Is there a way to rotate the object with the property rotation, and then calculate its x and y coordinates as if it was turned around some point
without measurement accuracy?
public static function pointRotate (object:DisplayObject, center:Point,angle:Number) : void
{
var r:Number = angle * Math.PI / 180;
var s:Number = Math.sin(r);
var c:Number = Math.cos(r);
var dX:Number = object.x - center.x;
var dY:Number = object.y - center.y;
object.rotation += angle;
object.x = center.x + dX * c - dY * s;
object.y = center.y + dX * s + dY * c;
}
package
{
import flash.geom.Point;
import flash.display.DisplayObject;
public function pointRotate(object:DisplayObject, center:Point, angle:Number) : void
{
// return to zero
angle += object.rotation;
var a0:Number = - object.rotation * Math.PI / 180;
var s0:Number = Math.sin(a0);
var c0:Number = Math.cos(a0);
var dX0:Number = object.x - center.x;
var dY0:Number = object.y - center.y;
object.rotation = 0;
object.x = Math.round(center.x + dX0 * c0 - dY0 * s0);
object.y = Math.round(center.y + dX0 * s0 + dY0 * c0);
// new rotation
var r:Number = angle * Math.PI / 180;
var s:Number = Math.sin(r);
var c:Number = Math.cos(r);
var dX:Number = object.x - center.x;
var dY:Number = object.y - center.y;
object.rotation += angle;
object.x = center.x + dX * c - dY * s;
object.y = center.y + dX * s + dY * c;
}
}
I have spheres bouncing off each other and the canvas walls, however im struggling on the speed. How would I control the speed? so maybe connected to the beginpath function? so they kind of explode and then bounce everywhere
<script type="text/javascript">
$(function () {
var canvas = $("#target");
var context = canvas.get(0).getContext("2d");
var canvasWidth = canvas.width();
var canvasHeight = canvas.height();
$(window).resize(resizeCanvas);
function resizeCanvas() {
canvas.attr("width", $(window).get(0).innerWidth);
canvas.attr("height", $(window).get(0).innerHeight);
canvasWidth = canvas.width();
canvasHeight = canvas.height();
};
var Sphere = function (x, y, radius, mass, vX, vY) {
this.x = x;
this.y = y;
this.radius = radius;
this.mass = mass;
this.vX = vX;
this.vY = vY;
this.updatePosition = function () {
this.x += this.vX;
this.y += this.vY;
};
this.checkBoundaryCollision = function () {
if (this.x - this.radius < 0) {
this.x = this.radius;
this.vX *= -1;
} else if (this.x + this.radius > canvasWidth) {
this.x = canvasWidth - this.radius;
this.vX *= -1;
}
if (this.y - this.radius < 0) {
this.y = this.radius;
this.vY *= -1;
} else if (this.y + this.radius > canvasHeight) {
this.y = canvasHeight - this.radius;
this.vY *= -1;
}
}
}
resizeCanvas();
var spheresLength = 20;
var spheres = new Array();
function loadContent() {
for (var i = 0; i < spheresLength; i++) {
var x = 20 + (Math.random() * (canvasWidth - 40));
var y = 20 + (Math.random() * (canvasHeight - 40));
var radius = 5 + Math.random() * 10;
var mass = radius / 2;
var vX = Math.random() * 4 - 2;
var vY = Math.random() * 4 - 2;
spheres.push(new Sphere(x, y, radius, mass, vX, vY));
};
animate();
}
loadContent();
function animate() {
update();
draw();
setTimeout(animate, 33);
}
function update() {
for (var i = 0; i < spheresLength; i++) {
var sphere1 = spheres[i];
for (var j = i + 1; j < spheresLength; j++) {
var sphere2 = spheres[j];
var dX = sphere2.x - sphere1.x;
var dY = sphere2.y - sphere1.y;
var distance = Math.sqrt((dX * dX) + (dY * dY));
if (distance < sphere1.radius + sphere2.radius) {
var angle = Math.atan2(dY, dX);
var sine = Math.sin(angle);
var cosine = Math.cos(angle);
var x = 0;
var y = 0;
var xB = dX * cosine + dY * sine;
var yB = dY * cosine - dX * sine;
var vX = sphere1.vX * cosine + sphere1.vY * sine;
var vY = sphere1.vY * cosine - sphere1.vX * sine;
var vXb = sphere2.vX * cosine + sphere2.vY * sine;
var vYb = sphere2.vY * cosine - sphere2.vX * sine;
var vTotal = vX - vXb;
vX = (
(sphere1.mass - sphere2.mass) * vX + 2 * sphere2.mass * vXb
)
/ (sphere1.mass + sphere2.mass);
vXb = vTotal + vX;
xB = x + (sphere1.radius + sphere2.radius);
sphere1.x = sphere1.x + (x * cosine - y * sine);
sphere1.y = sphere1.y + (y * cosine + x * sine);
sphere2.x = sphere1.x + (xB * cosine - yB * sine);
sphere2.y = sphere1.y + (yB * cosine + xB * sine);
sphere1.vX = vX * cosine - vY * sine;
sphere1.vY = vY * cosine + vX * sine;
sphere2.vX = vXb * cosine - vYb * sine;
sphere2.vY = vYb * cosine + vXb * sine;
}
}
sphere1.updatePosition();
sphere1.checkBoundaryCollision();
}
}
function draw() {
context.clearRect(0, 0, canvasWidth, canvasHeight);
context.fillStyle = "rgb(255, 255, 255)";
for (var i = 0; i < spheresLength; i++) {
var sphere = spheres[i];
context.beginPath();
context.arc(sphere.x, sphere.y, sphere.radius, 0, Math.PI * 2);
context.closePath();
context.fill();
}
}
});
</script>
The "speed" of the balls is a function of the distance they travel per frame. This code runs about 3 frames per second, and it looks like the distance is a function of the "mass." You can increase the speed by increasing the factor that determines the distance traveled in each frame (in the update() function.)
Incidentally, I wasn't able to get this code to work. In future, try prototyping on jsFiddle.net or Codepen.io.
UPDATE:
Here's the line that controls the velocity of the balls:
vX = ((sphere1.mass - sphere2.mass) * vX + 2 * sphere2.mass * vXb)
/ (sphere1.mass + sphere2.mass);
That value, 2, is the overall velocity modifier. Small increases to that value correlate to large increases in velocity. Kick it up to 2.25 and watch them fly.
I want to draw a cylinder on canvas with control box to re size the cylinder.
Here's some javascript code I created to answer my own question:
function drawCylinder ( x, y, w, h ) {
context.beginPath(); //to draw the top circle
for (var i = 0 * Math.PI; i < 2 * Math.PI; i += 0.001) {
xPos = (this.x + this.w / 2) - (this.w / 2 * Math.sin(i)) *
Math.sin(0 * Math.PI) + (this.w / 2 * Math.cos(i)) *
Math.cos(0 * Math.PI);
yPos = (this.y + this.h / 8) + (this.h / 8 * Math.cos(i)) *
Math.sin(0 * Math.PI) + (this.h / 8 *
Math.sin(i)) * Math.cos(0 * Math.PI);
if (i == 0) {
context.moveTo(xPos, yPos);
}
else
{
context.lineTo(xPos, yPos);
}
}
context.moveTo(this.x, this.y + this.h / 8);
context.lineTo(this.x, this.y + this.h - this.h / 8);
for (var i = 0 * Math.PI; i < Math.PI; i += 0.001) {
xPos = (this.x + this.w / 2) - (this.w / 2 * Math.sin(i)) * Math.sin(0 * Math.PI) + (this.w / 2 * Math.cos(i)) * Math.cos(0 * Math.PI);
yPos = (this.y + this.h - this.h / 8) + (this.h / 8 * Math.cos(i)) * Math.sin(0 * Math.PI) + (this.h / 8 * Math.sin(i)) * Math.cos(0 * Math.PI);
if (i == 0) {
context.moveTo(xPos, yPos);
}
else
{
context.lineTo(xPos, yPos);
}
}
context.moveTo(this.x + this.w, this.y + this.h / 8);
context.lineTo(this.x + this.w, this.y + this.h - this.h / 8);
context.stroke();
}
Thank you! This is just what I was looking for. While implementing your function in my own code I made some changes like passing in the canvas context as an argument, simplifying the math and getting the code to pass JSLint.
function drawCylinder(ctx, x, y, w, h) {
'use strict';
var i, xPos, yPos, pi = Math.PI, twoPi = 2 * pi;
ctx.beginPath();
for (i = 0; i < twoPi; i += 0.001) {
xPos = (x + w / 2) - (w / 2 * Math.cos(i));
yPos = (y + h / 8) + (h / 8 * Math.sin(i));
if (i === 0) {
ctx.moveTo(xPos, yPos);
} else {
ctx.lineTo(xPos, yPos);
}
}
ctx.moveTo(x, y + h / 8);
ctx.lineTo(x, y + h - h / 8);
for (i = 0; i < pi; i += 0.001) {
xPos = (x + w / 2) - (w / 2 * Math.cos(i));
yPos = (y + h - h / 8) + (h / 8 * Math.sin(i));
if (i === 0) {
ctx.moveTo(xPos, yPos);
} else {
ctx.lineTo(xPos, yPos);
}
}
ctx.moveTo(x + w, y + h / 8);
ctx.lineTo(x + w, y + h - h / 8);
ctx.stroke();
}
If you want to draw a 3D cylinder, the easiest way is to use a library like tQuery (http://jeromeetienne.github.com/tquery/) :
var world = tQuery.createWorld().boilerplate().start();
var object = tQuery. createCylinder().addTo(world);
If you want to draw a '2d' cylinder, you can do so using canvas 2d API to draw a rectangle then a elipse in top of it. It will appear as a cylinder.
var canvas = document.getElementById('canvas')
var ctx = canvas.getContext('2d');
var pos={};
const angleToRadian = function (angle) {
return Math.PI / 180 * angle;
}
var Arc = function (x, y, r, d,s) {
this.r = r;
this.x = x;
this.y = y;
// this.d=d;
ctx.beginPath();
ctx.arc(x, y, r, angleToRadian(0), angleToRadian(180));
ctx.moveTo((Number(x) + Number(r)), y);
// ctx.lineTo((Number(x) + Number(r)), d);
ctx.arc(x, y - d, r, angleToRadian(0), angleToRadian(360));
ctx.moveTo((Number(x)+Number(r)),y);
ctx.lineTo((Number(x)+Number(lX())), ((Number(y)-Number(d))+Number(r)-Number(lY())));
// ctx.moveTo((Number(x)+Number(lX())), ((Number(y)-Number(d))-Number(lY())+Number(r)));
ctx.lineTo((Number(x)+Number(lX())),(Number(y)+Number(r)-Number(lY())));
// ctx.moveTo((Number(x)+Number(lX())),(Number(y)+Number(r)-Number(lY())));
ctx.lineTo(Number(x), ((Number(y)+Number(r))-Number(d)));
// ctx.moveTo(Number(x), ((Number(y)+Number(r))-Number(d)));
ctx.lineTo(Number(x),(Number(y)+Number(r)));
// ctx.moveTo(Number(x),(Number(y)+Number(r)));
ctx.lineTo((Number(x)-Number(lX())), (Number(y)-Number(d)+Number(r)-Number(lY())));
// ctx.moveTo((Number(x)-Number(lX())), (Number(y)-Number(d)+Number(r)-Number(lY())));
ctx.lineTo((Number(x)-Number(lX())), (Number(y)+Number(r)-Number(lY())));
// ctx.moveTo((Number(x)-Number(lX())), (Number(y)+Number(r)-Number(lY())));
ctx.lineTo((Number(x)-Number(r)), (Number(y)-Number(d)));
// ctx.moveTo((Number(x)-Number(r)), (Number(y)-Number(d)));
ctx.lineTo((Number(x)-Number(r)), y);
ctx.strokeStyle = "#9c3028";
ctx.closePath();
// ctx.stroke();
ctx.fillStyle="#9b3028"
ctx.fill();
}
var lY = function () {
return Math.sqrt((Math.pow(((Math.cos(67.5 * Math.PI / 180) * this.r) * 2), 2) -
Math.pow((Math.cos(22.5 * Math.PI / 180) * (Math.cos(67.5 * Math.PI / 180) * this.r) * 2), 2)));
}
var lX = function () {
return Math.sqrt((Math.pow(((Math.cos(67.5 * Math.PI / 180) * this.r) * 2), 2) - (Math.pow(((Math.cos(67.5 * Math.PI / 180) * this.r) * 2), 2) -
Math.pow((Math.cos(22.5 * Math.PI / 180) * (Math.cos(67.5 * Math.PI / 180) * this.r) * 2), 2))));
}
document.addEventListener('mouseup',mouseUp);
document.addEventListener('mousedown',mouseDown);
document.addEventListener('mousemove',draw);
function mouseDown(e){
pos.x=e.clientX;
pos.y=e.clientY;
}
function mouseUp(e){
pos.pozX=e.clientX;
pos.pozY=e.clientY;
}
function draw(e){
if(e.buttons!==1) return;
ctx.clearRect(0,0,500,500);
Arc(pos.x, pos.y, e.clientY, e.clientX);
}
package {
import flash.display.Sprite;
import flash.geom.Point;
import flash.events.Event;
public class Game2 extends Sprite {
var balls:Array;
var radius:Number = 50;
var centerX:Number = stage.stageWidth / 2;
var centerY:Number = stage.stageHeight / 2;
var i:int = 0;
var angle:Number = 0.1;
var sin:Number = Math.sin(angle);
var cos:Number = Math.cos(angle);
public function Game2() {
init();
}
function init():void
{
balls = new Array();
for(i = 0; i < 8; i++)
{
var ball:Ball = new Ball(10, 0x00FF00);
var xposition = centerX + Math.cos(i / 8 * Math.PI * 2) * radius;
var yposition = centerY + Math.sin(i / 8 * Math.PI * 2) * radius;
ball.x = xposition;
ball.y = yposition;
addChild(ball);
balls.push(ball);
}
addEventListener(Event.ENTER_FRAME, onEnterFrame);
}
function onEnterFrame(e:Event):void
{
for(i = 0; i < balls.length; i++)
{
var ball:Ball = balls[i];
var x1:Number = ball.x - stage.stageWidth / 2;
var y1:Number = ball.y - stage.stageHeight / 2;
var x2:Number = cos * x1 - sin * y1;
var y2:Number = cos * y1 + sin * x1;
ball.x = stage.stageWidth / 2 + x2;
ball.y = stage.stageHeight / 2 + y2;
}
}
}
}
Can someone explain the work of this formula?:
var x2:Number = cos * x1 - sin * y1;
var y2:Number = cos * y1 + sin * x1;
i just can't figure it out, if we edit it like this:
var x2:Number = x1 - y1;
var y2:Number = x1 + y1;
all the balls are moving so fast and get out of screen bounds, and also why if we change it like this:
var x2:Number = cos * x1 - sin * y1;
var y2:Number = cos * y1 + sin * x1;
or
var x2:Number = cos * x1 - sin * y1;
var y2:Number = cos * y1 + sin * x1;
it will work equal, as far as i understanded is that here happens some kind of simetry, if we are on the left or right sides the velocity x == 0 and y is at the maximum velocity of its position the y slows down each time he get closer to the top or bottom, if we are on the top or bottom the velocity y == 0 and x is at maximum speed of his position then also slows down each time he gets closer to the right or left sides, i traced it, but i can't understand why we have to multiply it by cos and sin, i've traced this moments but still can't figure it out, can anyone explain this moment?
The two formulas represent a rotation matrix multiplied with a vector.
If I'd like to make a circle with particles, I'd define random coordinates for particles like this:
for(var i:int = 0; i != 100; i++)
{
var angle:Number = Math.random() * 360;
var r:Number = 600;
var nX:Number = r * Math.cos(angle / 180 * Math.PI);
var nY:Number = r * Math.sin(angle / 180 * Math.PI);
}
But I want to make a ball with particles on 3d space but I don't know how to define random coordinates for particles. Radius is fixed again but there should be a "nZ" value. Can you help me to define these coordinates?
for(var i:int = 0; i != 100; i++)
{
var angle:Number = Math.random() * 360;
var r:Number = 600;
var nX:Number = ???
var nY:Number = ???
var nZ:Number = ???
}
Thanks in advance...
Spherical coordinates are what you want.
You need two angles:
for(var i:int = 0; i != 100; i++)
{
var azimuthAngle:Number = Math.random() * 360;
var elevationAngle:Number = (Math.random() * 180) - 90;
var r:Number = 600;
var nX:Number =
r * Math.cos(azimuthAngle / 180 * Math.PI) * Math.sin(elevationAngle / 180 * Math.PI);
var nY:Number =
r * Math.sin(azimuthAngle / 180 * Math.PI) * Math.sin(elevationAngle / 180 * Math.PI);
var nZ:Number =
r * Math.cos(elevationAngle / 180 * Math.PI);
}