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I'm trying to achieve that, everytime you type a different letter key, the lines of the letters 'merge' into eachother instead of just 'jumping' to the next letter like it's doing now. I'm looking into the lerp() function but i'm not sure how to apply this to my code. Can someone help me into the right direction? This is what i have untill now:
var redtown;
var fontSize = 500;
var myArray;
var r = 3;
function preload(){
redtown = loadFont('redtown.otf');
}
function setup(){
createCanvas(windowWidth,windowHeight);
textFont(redtown);
textSize(fontSize);
}
function draw(){
background(0);
myArray = redtown.textToPoints(key, width/2, 500, fontSize, {
sampleFactor:0.5
});
// text(key, width/2, height/2 );
for (var i = 0; i < myArray.length; i++) {
// ellipse(myArray[i].x, myArray[i].y, 10, 10)
push();
translate(myArray[i].x, myArray[i].y);
rotate(r);
r++;
stroke(255);
strokeWeight(1);
line(-10,-10,10,10,10);
frameRate(17);
pop();
}
}
Here is a snippet that transitions from one character to another by using textToPoints to get the points from the last two keys that have been pressed and then slides each point in the old character to its position in the new character.
It uses this formula to get the x and y positions of points along a line from the point in the old character to the point in the new character.
x = (1-t)*x+t*nextX;
y = (1-t)*y+t*nextY;
It also uses the spinning lines idea from the question to give the points some motion although it pins the line size to a constant.
rotate(r+=0.1);
line(-1,-1,1,1);
You can see it in action here Fonts Transition
var myFont;
var fontSize = 160;
var fontPoints =[];
var previousFontPoints = [];
var r = 0;
var oldKey = ' ';
function preload(){
myFont = loadFont('inconsolata.otf');
}
function setup(){
createCanvas(500, 500);
textFont(myFont);
textSize(fontSize);
frameRate(30);
stroke(255);
strokeWeight(1);
background(0);
}
function draw(){
if (oldKey != key){
previousFontPoints =
myFont.textToPoints(oldKey, width/10, height/2, fontSize, {
sampleFactor:1
});
oldKey = key;
fontPoints = myFont.textToPoints(key, width/10, height/2, fontSize, {
sampleFactor:1
});
t = 0.025;
}
t += .01;
if (fontPoints.length > 0 && t< 1.0){
background(0);
for (i = 0; i < fontPoints.length; i++){
let x = 0;
let y = 0;
// if we don't have enought points we will just float in from 0,0
let nextX = 0;
let nextY = 0;
push();
if (previousFontPoints.length > i){
x = previousFontPoints[i].x;
y = previousFontPoints[i].y;
// in case the new array does not have enough points
nextX = x;
nextY = y;
}
if (fontPoints.length > i){
nextX = fontPoints[i].x;
nextY = fontPoints[i].y;
}
x = (1-t)*x+t*nextX;
y = (1-t)*y+t*nextY;
translate(x, y);
rotate(r+=0.1);
line(-1,-1,1,1);
pop();
}
}
}
I have a Polyline on the HiDPICanvas (html5 canvas). When I move mouse left and right I track its coordinates and on corresponding point with same X coordinate on the polyline I draw a Circle. You can try it now to see the result.
// Create a canvas
var HiDPICanvas = function(container_id, color, w, h) {
/*
objects are objects on the canvas, first elements of dictionary are background elements, last are on the foreground
canvas will be placed in the container
canvas will have width w and height h
*/
var objects = {
box : [],
borders : [],
circles : [],
polyline: []
}
var doNotMove = ['borders']
// is mouse down & its coords
var mouseDown = false
lastX = window.innerWidth/2
lastY = window.innerHeight/2
// return pixel ratio
var getRatio = function() {
var ctx = document.createElement("canvas").getContext("2d");
var dpr = window.devicePixelRatio || 1;
var bsr = ctx.webkitBackingStorePixelRatio ||
ctx.mozBackingStorePixelRatio ||
ctx.msBackingStorePixelRatio ||
ctx.oBackingStorePixelRatio ||
ctx.backingStorePixelRatio || 1;
return dpr / bsr;
}
// return high dots per inch canvas
var createHiDPICanvas = function() {
var ratio = getRatio();
var chart_container = document.getElementById(container_id);
var can = document.createElement("canvas");
can.style.backgroundColor = color
can.width = w * ratio;
can.height = h * ratio;
can.style.width = w + "px";
can.style.height = h + "px";
can.getContext("2d").setTransform(ratio, 0, 0, ratio, 0, 0);
chart_container.appendChild(can);
return can;
}
// add object to the canvas
var add = function(object, category) {
objects[category].push(object)
}
// clear canvas
var clearCanvas = function(x0, y0, x1, y1) {
ctx.clearRect(x0, y0, x1, y1);
ctx.beginPath();
ctx.globalCompositeOperation = "source-over";
ctx.globalAlpha = 1;
ctx.closePath();
}
// check function do I can move this group of objects
var canMove = function(groupname) {
for (var i = 0; i < doNotMove.length; i++) {
var restricted = doNotMove[i]
if (restricted == groupname) {
return false
}
}
return true
}
// refresh all objects on the canvas
var refresh = function() {
clearCanvas(0, 0, w, h)
var object
for (var key in objects) {
for (var i = 0; i < objects[key].length; i++) {
object = objects[key][i]
object.refresh()
}
}
}
// shift all objects on the canvas except left and down borders and its content
var shiftObjects = function(event) {
event.preventDefault()
// if mouse clicked now -> we can move canvas view left\right
if (mouseDown) {
var object
for (var key in objects) {
if (canMove(key)) {
for (var i = 0; i < objects[key].length; i++) {
object = objects[key][i]
object.move(event.movementX, event.movementY)
}
}
}
cci.refresh()
}
}
// transfer x to canvas drawing zone x coord (for not drawing on borders of the canvas)
var transferX = function(x) {
return objects.borders[0].width + x
}
var transferCoords = function(x, y) {
// no need to transfer y because borders are only at the left
return {
x : transferX(x),
y : y
}
}
// change mouse state on the opposite
var toggleMouseState = function() {
mouseDown = !mouseDown
}
// make mouseDown = false, (bug removal function when mouse down & leaving the canvas)
var refreshMouseState = function() {
mouseDown = false
}
// print information about all objects on the canvas
var print = function() {
var groupLogged = true
console.log("Objects on the canvas:")
for (var key in objects) {
groupLogged = !groupLogged
if (!groupLogged) {console.log(key, ":"); groupLogged = !groupLogged}
for (var i = 0 ; i < objects[key].length; i++) {
console.log(objects[key][i])
}
}
}
var restrictEdges = function() {
console.log("offsetLeft", objects['borders'][0])
}
var getMouseCoords = function() {
return {
x : lastX,
y : lastY
}
}
var addCircleTracker = function() {
canvas.addEventListener("mousemove", (e) => {
var polyline = objects.polyline[0]
var mouseCoords = getMouseCoords()
var adjNodes = polyline.get2NeighbourNodes(mouseCoords.x)
if (adjNodes != -1) {
var prevNode = adjNodes.prev
var currNode = adjNodes.curr
var cursorNode = polyline.linearInterpolation(prevNode, currNode, mouseCoords.x)
// cursorNode.cursorX, cursorNode.cursorY are coords
// for circle that should be drawn on the polyline
// between the closest neighbour nodes
var circle = objects.circles[0]
circle.changePos(cursorNode.x, cursorNode.y)
refresh()
}
})
}
// create canvas
var canvas = createHiDPICanvas()
addCircleTracker()
// we created canvas so we can track mouse coords
var trackMouse = function(event) {
lastX = event.offsetX || (event.pageX - canvas.offsetLeft)
lastY = event.offsetY || (event.pageY - canvas.offsetTop)
}
// 2d context
var ctx = canvas.getContext("2d")
// add event listeners to the canvas
canvas.addEventListener("mousemove" , shiftObjects )
canvas.addEventListener("mousemove", (e) =>{ trackMouse(e) })
canvas.addEventListener("mousedown" , () => { toggleMouseState () })
canvas.addEventListener("mouseup" , () => { toggleMouseState () })
canvas.addEventListener("mouseleave", () => { refreshMouseState() })
canvas.addEventListener("mouseenter", () => { refreshMouseState() })
return {
// base objects
canvas : canvas,
ctx : ctx,
// sizes of the canvas
width : w,
height : h,
color : color,
// add object on the canvas for redrawing
add : add,
print : print,
// refresh canvas
refresh: refresh,
// objects on the canvas
objects: objects,
// get mouse coords
getMouseCoords : getMouseCoords
}
}
// cci -> canvas ctx info (dict)
var cci = HiDPICanvas("lifespanChart", "bisque", 780, 640)
var ctx = cci.ctx
var canvas = cci.canvas
var Polyline = function(path, color) {
var create = function() {
if (this.path === undefined) {
this.path = path
this.color = color
}
ctx.save()
ctx.beginPath()
p = this.path
ctx.fillStyle = color
ctx.moveTo(p[0].x, p[0].y)
for (var i = 0; i < p.length - 1; i++) {
var currentNode = p[i]
var nextNode = p[i+1]
// draw smooth polyline
// var xc = (currentNode.x + nextNode.x) / 2;
// var yc = (currentNode.y + nextNode.y) / 2;
// taken from https://stackoverflow.com/a/7058606/13727076
// ctx.quadraticCurveTo(currentNode.x, currentNode.y, xc, yc);
// draw rough polyline
ctx.lineTo(currentNode.x, currentNode.y)
}
ctx.stroke()
ctx.restore()
ctx.closePath()
}
// circle that will track mouse coords and be
// on the corresponding X coord on the path
// following mouse left\right movements
var circle = new Circle(50, 50, 5, "purple")
cci.add(circle, "circles")
create()
var get2NeighbourNodes = function(x) {
// x, y are cursor coords on the canvas
//
// Get 2 (left and right) neighbour nodes to current cursor x,y
// N are path nodes, * is Node we search coords for
//
// N-----------*----------N
//
for (var i = 1; i < this.path.length; i++) {
var prevNode = this.path[i-1]
var currNode = this.path[i]
if ( prevNode.x <= x && currNode.x >= x ) {
return {
prev : prevNode,
curr : currNode
}
}
}
return -1
}
var linearInterpolation = function(prevNode, currNode, cursorX) {
// calculate x, y for the node between 2 nodes
// on the path using linearInterpolation
// https://en.wikipedia.org/wiki/Linear_interpolation
var cursorY = prevNode.y + (cursorX - prevNode.x) * ((currNode.y - prevNode.y)/(currNode.x - prevNode.x))
return {
x : cursorX,
y : cursorY
}
}
var move = function(diff_x, diff_y) {
for (var i = 0; i < this.path.length; i++) {
this.path[i].x += diff_x
this.path[i].y += diff_y
}
}
return {
create : create,
refresh: create,
move : move,
get2NeighbourNodes : get2NeighbourNodes,
linearInterpolation : linearInterpolation,
path : path,
color : color
}
}
var Circle = function(x, y, radius, fillStyle) {
var create = function() {
if (this.x === undefined) {
this.x = x
this.y = y
this.radius = radius
this.fillStyle = fillStyle
}
ctx.save()
ctx.beginPath()
ctx.arc(this.x, this.y, radius, 0, 2*Math.PI)
ctx.fillStyle = fillStyle
ctx.strokeStyle = fillStyle
ctx.fill()
ctx.stroke()
ctx.closePath()
ctx.restore()
}
create()
var changePos = function(new_x, new_y) {
this.x = new_x
this.y = new_y
}
var move = function(diff_x, diff_y) {
this.x += diff_x
this.y += diff_y
}
return {
refresh : create,
create : create,
changePos: changePos,
move : move,
radius : radius,
x : this.x,
y : this.y
}
}
var Node = function(x, y) {
this.x = x
this.y = y
return {
x : this.x,
y : this.y
}
}
var poly = new Polyline([
Node(30,30), Node(150,150),
Node(290, 150), Node(320,200),
Node(350,350), Node(390, 250),
Node(450, 140)
], "green")
cci.add(poly, "polyline")
<div>
<div id="lifespanChart"></div>
</div>
But if you go to the comment draw smooth polyline and uncomment code below (and comment line that draws rough polyline) - it will draw smooth polyline now (quadratic Bézier curve). But when you try to move mouse left and right - Circle sometimes goes out of polyline bounds.
before quadratic curve:
after quadratic curve:
Here is a question : I calculated x, y coordinates for the Circle on the rough polyline using linear interpolation, but how could I calculate x, y coordinates for the Circle on the smooth quadratic curve?
ADD 1 : QuadraticCurve using Beizer curve as a base in calculations when smoothing polyline
ADD 2 For anyone who a little stucked with the implementation I found & saved easier solution from here, example:
var canvas = document.getElementById("canv")
var canvasRect = canvas.getBoundingClientRect()
var ctx = canvas.getContext('2d')
var p0 = {x : 30, y : 30}
var p1 = {x : 20, y :100}
var p2 = {x : 200, y :100}
var p3 = {x : 200, y :20}
// Points are objects with x and y properties
// p0: start point
// p1: handle of start point
// p2: handle of end point
// p3: end point
// t: progression along curve 0..1
// returns an object containing x and y values for the given t
// link https://stackoverflow.com/questions/14174252/how-to-find-out-y-coordinate-of-specific-point-in-bezier-curve-in-canvas
var BezierCubicXY = function(p0, p1, p2, p3, t) {
var ret = {};
var coords = ['x', 'y'];
var i, k;
for (i in coords) {
k = coords[i];
ret[k] = Math.pow(1 - t, 3) * p0[k] + 3 * Math.pow(1 - t, 2) * t * p1[k] + 3 * (1 - t) * Math.pow(t, 2) * p2[k] + Math.pow(t, 3) * p3[k];
}
return ret;
}
var draw_poly = function () {
ctx.beginPath()
ctx.lineWidth=2
ctx.strokeStyle="white"
ctx.moveTo(p0.x, p0.y)// start point
// cont cont end
ctx.bezierCurveTo(p1.x, p1.y, p2.x, p2.y, p3.x, p3.y)
ctx.stroke()
ctx.closePath()
}
var clear_canvas = function () {
ctx.clearRect(0,0,300,300);
ctx.beginPath();
ctx.globalCompositeOperation = "source-over";
ctx.globalAlpha = 1;
ctx.closePath();
};
var draw_circle = function(x, y) {
ctx.save();
// semi-transparent arua around the circle
ctx.globalCompositeOperation = "source-over";
ctx.beginPath()
ctx.fillStyle = "white"
ctx.strokeStyle = "white"
ctx.arc(x, y, 5, 0, 2 * Math.PI);
ctx.stroke();
ctx.closePath();
ctx.restore();
}
var refresh = function(circle_x, circle_y) {
clear_canvas()
draw_circle(circle_x, circle_y)
draw_poly()
}
var dist = function(mouse, point) {
return Math.abs(mouse.x - point.x)
// return ((mouse.x - point.x)**2 + (mouse.y - point.y)**2)**0.5
}
var returnClosest = function(curr, prev) {
if (curr < prev) {
return curr
}
return prev
}
refresh(30,30)
canvas.addEventListener("mousemove", (e) => {
var mouse = {
x : e.clientX - canvasRect.left,
y : e.clientY - canvasRect.top
}
var Point = BezierCubicXY(p0, p1, p2, p3, 0)
for (var t = 0; t < 1; t += 0.01) {
var nextPoint = BezierCubicXY(p0, p1, p2, p3, t)
if (dist(mouse, Point) > dist(mouse, nextPoint)) {
Point = nextPoint
}
// console.log(Point)
}
refresh(Point.x, Point.y)
})
canvas {
background: grey;
}
<canvas id="canv" width = 300 height = 300></canvas>
Just iterate through all the lines of the curve & find closest position using this pattern
This can be done using an iterative search, as you have done with the lines.
BTW there is a much better way to find the closest point on a line that has a complexity of O(1) rather than O(n) where n is length of line segment.
Search for closest point
The following function can be used for both quadratic and cubic beziers and returns the unit position of closest point on bezier to a given coordinate.
The function also has a property foundPoint that has the position of the point found
The function uses the object Point that defines a 2D coordinate.
Signatures
The function has two signatures, one for quadratic beziers and the other for cubic.
closestPointOnBezier(point, resolution, p1, p2, cp1)
closestPointOnBezier(point, resolution, p1, p2, cp1, cp2)
Where
point as Point is the position to check
resolution as Number The approx resolution to search the bezier. If 0 then this is fixed to DEFAULT_SCAN_RESOLUTION else it is the distance between start and end points times resolution IE if resolution = 1 then approx scan is 1px, if resolution = 2 then approx scan is 1/2px
p1, p2 as Point's are the start and end points of the bezier
cp1, cp2 as Point's are the first and/or second control points of the bezier
Results
They both return Number that is the unit pos on the bezier of closest point. The value will be 0 <= result <= 1 Where 0 is at start of bezier and 1 is end
The function property closestPointOnBezier.foundPoint as Point has the coordinate of the closest point on the bezier and can be used to calculate the distance to the point on the bezier.
The function
const Point = (x = 0, y = 0) => ({x, y});
const MAX_RESOLUTION = 2048;
const DEFAULT_SCAN_RESOLUTION = 256;
closestPointOnBezier.foundPoint = Point();
function closestPointOnBezier(point, resolution, p1, p2, cp1, cp2) {
var unitPos, a, b, b1, c, i, vx, vy, closest = Infinity;
const v1 = Point(p1.x - point.x, p1.y - point.y);
const v2 = Point(p2.x - point.x, p2.y - point.y);
const v3 = Point(cp1.x - point.x, cp1.y - point.y);
resolution = resolution > 0 && reolution < MAX_RESOLUTION ? (Math.hypot(p1.x - p2.x, p1.y - p2.y) + 1) * resolution : 100;
const fp = closestPointOnBezier.foundPoint;
const step = 1 / resolution;
const end = 1 + step / 2;
const checkClosest = (e = (vx * vx + vy * vy) ** 0.5) => {
if (e < closest ){
unitPos = i;
closest = e;
fp.x = vx;
fp.y = vy;
}
}
if (cp2 === undefined) { // find quadratic
for (i = 0; i <= end; i += step) {
a = (1 - i);
c = i * i;
b = a*2*i;
a *= a;
vx = v1.x * a + v3.x * b + v2.x * c;
vy = v1.y * a + v3.y * b + v2.y * c;
checkClosest();
}
} else { // find cubic
const v4 = Point(cp2.x - point.x, cp2.y - point.y);
for (i = 0; i <= end; i += step) {
a = (1 - i);
c = i * i;
b = 3 * a * a * i;
b1 = 3 * c * a;
a = a * a * a;
c *= i;
vx = v1.x * a + v3.x * b + v4.x * b1 + v2.x * c;
vy = v1.y * a + v3.y * b + v4.y * b1 + v2.y * c;
checkClosest();
}
}
return unitPos < 1 ? unitPos : 1; // unit pos on bezier. clamped
}
Usage
Example usage to find closest point on two beziers
The defined geometry
const bzA = {
p1: Point(10, 100), // start point
p2: Point(200, 400), // control point
p3: Point(410, 500), // end point
};
const bzB = {
p1: bzA.p3, // start point
p2: Point(200, 400), // control point
p3: Point(410, 500), // end point
};
const mouse = Point(?,?);
Finding closest
// Find first point
closestPointOnBezier(mouse, 2, bzA.p1, bzA.p3, bzA.p2);
// copy point
var found = Point(closestPointOnBezier.foundPoint.x, closestPointOnBezier.foundPoint.y);
// get distance to mouse
var dist = Math.hypot(found.x - mouse.x, found.y - mouse.y);
// find point on second bezier
closestPointOnBezier(mouse, 2, bzB.p1, bzB.p3, bzB.p2);
// get distance of second found point
const distB = Math.hypot(closestPointOnBezier.foundPoint.x - mouse.x, closestPointOnBezier.foundPoint.y - mouse.y);
// is closer
if (distB < dist) {
found.x = closestPointOnBezier.foundPoint.x;
found.y = closestPointOnBezier.foundPoint.y;
dist = distB;
}
The closet point is found as Point
Good day,
I am generating some circles with colors, sizes and positions. All of this things randomly.
But, my problem is that I do not want them to collide, so that no circle is inside another, not even a little bit.
The logic explained in detail within the code, I would like to know why the failure and why the infinite loop.
The important functions are:
checkSeparation and setPositions
window.addEventListener("load", draw);
function draw() {
var canvas = document.getElementById("balls"), // Get canvas
ctx = canvas.getContext("2d"); // Context
canvas.width = document.body.clientWidth; // Set canvas width
canvas.height = document.documentElement.scrollHeight; // Height
var cW = canvas.width, cH = canvas.height; // Save in vars
ctx.fillStyle = "#fff022"; // Paint background
ctx.fillRect(0, 0, cW, cH); // Coordinates to paint
var arrayOfBalls = createBalls(); // create all balls
setPositions(arrayOfBalls, cW, cH);
arrayOfBalls.forEach(ball => { // iterate balls to draw
ctx.beginPath(); // start the paint
ctx.fillStyle = ball.color;
ctx.arc(ball.x, ball.y, ball.radius, 0, (Math.PI/180) * 360, false); // draw the circle
ctx.fill(); // fill
ctx.closePath(); // end the paint
});
}
function Ball() {
this.x = 0; // x position of Ball
this.y = 0; // y position of Ball
this.radius = Math.floor(Math.random() * ( 30 - 10 + 1) + 10);
this.color = "";
}
Ball.prototype.setColor = function(){
for(var j = 0, hex = "0123456789ABCDEF", max = hex.length,
random, str = ""; j <= 6; j++, random = Math.floor(Math.random() * max), str += hex[random])
this.color = "#" + str;
};
function random(val, min) {
return Math.floor(Math.random() * val + min); // Random number
}
function checkSeparation(value, radius, toCompare) {
var min = value - radius, // Min border of circle
max = value + radius; // Max border of circle
// Why ? e.g => x position of circle + this radius it will be its right edge
for(; min <= max; min++) {
if(toCompare.includes(min)) return false;
/*
Since all the positions previously obtained, I add them to the array, in order to have a reference when verifying the other positions and that they do NOT collide.
Here I check if they collide.
In the range of:
[pos x - its radius, pos x + its radius]
*/
}
return true; // If they never collided, it returns true
}
function createBalls() {
var maxBalls = 50, // number of balls
balls = []; // array of balls
for(var j = 0; j < maxBalls; j++) { // create 50 balls
var newBall = new Ball(); // create ball
newBall.setColor(); // set the ball color
balls.push(newBall); //push the ball to the array of balls
}
return balls; // return all balls to draw later
}
function setPositions(balls, canvasW, canvasH) {
var savedPosX = [], // to save x pos of balls
savedPosY = []; // to save y pos of balls
for(var start = 0, max = balls.length; start < max; start++) {
var current = balls[start], // current ball
randomX = random(canvasW, current.radius), // get random value for x pos
randomY = random(canvasH, current.radius); // get random value for y pos
if(checkSeparation(randomX, current.radius, savedPosX)) {
current.x = randomX; // If it position, along with your radio does not touch another circle, I add the position
} else {
// start--; continue;
console.log("X: The above code causes an infinite loop");
}
if(checkSeparation(randomY, current.radius, savedPosY)) {
current.y = randomY;
} else {
// start--; continue;
console.log("Y: The above code causes an infinite loop");
}
}
}
body,html {
margin: 0; border: 0; padding: 0; overflow: hidden;
}
<canvas id="balls"></canvas>
In your code, you test possible collisions by means of arrays of already used x and y positions, but you never add new positions to these arrays. You also check the x and y coordinates separately, which means you are really testing a collision of a bounding box.
Two circles collide when the distance between their centres is smaller than the sum of their radii, so you could use:
function collides(balls, n, x, y, r) {
for (let i = 0; i < n; i++) {
let ball = balls[i];
let dx = ball.x - x;
let dy = ball.y - y;
let dd = dx*dx + dy*dy;
let rr = r + ball.radius;
if (dd < rr * rr) return true;
}
return false;
}
function setPositions(balls, canvasW, canvasH) {
for (let i = 0, max = balls.length; i < max; i++) {
let ball = balls[i],
r = ball.radius,
maxTries = 20;
ball.x = -canvasW;
ball.y = -canvasH;
for (let tries = 0; tries = maxTries; tries++) {
let x = random(canvasW - 2*r, r),
y = random(canvasH - 2*r, r);
if (!collides(balls, i, x, y, r)) {
ball.x = x;
ball.y = y;
break;
}
}
}
}
This is reasonably fast for 50 balls, but will be slow if you have more balls. In that case, some spatial data structures can speed up the collision search.
You must also guard against the case that no good place can be found. The code above gives up after 20 tries and moves the ball outside the visible canvas. You can improve the chances of placing balls by sorting the balls by radius and plaing the large balls first.
Finally, you add one hex digit too many to your random colour. (That for loop, where everything happens in the loop control is horrible, by the way.)
I have two questions, the first being how do I access the indexes within my array separately, because my console.log of [n][0] results in two values - x and y. Secondly, for the butterfly curve, https://en.wikipedia.org/wiki/Butterfly_curve_%28transcendental%29, how would I determine the values of t? and reiterate through a certain minimum and maximum. In need of logic support.
Here's my progress so far.
/*function drawButterFly(n){
c.beginPath();
console.log(n[2])
for (var i = 0; i < n.length; i++){
if (i === 0) {
c.moveTo();
} else {
c.lineTo();
}
c.stroke();
}
}*/
function butterFly() {
var r = 5;
var N = 3;
var value = [];
for (var a = 0.2; a < 2*Math.PI; a = a + 0.1){
value.push(a);
}
var t = value[Math.floor(Math.random()*value.length)];
var cos = r*Math.cos(t)*( (Math.exp(Math.cos(t))) - (2*Math.cos(4*t)) - (Math.sin(t/12)^5) );
var sin = r*Math.sin(t)*( (Math.exp(Math.cos(t))) - (2*Math.cos(4*t)) - (Math.sin(t/12)^5) );
var n = [];
for (var u = 0; u < N; u++){
var x = sin * -u;
var y = cos * -u;
n.push([x,y]);
}
drawButterFly(n);
}
Since you're pushing an array here: n.push([x,y]) you can access the x component of the first element with n[0][0] and the y component of the same element with n[0][1]
Example:
var n = [];
n.push( ["x", "y"] );
console.log( n[0][0] );
console.log( n[0][1] );
As for the useful values of t - in the image you've shown, you'll notice that the same butterfly is drawn several times at different sizes. To draw a complete butterfly, you need to use the range for t of [0..2pi]. If you want to draw two butterflies, you need to use the range [0..4pi]. That is it's cyclic over the same period that a circle is. Unlike a circle however, each cycle doesn't draw over the previous one.
Here's a quick and nasty example:
function byId(id) {
return document.getElementById(id);
}
window.addEventListener('load', onDocLoaded, false);
function onDocLoaded(evt) {
butterFly();
}
function butterFly() {
var pointArray = [];
var stepSize = 0.05; // ~125 steps for every 360°
var upperLimit = 4 * Math.PI;
var scale = 20;
for (var t = 0.0; t < upperLimit; t += stepSize) {
var xVal = Math.sin(t) * ((Math.exp(Math.cos(t))) - (2 * Math.cos(4 * t)) - (Math.pow(Math.sin(t / 12), 5)));
var yVal = Math.cos(t) * ((Math.exp(Math.cos(t))) - (2 * Math.cos(4 * t)) - (Math.pow(Math.sin(t / 12), 5)));
pointArray.push([scale * xVal, -scale * yVal]); // -1 value since screen-y direction is opposite direction to cartesian coords y
}
drawButterFly(pointArray);
}
function drawButterFly(pointArray) {
var can = byId('myCan');
var ctx = can.getContext('2d');
var originX, originY;
originX = can.width / 2;
originY = can.height / 2;
ctx.beginPath();
for (var i = 0; i < pointArray.length; i++) {
if (i === 0) {
ctx.moveTo(originX + pointArray[i][0], originX + pointArray[i][1]);
} else {
ctx.lineTo(originX + pointArray[i][0], originY + pointArray[i][1]);
}
}
ctx.closePath();
ctx.stroke();
}
canvas {
border: solid 1px red;
}
<canvas id='myCan' width='256' height='256' />
If I'm not mistaken, the Butterfly curve is given as a pair of parametric equations, meaning you increment t to get the next (x, y) points on your curve. In other words, your t is what you should be using in place of u in your code, and the range of values for t should be 0 .. 24*pi as that's the range in which sin(t / 12) has its unique values).
Here's a version that demonstrates the drawing of the curve to a canvas:
function getPoint(t, S, O) {
var cos_t = Math.cos(t);
var factor = Math.exp(cos_t) - 2 * Math.cos(4*t) - Math.pow(Math.sin(t/12), 5);
return {
x: S * Math.sin(t) * factor + O.x,
y: S * cos_t * factor + O.y
};
}
var canvas = document.getElementById("c");
canvas.width = 300;
canvas.height = 300;
var ctx = canvas.getContext("2d");
// First path
ctx.beginPath();
ctx.strokeStyle = 'blue';
var offset = {x:150, y:120};
var scale = 40;
var maxT = 24 * Math.PI;
var p = getPoint(0, scale, offset);
ctx.moveTo(p.x, canvas.height - p.y);
for (var t = 0.01; t <= maxT; t += 0.01) {
p = getPoint(t, scale, offset);
ctx.lineTo(p.x, canvas.height - p.y);
}
ctx.stroke();
#c {
border: solid 1px black;
}
<canvas id="c"></canvas>
One thing to note: canvases have y = 0 start at the top, so you need to inverse your y (i.e. canvas.height - y) to have your curve orient correctly.
UPDATE: Added animated version
As requested by royhowie, here's an animated version, using requestAnimationFrame:
function getPoint(t, S, O) {
var cos_t = Math.cos(t);
var factor = Math.exp(cos_t) - 2 * Math.cos(4*t) - Math.pow(Math.sin(t/12), 5);
return {
x: S * Math.sin(t) * factor + O.x,
y: S * cos_t * factor + O.y
};
}
var canvas = document.getElementById("c");
canvas.width = 300;
canvas.height = 300;
var ctx = canvas.getContext("2d");
var offset = {x:150, y:120};
var scale = 40;
var maxT = 24 * Math.PI;
var animationID;
var started = false;
var t = 0;
document.getElementById('start').addEventListener('click', function(e) {
e.preventDefault();
if (!started) {
animationID = requestAnimationFrame(animate);
started = true;
}
});
document.getElementById('pause').addEventListener('click', function(e) {
e.preventDefault();
if (started) {
cancelAnimationFrame(animationID);
started = false;
}
});
function animate() {
animationID = requestAnimationFrame(animate);
var p = getPoint(t, scale, offset);
if (t === 0) {
ctx.beginPath();
ctx.strokeStyle = 'blue';
ctx.moveTo(p.x, canvas.height - p.y);
t += 0.01;
} else if (t < maxT) {
ctx.lineTo(p.x, canvas.height - p.y);
ctx.stroke();
t += 0.01;
} else {
cancelAnimationFrame(animationID);
}
}
#c {
border: solid 1px black;
}
<div>
<button id="start">Start</button>
<button id="pause">Pause</button>
</div>
<canvas id="c"></canvas>
Question 1
For an arbitrary integer i, let n[i] = [xi, yi]. xi can then be accessed via n[i][0] and yi via n[i][1]
Question 2
For values of t, I am sure you're gonna want to use sub-integer values, so I recommend using a constant increment value representing the "resolution" of your graph.
Let's call it dt. Also, I'd advise changing your variable names from single letters to something more descriptive, like min_t and max_t, and instead of n I'm going to call your array points.
function drawButterFly(points){
for (var i = 0, n = points.count; i < n; ++i) {
var x = points[i][0];
var y = points[i][1];
...
}
}
function butterFly(min_t, max_t, dt, r) {
var points = [];
for (var t = min_t; t < max_t; t+=dt){
var x = r*Math.sin(t)*...
var y = r*Math.cos(t)*...
points.push([x,y]);
}
drawButterFly(points, dt);
}
I'm not sure what the other loop inside of that function was for, but if you need it, you can adapt from the pattern above.
Usage example: butterFly(0, 10, 0.01, 3) -> t goes from 0 to 10 with an increment of 0.01, and r=3
Regarding your first question it's a better option to replace the multidimensional array containing the x and y coordinates with an object. Then when iterating over the array you can check for the object values.
So instead of:
n.push([x,y]);
you should do:
m.push({
'xPos' : x,
'yPos' : y
})
Later you can access this by m.xPos or m.yPos
Then you can access the x and y values by object literal names.
Regarding the second question: for a good pseudo code implementation of butterfly curves you might check Paul Burke site: http://paulbourke.net/geometry/butterfly/. So t in your case is:
t = i * 24.0 * PI / N;
As you see t is a parametric value which got incremented on each step when iterating over the array.
JSFiddle
After each circle object is created, it should increase in size while the mouse is down, and stop when mouse is up. clearInterval doesn't seem to reach the internal variable "growLoop" even though it's supposed to be global by declaring it first(which was the advice on many other posts about this same issue). In the console it shows growLoop undefined, but it's defined in line 95, right?
Also, the time interval seems to decrease with every new circle created, and they grow faster. How could the value of setInterval change?
//set up canvas
var canvas = document.getElementById("canvas");
var ctx = canvas.getContext("2d");
var circles = [];
//create circle
function create(location) {
circles.push({
x: location.x,
y: location.y,
radius: 10,
color: '#' + Math.floor(Math.random() * 16777215).toString(16)
});
}
//figure out mouse position
var rect = document.getElementById("canvas").getBoundingClientRect();
// Get canvas offset on page
var offset = {
x: rect.left,
y: rect.top
};
function isOnCanvas(a) {
if ((a.x >= 0 && a.x <= rect.width) && (a.y >= 0 && a.y <= rect.height)) {
return true;
}
return false;
}
function isOnCircle(a) {
var i = 0,
l = circles.length,
x, y, d, c;
for (; i < l; ++i) {
c = circles[i];
x = a.x - c.x;
y = a.y - c.y;
d = (a.radius || 10) + c.radius;
if (x * x + y * y <= d * d) {
return true;
}
}
return false;
}
// draw all circles
function draw() {
ctx.clearRect(0, 0, canvas.width, canvas.height);
for (var i = 0; i < circles.length; i++) {
var p = circles[i];
ctx.beginPath();
ctx.arc(p.x, p.y, p.radius, 0, 2 * Math.PI);
ctx.fillStyle = p.color;
ctx.fill();
}
}
//make last drawn circle 1px bigger
function grow(){
var a = circles[circles.length-1];
a.radius += 1;
}
//find percentage of canvas filled in
var totalSpace = canvas.width * canvas.height;
var totalFilled = function () {
total = 0;
for (var i = 0; i < circles.length; i++) {
var p = circles[i];
total += Math.PI * Math.pow(p.radius, 2);
}
return total;
console.log(total);
}
function findPercentage() {
return (totalFilled() / totalSpace) * 100;
}
function updateInfo() {
percentage = findPercentage();
document.getElementById("percentage").innerHTML = "You've filled in " + percentage.toFixed(1) + "%";
}
//do all the stuff
var animate = function(){
draw();
grow();
updateInfo();}
var growLoop = 0;
window.onmousedown = function (e) {
// get event location on page offset by canvas location
var location = {
x: e.pageX - offset.x,
y: e.pageY - offset.y
};
if (isOnCanvas(location) && !isOnCircle(location)) {
create(location);
var growLoop = setInterval(animate, 100);
}
};
window.onmouseup = function (e) {
clearInterval(growLoop);
}
window.onmouseout = function (e) {
clearInterval(growLoop);
}
var growLoop = setInterval(animate, 100);
By adding var here you are declaring an internal variable also named growLoop and not assigning to the global. Remove var.
growLoop = setInterval(animate, 100);
http://jsfiddle.net/SeAGU/85/