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<h2>How to know when 2 rotated rects are colliding ?</h2>
<div class="flex-container">
<canvas id="canvas" width="500" height="500"></canvas>
<div id="settings">
<h2>Settings</h2>
<div class="actions">
<a href="#play" class="action" data-action="play"><i class="fa fa-play"></i></a>
<a href="#pause" class="action" data-action="pause"><i class="fa fa-pause"></i></a>
</div>
<!-- Setting Rect Template -->
<div id="rect-settings">
<div id="rect-settings-template" class="rect-settings" style="--primary-color: blue;">
<h3 class="title"></h3>
<div class="flex">
<div>
<h4>Position</h4>
<div class="input">
<span>X:</span>
<input type="range" class="x" min="0" max="1000"/>
<span class="x-value"></span>
</div>
<div class="input">
<span>Y:</span>
<input type="range" class="y" min="0" max="1000"/>
<span class="y-value"></span>
</div>
</div>
<div>
<h4>Size</h4>
<div class="input">
<span>W:</span>
<input type="range" class="w" min="0" max="500"/>
<span class="w-value"></span>
</div>
<div class="input">
<span>H:</span>
<input type="range" class="h" min="0" max="500"/>
<span class="h-value"></span>
</div>
</div>
</div>
<div class="flex">
<div>
<h4>Rotation</h4>
<div class="input">
<span>Angle:</span>
<input type="range" class="angle" min="-360" max="360"/>
<span class="angle-value"></span>
</div>
<div class="input">
<span>Speed:</span>
<input type="range" class="speed" min="-90" max="90"/>
<span class="speed-value"></span>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
@import url(https://fonts.googleapis.com/css?family=Overpass+Mono&display=swap);
@import url(https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css);
* { margin:0; padding:0; } /* to remove the top and left whitespace */
html, body { width:100%; height:100%; } /* just to be sure these are full screen*/
canvas { display:block; flex-basis: 50%;} /* To remove the scrollbars */
body {
font-family: 'Overpass Mono', monospace;
}
h2 {
padding: 1em 0;
}
.flex-container {display:flex;}
.flex-container > * {flex-grow:1}
#settings {
flex-basis: 50%;
overflow: auto;
padding: 1em;
margin-top: 1px;
border-left: 1px solid #DDD;
border-top: 1px solid #DDD;
background: #F3F3F3;
}
a {
color: #666;
text-decoration: none;
}
.actions {
text-align: center;
}
h2, h3, h4 {
text-transform: uppercase;
text-align: center;
font-weight: 100;
}
h2, h3 {
color: var(--primary-color);
}
h4 {
color: #555;
}
.rect-settings {
margin: 1.5em 0;
padding: .5em;
border: 1px solid #DFDFDF;
background-color: #f6f6f6;
}
.rect-settings .flex {
margin-top: 1em;
display: flex;
}
.rect-settings .flex > * {
flex-grow: 1;
padding: 0 1em;
}
.rect-settings .input {
display: flex;
}
.rect-settings .input > * {
padding: 0 0.5em;
}
.rect-settings input[type="range"] {
flex-grow: 1;
flex-basis: 50%;
}
.rect-settings .input span:first-child, .rect-settings .label {
color: var(--primary-color);
}
.rect-settings .input span:last-child {
display: inline-block;
flex-basis: 75px;
}
.rect-settings ul {
margin: .5em 0 0 2em;
}
// Helpers
const toRadians = (degrees) => degrees * Math.PI / 180;
const toDegrees = (radians) => radians * 180 / Math.PI;
// .1 - .3 > -0.19999999999999998
// fixFloat(.1 - .3) > -0.2
const fixFloat = (number, precision=Math.log10(1/Number.EPSILON)) => number ? parseFloat(number.toFixed(precision)) : 0;
// Utils
class Vector {
constructor({x=0,y=0}={}) {
this.x = x;
this.y = y;
}
get magnitude() {
return Math.sqrt(this.x * this.x + this.y * this.y);
}
// Add(5)
// Add(Vector)
// Add({x, y})
Add(factor) {
const f = typeof factor === 'object'
? { x:0, y:0, ...factor}
: {x:factor, y:factor}
return new Vector({
x: this.x + f.x,
y: this.y + f.y,
})
}
Minus(factor) {
const f = typeof factor === 'object'
? { x:0, y:0, ...factor}
: {x:factor, y:factor}
return new Vector({
x: this.x - f.x,
y: this.y - f.y,
})
}
// Multiply(5)
// Multiply(Vector)
// Multiply({x, y})
Multiply(factor) {
// @LATER: Use an helper in order to transform `factor`
// into a Vector of same Dimensions than this
const f = typeof factor === 'object'
? { x:0, y:0, ...factor}
: {x:factor, y:factor}
return new Vector({
x: this.x * f.x,
y: this.y * f.y,
})
}
Rotate(theta) {
// https://en.wikipedia.org/wiki/Rotation_matrix#In_two_dimensions
return new Vector({
x: this.x * Math.cos(theta) - this.y * Math.sin(theta),
y: this.x * Math.sin(theta) + this.y * Math.cos(theta),
});
}
// Todo: Use scalar product
Project(line) {
let dotvalue = line.direction.x * (this.x - line.origin.x)
+ line.direction.y * (this.y - line.origin.y);
return new Vector({
x: line.origin.x + line.direction.x * dotvalue,
y: line.origin.y + line.direction.y * dotvalue,
})
}
}
class Line {
constructor({x=0,y=0, dx=0, dy=0}) {
this.origin = new Vector({x,y});
this.direction = new Vector({x:dx,y:dy});
}
}
class Rect {
constructor({
x=0, y=0, w=10, h=10,
// 0 is Horizontal to right (following OX) - Rotate clockwise
theta=null, angle=0, // theta (rad) or angle (deg)
rgb='0,0,0'
}) {
this.center = new Vector({x,y});
this.size = new Vector({x:w,y:h});
this.theta = theta || toRadians(angle);
this.rgb = rgb;
}
getAxis() {
const OX = new Vector({x:1, y:0});
const OY = new Vector({x:0, y:1});
const RX = OX.Rotate(this.theta);
const RY = OY.Rotate(this.theta);
return [
new Line({...this.center, dx: RX.x, dy: RX.y}),
new Line({...this.center, dx: RY.x, dy: RY.y}),
];
}
getCorners() {
const axis = this.getAxis();
const RX = axis[0].direction.Multiply(this.size.x/2);
const RY = axis[1].direction.Multiply(this.size.y/2);
return [
this.center.Add(RX).Add(RY),
this.center.Add(RX).Add(RY.Multiply(-1)),
this.center.Add(RX.Multiply(-1)).Add(RY.Multiply(-1)),
this.center.Add(RX.Multiply(-1)).Add(RY),
]
}
}
// Demo App
const Settings = {
root:null,
TemplateSettings: null,
rectSettings: [], // Settings per rect {el: DOM Element, refs: {}, settings: {}}
settings: {}, // Global settings
init ({settings, rects, onPlay, onPause, onRectChange}) {
Settings.root = document.getElementById('rect-settings');
Settings.TemplateSettings = document.getElementById('rect-settings-template');
Settings.settings = settings;
// Clean
Settings.root.innerHTML = "";
// Create from Template
Settings.rectSettings = rects.map((rect, idx) => {
return cloneTemplate({rect, idx});
});
// Append all
Settings.rectSettings.forEach(rectSetting => {
Settings.root.appendChild(rectSetting.el);
addRectSettingEvents(rectSetting, onRectChange);
});
// Actions
Array.from(document.getElementsByClassName('action')).forEach(action => {
action.addEventListener('click', () => {
if (action.dataset.action == "play") {
onPlay && onPlay();
}
else if (action.dataset.action == "pause") {
onPause && onPause();
}
})
})
},
// Values has been updated
refresh(rects) {
Settings.rectSettings.forEach(rectSetting => {
refreshSetting({
...rectSetting,
settings: rects[rectSetting.idx],
});
});
},
// Manually refresh settings for moving rect.
refreshOnMove(rect) {
// Manually redraw settings.
document.querySelector('#rect-1 input[type="range"].x').value = parseInt(rect.x);
document.querySelector('#rect-1 input[type="range"].y').value = parseInt(rect.y);
document.querySelector('#rect-1 .x-value').innerHTML = parseInt(rect.x);
document.querySelector('#rect-1 .y-value').innerHTML = parseInt(rect.y);
},
get(key){
return Settings.settings[key];
},
};
const cloneTemplate = ({rect, idx}) => {
let el = Settings.TemplateSettings.cloneNode(true);
const classes = [
'title',
'x', 'y', 'w', 'h', 'angle', 'speed',
'x-value', 'y-value', 'w-value', 'h-value', 'angle-value', 'speed-value',
'axes', 'corners'
];
let rectSetting = {
el,
refs: Object.fromEntries(classes.map(key => [key, Array.from(el.getElementsByClassName(key))[0]])),
idx,
settings: rect
}
// Attr
el.id = `rect-${idx}`;
el.style=`--primary-color:rgb(${rect.rgb})`;
// Title
rectSetting.refs.title.innerHTML = rect.label;
refreshSetting(rectSetting);
return rectSetting;
}
// Refresh DOM
const toLi = arr => `<ul>${arr.map(item => `<li>${item}</li>`).join('')}</ul>`;
const renderLabel = (label, value) => `<span class="label">${label}:</span> ${fixFloat(value, 2)}`;
const refreshSetting = ({ refs, settings}, skipInputs=false) => {
const classes = [
'x', 'y', 'w', 'h', 'angle', 'speed',
];
classes.forEach(key => {
if (!skipInputs) {
refs[key].value = parseInt(settings[key]) || 0;
}
refs[`${key}-value`].innerHTML = fixFloat(settings[key], 2);
});
};
const addRectSettingEvents = (rectSetting, onRectChange) => {
const classes= [
'x', 'y', 'w', 'h', 'angle', 'speed',
];
rectSetting.el.querySelectorAll('input[type="range"]').forEach(input => {
input.addEventListener('input', () => {
// Update rect with settings
const rect = {
...rectSetting.settings,
...Object.fromEntries(classes.map(key => [
key,
parseFloat(rectSetting.refs[key].value),
])),
};
// Refresh labels (without inputs)
refreshSetting({...rectSetting, settings: rect}, true);
// Propagate
onRectChange({
idx: rectSetting.idx,
rect,
})
});
})
};
const CanvasResize = (function({canvas, onRezise, x, y}={}) {
// resize the canvas to fill browser window dynamically
window.addEventListener("resize", resizeCanvas, false);
function resizeCanvas() {
canvas.width = window.innerWidth * (x || 1);
canvas.height = window.innerHeight * (y || 1);
onRezise && onRezise();
}
resizeCanvas();
});
const Canvas = {
canvas: null,
ctx: null,
init(canvas) {
Canvas.canvas = canvas;
Canvas.ctx = Canvas.canvas.getContext('2d');
return Canvas.canvas;
},
clean() {
Canvas.ctx.clearRect(0, 0, Canvas.canvas.width, Canvas.canvas.height);
},
draw(rects) {
// Get isColligind using lib function (no visual)
const isColliding = isRectCollide(rects[0], rects[1]);
// Visual Example:
Canvas.clean();
// Map in order to use Class Rect
const rs = rects.map(rect => new Rect(rect))
rs.forEach((rect, idx) => {
Canvas.drawRect(rect, isColliding);
Canvas.drawAxis(rect);
Canvas.drawCorners(rect);
});
Canvas.drawProjections({rect: rs[0], onRect: rs[1]})
Canvas.drawProjections({rect: rs[1], onRect: rs[0]});
},
drawRect(rect, isColliding) {
Canvas.ctx.save();
// Draw Rect
Canvas.ctx.translate(rect.center.x, rect.center.y);
Canvas.ctx.rotate( rect.theta );
Canvas.ctx.fillStyle = `rgba( ${isColliding ? '255,0,0' : rect.rgb },.2)`;
Canvas.ctx.fillRect(rect.size.x / -2, rect.size.y / -2, rect.size.x, rect.size.y);
Canvas.ctx.restore();
},
drawAxis(rect) {
const axis = rect.getAxis();
axis.forEach(a => {
Canvas.drawLine({
from: a.origin.Add(a.direction.Multiply(-1000)),
to: a.origin.Add(a.direction.Multiply(1000)),
rgb: rect.rgb,
});
});
},
drawLine({
from, to,
rgb=null, rgba=null
}) {
Canvas.ctx.save();
Canvas.ctx.translate(from.x, from.y);
Canvas.ctx.beginPath();
Canvas.ctx.strokeStyle = rgba ? `rgba(${rgba})` : `rgba(${rgb}, 1)`;
Canvas.ctx.moveTo(0, 0);
Canvas.ctx.lineTo(to.x - from.x, to.y - from.y);
Canvas.ctx.stroke();
Canvas.ctx.restore();
},
drawCorners(rect) {
rect.getCorners().forEach(corner => {
Canvas.drawPoint({...corner, rgb: rect.rgb});
})
},
drawPoint({x,y, rgb}) {
Canvas.ctx.save();
Canvas.ctx.translate(x, y);
Canvas.ctx.beginPath();
Canvas.ctx.fillStyle = `rgba(${rgb},1)`;
Canvas.ctx.arc(0, 0, 2, 0, Math.PI*2, true);
Canvas.ctx.closePath();
Canvas.ctx.fill();
Canvas.ctx.restore();
},
drawProjections({rect, onRect}) {
const lines = onRect.getAxis();
const corners = rect.getCorners();
lines.forEach((line, dimension) => {
let futhers = {min:null, max:null};
// Size of onRect half size on line direction
const rectHalfSize = (dimension === 0 ? onRect.size.x : onRect.size.y) / 2;
corners.forEach(corner => {
const projected = corner.Project(line);
const CP = projected.Minus(onRect.center);
// Sign: Same directon of OnRect axis : true.
const sign = (CP.x * line.direction.x) + (CP.y * line.direction.y) > 0;
const signedDistance = CP.magnitude * (sign ? 1 : -1);
if (!futhers.min || futhers.min.signedDistance > signedDistance) {
futhers.min = {signedDistance, corner, projected};
}
if (!futhers.max || futhers.max.signedDistance < signedDistance) {
futhers.max = {signedDistance, corner, projected};
}
});
// Draw min/max projecteds corners
Canvas.drawPoint({...futhers.min.projected, rgb: rect.rgb});
Canvas.drawLine({from: futhers.min.corner, to: futhers.min.projected, rgba: `${rect.rgb},.2`});
Canvas.drawPoint({...futhers.max.projected, rgb: rect.rgb});
Canvas.drawLine({from: futhers.max.corner, to: futhers.max.projected, rgba: `${rect.rgb},.2`});
// Projection collide ?
const projectionCollide = (futhers.min.signedDistance < 0 && futhers.max.signedDistance > 0
|| Math.abs(futhers.min.signedDistance) < rectHalfSize
|| Math.abs(futhers.max.signedDistance) < rectHalfSize);
const w = Canvas.ctx.lineWidth;
Canvas.ctx.lineWidth = 2;
// Draw projection line on other Rect axis
Canvas.drawLine({
from: futhers.min.projected,
to: futhers.max.projected,
rgb: projectionCollide ? '255,0,0' : rect.rgb,
});
Canvas.ctx.lineWidth = w;
});
},
};
// App
let rects = [
{x:200, y: 250, w:250, h:200, angle: 60, speed: -10, rgb: '50,100,225', label:"Fixed Rect"},
{x:350, y: 100, w:50, h:125, angle: -10, rgb: '220,150,5', label:"Cursor Rect"},
];
const App = {
runId: null,
init() {
let canvas = document.getElementById("canvas");
Canvas.init(canvas);
CanvasResize({
canvas,
onRezise: App.draw,
x: .5
});
Settings.init({
settings: {FPS: 60},
rects,
onPlay: App.play,
onPause: App.pause,
onRectChange: App.updateRectFromSettings,
});
canvas.addEventListener('mousemove', e => {
rects[1].x = e.offsetX;
rects[1].y = e.offsetY;
App.draw();
Settings.refreshOnMove(rects[1]);
});
App.play();
},
play() {
if (!App.runId) {
App.runId = setInterval(App.run, 1000 / Settings.get('FPS'));
}
},
pause() {
if (App.runId) {
clearInterval(App.runId);
App.runId = null;
}
},
run() {
rects = rects.map(rotateRect)
Settings.refresh(rects);
App.draw();
// Test and log result (without any display)
if (isRectCollide(rects[0], rects[1]))
console.log("Both rects are colliding");
else
console.log("Both rects are NOT colliding");
},
draw() {
Canvas.draw(rects);
},
updateRectFromSettings({rect, idx}) {
rects[idx] = rect;
App.draw();
}
};
const rotateRect = (rect) => {
if (rect.speed) {
rect.angle += rect.speed / Settings.get('FPS');
}
rect.angle %= 360;
return rect;
};
const isRectCollide = (rectA, rectB) => {
const rA = typeof rectA !== Rect ? new Rect(rectA) : rectA;
const rB = typeof rectB !== Rect ? new Rect(rectB) : rectB;
return isProjectionCollide({rect: rA, onRect: rB})
&& isProjectionCollide({rect: rB, onRect: rA});
};
const isProjectionCollide = ({rect, onRect}) => {
const lines = onRect.getAxis();
const corners = rect.getCorners();
let isCollide = true;
lines.forEach((line, dimension) => {
let futhers = {min:null, max:null};
// Size of onRect half size on line direction
const rectHalfSize = (dimension === 0 ? onRect.size.x : onRect.size.y) / 2;
corners.forEach(corner => {
const projected = corner.Project(line);
const CP = projected.Minus(onRect.center);
// Sign: Same directon of OnRect axis : true.
const sign = (CP.x * line.direction.x) + (CP.y * line.direction.y) > 0;
const signedDistance = CP.magnitude * (sign ? 1 : -1);
if (!futhers.min || futhers.min.signedDistance > signedDistance) {
futhers.min = {signedDistance, corner, projected};
}
if (!futhers.max || futhers.max.signedDistance < signedDistance) {
futhers.max = {signedDistance, corner, projected};
}
});
if (!(futhers.min.signedDistance < 0 && futhers.max.signedDistance > 0
|| Math.abs(futhers.min.signedDistance) < rectHalfSize
|| Math.abs(futhers.max.signedDistance) < rectHalfSize)) {
isCollide = false;
}
});
return isCollide;
};
// Finaly run
App.init();
Also see: Tab Triggers