
i -= 1;
minDist = Math.min(objects[i].rayDist(ray), minDist);
}
ray.len = minDist;
}
//========================================================================
// Draws all objects
// objects an array of objects
var drawObjects = function(objects){
var i = objects.length; // number of objects to check
while(i > 0){
objects[--i].draw(COLOUR, LINE_WIDTH);
}
}
//========================================================================
// called on start and resize
// creats a new scene each time
// fits the canvas to the avalible realestate
function reMakeAll(){
w = canvas.width = window.innerWidth;
h = canvas.height = window.innerHeight;
ctx = canvas.getContext("2d");
screenDiagonal = Math.hypot(window.innerWidth,window.innerHeight);
if(ray === undefined){
ray = createRay(0,0,0,screenDiagonal);
}
objects.length = 0;
var i = OBJ_COUNT;
while( i > 0 ){
var objectRandom = Math.floor(rand(0, 4));
if(objectRandom === 1){
objects.push(createWall(rand(0, w), rand(0, h), rand(screenDiagonal * 0.1, screenDiagonal * 0.2), rand(0, Math.PI * 2)));
}else if(objectRandom === 2){
objects.push(createPolygon(rand(0, w), rand(0, h)));
}else if(objectRandom === 3){
objects.push(createSquare(rand(0, w), rand(0, h), rand(screenDiagonal * 0.02, screenDiagonal * 0.05), rand(screenDiagonal * 0.02, screenDiagonal * 0.05)));
}else{
objects.push(createCircle(rand(0, w), rand(0, h), rand(screenDiagonal * 0.02, screenDiagonal * 0.05)));
}
i -= 1;
}
}
//========================================================================
function mouseMoveEvent(event){
mouse.x = event.clientX;
mouse.y = event.clientY;
}
//========================================================================
// updates all that is needed when needed
function updateAll(time){
var i;
ctx.clearRect(0,0,w,h);
ray.x = mouse.x;
ray.y = mouse.y;
drawObjects(objects);
i = 0;
while(i < NUMBER_RAYS){
ray.setDir(i * RAY_DIR_SPACING + time * RAY_ROTATE_SPEED);
ray.len = screenDiagonal;
castRay(ray,objects);
ray.draw(RAY_COLOUR, RAY_LINE_WIDTH);
i ++;
}
requestAnimationFrame(updateAll);
}
// add listeners
window.addEventListener("resize",reMakeAll);
canvas.addEventListener("mousemove",mouseMoveEvent);
// set it all up
reMakeAll();
// start the ball rolling
requestAnimationFrame(updateAll);
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>
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.