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I am trying to make my own 3D renderer in JavaScript using raycasting, but despite checking over the math and the code countless times, it still does not seem to be working. I've tried everything I possibly could to get this thing to work and it won't, so I'm hoping someone else can figure it out.
My code runs an Update method every frame, increasing the yaw (Camera.Rot.Yaw) by 0.1 radians every iteration, but it ends up looking weird and unrealistic, and I can't figure out why. Sorry if it's confusing and long, I can't really think of a way to make a minimal reproducible example of this.
This is the Update method:
Update(Canvas, Ctx, Map, Camera) {
var id = Ctx.getImageData(0, 0, Canvas.width, Canvas.height);
var Pixels = id.data;
//Distance of projection plane from camera
//It should be behind I think
var PlaneDist = 64;
//Divides the second slopes by this so each ray goes a shorter
//distance each iteration, effectively increasing quality
var Quality = 160;
//The midpoint of the projection plane for each coordinate
var MidX =
Camera.Pos.X +
PlaneDist * Math.cos(Camera.Rot.Pitch) * Math.cos(Camera.Rot.Yaw);
var MidY = Camera.Pos.Y + PlaneDist * Math.sin(Camera.Rot.Pitch);
var MidZ =
Camera.Pos.Z +
PlaneDist * Math.cos(Camera.Rot.Pitch) * Math.sin(Camera.Rot.Yaw);
//Slopes to get to other points on the projection plane
var SlopeX =
Math.sin(Camera.Rot.Yaw) +
(Canvas.height / Canvas.width) *
Math.cos(Camera.Rot.Yaw) *
Math.sin(Camera.Rot.Pitch);
var SlopeY = -Math.cos(Camera.Rot.Pitch);
var SlopeZ =
Math.cos(Camera.Rot.Yaw) +
(Canvas.height / Canvas.width) *
Math.sin(Camera.Rot.Yaw) *
Math.sin(Camera.Rot.Pitch);
//Loops for every point on the projection plane
for (let i = 0; i < Canvas.height; i++) {
for (let j = 0; j < Canvas.width; j++) {
let NewX = Camera.Pos.X;
let NewY = Camera.Pos.Y;
let NewZ = Camera.Pos.Z;
//Slopes for the actual ray to follow, just the distance between
//the plane point and the camera divided by quality
let SlopeX2 = (Camera.Pos.X-(MidX - SlopeX * (j - Canvas.width / 2)))/ Quality;
let SlopeY2 = (Camera.Pos.Y-(MidY - SlopeY * (i - Canvas.height / 2))) / Quality;
let SlopeZ2 = (Camera.Pos.Z-(MidZ - SlopeZ * (j - Canvas.width / 2)))/ Quality;
//Ray's current map position, divides the map into a 16x32x16
//list of blocks (map initialization shown elsewhere)
let MapPos =
Map.MData[0][Math.floor(NewX / 16) + 2][Math.floor(NewY / 16)][
Math.floor(NewZ / 16)
];
//Iterates until ray either hits a block with max opacity, or
//hits the boundary of the map
while (
MapPos[3] !== 255 &&
NewX + SlopeX2 < 256 &&
NewY + SlopeY2 < 512 &&
NewZ + SlopeZ2 < 256 &&
NewX + SlopeX2 >= 0 &&
NewY + SlopeY2 >= 0 &&
NewZ + SlopeZ2 >= 0
) {
//Advances ray's current position according to slopes
NewX += SlopeX2;
NewY += SlopeY2;
NewZ += SlopeZ2;
MapPos =
Map.MData[0][Math.floor(NewX / 16) + 2][Math.floor(NewY / 16)][
Math.floor(NewZ / 16)
];
}
//Sets pixel on screen to the color of the block the ray hit
//or just white (opacity 0) if it hit the boundary
Pixels[(i * id.width + j) * 4] = MapPos[0];
Pixels[(i * id.width + j) * 4 + 1] = MapPos[1];
Pixels[(i * id.width + j) * 4 + 2] = MapPos[2];
Pixels[(i * id.width + j) * 4 + 3] = MapPos[3];
}
}
//Displays the final image
Ctx.putImageData(id, 0, 0);
}
The map initialization (CreateChunk) looks like this:
constructor() {
this.MData = [];
}
CreateChunk(X, Y) {
let Chunk = [X, Y];
for (let x = 0; x < 16; x++) {
let Plane = [];
for (let y = 0; y < 32; y++) {
let Row = [];
for (let z = 0; z < 16; z++) {
//Colors are just to help tell which pixels are at what coordinates
if (y < 8) Row.push([x * 15, y * 7, z * 15, 255]);
else Row.push([0, 0, 0, 0]);
}
Plane.push(Row);
}
Chunk.push(Plane);
}
this.MData.push(Chunk);
}
I'm hoping it's just some coding mistake I've made, but despite my countless checks it may be the trigonometry that's wrong.
I am visualising flight paths with D3 and Canvas. In short, I have data for each flight's origin and destination
as well as the airport coordinates. The ideal end state is to have an indiviudal circle representing a plane moving
along each flight path from origin to destination. The current state is that each circle gets visualised along the path,
yet the removal of the previous circle along the line does not work as clearRect gets called nearly constantly.
Current state:
Ideal state (achieved with SVG):
The Concept
Conceptually, an SVG path for each flight is produced in memory using D3's custom interpolation with path.getTotalLength() and path.getPointAtLength() to move the circle along the path.
The interpolator returns the points along the path at any given time of the transition. A simple drawing function takes these points and draws the circle.
Key functions
The visualisation gets kicked off with:
od_pairs.forEach(function(el, i) {
fly(el[0], el[1]); // for example: fly('LHR', 'JFK')
});
The fly() function creates the SVG path in memory and a D3 selection of a circle (the 'plane') - also in memory.
function fly(origin, destination) {
var pathElement = document.createElementNS(d3.namespaces.svg, 'path');
var routeInMemory = d3.select(pathElement)
.datum({
type: 'LineString',
coordinates: [airportMap[origin], airportMap[destination]]
})
.attr('d', path);
var plane = custom.append('plane');
transition(plane, routeInMemory.node());
}
The plane gets transitioned along the path by the custom interpolater in the delta() function:
function transition(plane, route) {
var l = route.getTotalLength();
plane.transition()
.duration(l * 50)
.attrTween('pointCoordinates', delta(plane, route))
// .on('end', function() { transition(plane, route); });
}
function delta(plane, path) {
var l = path.getTotalLength();
return function(i) {
return function(t) {
var p = path.getPointAtLength(t * l);
draw([p.x, p.y]);
};
};
}
... which calls the simple draw() function
function draw(coords) {
// contextPlane.clearRect(0, 0, width, height); << how to tame this?
contextPlane.beginPath();
contextPlane.arc(coords[0], coords[1], 1, 0, 2*Math.PI);
contextPlane.fillStyle = 'tomato';
contextPlane.fill();
}
This results in an extending 'path' of circles as the circles get drawn yet not removed as shown in the first gif above.
Full code here: http://blockbuilder.org/larsvers/8e25c39921ca746df0c8995cce20d1a6
My question is, how can I achieve to draw only a single, current circle while the previous circle gets removed without interrupting other circles being drawn on the same canvas?
Some failed attempts:
The natural answer is of course context.clearRect(), however, as there's a time delay (roughly a milisecond+) for each circle to be drawn as it needs to get through the function pipeline clearRect gets fired almost constantly.
I tried to tame the perpetual clearing of the canvas by calling clearRect only at certain intervals (Date.now() % 10 === 0 or the like) but that leads to no good either.
Another thought was to calculate the previous circle's position and remove the area specifically with a small and specific clearRect definition within each draw() function.
Any pointers very much appreciated.
Handling small dirty regions, especially if there is overlap between objects quickly becomes very computationally heavy.
As a general rule, a average Laptop/desktop can easily handle 800 animated objects if the computation to calculate position is simple.
This means that the simple way to animate is to clear the canvas and redraw every frame. Saves a lot of complex code that offers no advantage over the simple clear and redraw.
const doFor = (count,callback) => {var i=0;while(i < count){callback(i++)}};
function createIcon(drawFunc){
const icon = document.createElement("canvas");
icon.width = icon.height = 10;
drawFunc(icon.getContext("2d"));
return icon;
}
function drawPlane(ctx){
const cx = ctx.canvas.width / 2;
const cy = ctx.canvas.height / 2;
ctx.beginPath();
ctx.strokeStyle = ctx.fillStyle = "red";
ctx.lineWidth = cx / 2;
ctx.lineJoin = "round";
ctx.lineCap = "round";
ctx.moveTo(cx/2,cy)
ctx.lineTo(cx * 1.5,cy);
ctx.moveTo(cx,cy/2)
ctx.lineTo(cx,cy*1.5)
ctx.stroke();
ctx.lineWidth = cx / 4;
ctx.moveTo(cx * 1.7,cy * 0.6)
ctx.lineTo(cx * 1.7,cy*1.4)
ctx.stroke();
}
const planes = {
items : [],
icon : createIcon(drawPlane),
clear(){
planes.items.length = 0;
},
add(x,y){
planes.items.push({
x,y,
ax : 0, // the direction of the x axis of this plane
ay : 0,
dir : Math.random() * Math.PI * 2,
speed : Math.random() * 0.2 + 0.1,
dirV : (Math.random() - 0.5) * 0.01, // change in direction
})
},
update(){
var i,p;
for(i = 0; i < planes.items.length; i ++){
p = planes.items[i];
p.dir += p.dirV;
p.ax = Math.cos(p.dir);
p.ay = Math.sin(p.dir);
p.x += p.ax * p.speed;
p.y += p.ay * p.speed;
}
},
draw(){
var i,p;
const w = canvas.width;
const h = canvas.height;
for(i = 0; i < planes.items.length; i ++){
p = planes.items[i];
var x = ((p.x % w) + w) % w;
var y = ((p.y % h) + h) % h;
ctx.setTransform(-p.ax,-p.ay,p.ay,-p.ax,x,y);
ctx.drawImage(planes.icon,-planes.icon.width / 2,-planes.icon.height / 2);
}
}
}
const ctx = canvas.getContext("2d");
function mainLoop(){
if(canvas.width !== innerWidth || canvas.height !== innerHeight){
canvas.width = innerWidth;
canvas.height = innerHeight;
planes.clear();
doFor(800,()=>{ planes.add(Math.random() * canvas.width, Math.random() * canvas.height) })
}
ctx.setTransform(1,0,0,1,0,0);
// clear or render a background map
ctx.clearRect(0,0,canvas.width,canvas.height);
planes.update();
planes.draw();
requestAnimationFrame(mainLoop)
}
requestAnimationFrame(mainLoop)
canvas {
position : absolute;
top : 0px;
left : 0px;
}
<canvas id=canvas></canvas>
800 animated points
As pointed out in the comments some machines may be able to draw a circle if one colour and all as one path slightly quicker (not all machines). The point of rendering an image is that it is invariant to the image complexity. Image rendering is dependent on the image size but colour and alpha setting per pixel have no effect on rendering speed. Thus I have changed the circle to show the direction of each point via a little plane icon.
Path follow example
I have added a way point object to each plane that in the demo has a random set of way points added. I called it path (could have used a better name) and a unique path is created for each plane.
The demo is to just show how you can incorporate the D3.js interpolation into the plane update function. The plane.update now calls the path.getPos(time) which returns true if the plane has arrived. If so the plane is remove. Else the new plane coordinates are used (stored in the path object for that plane) to set the position and direction.
Warning the code for path does little to no vetting and thus can easily be made to throw an error. It is assumed that you write the path interface to the D3.js functionality you want.
const doFor = (count,callback) => {var i=0;while(i < count){callback(i++)}};
function createIcon(drawFunc){
const icon = document.createElement("canvas");
icon.width = icon.height = 10;
drawFunc(icon.getContext("2d"));
return icon;
}
function drawPlane(ctx){
const cx = ctx.canvas.width / 2;
const cy = ctx.canvas.height / 2;
ctx.beginPath();
ctx.strokeStyle = ctx.fillStyle = "red";
ctx.lineWidth = cx / 2;
ctx.lineJoin = "round";
ctx.lineCap = "round";
ctx.moveTo(cx/2,cy)
ctx.lineTo(cx * 1.5,cy);
ctx.moveTo(cx,cy/2)
ctx.lineTo(cx,cy*1.5)
ctx.stroke();
ctx.lineWidth = cx / 4;
ctx.moveTo(cx * 1.7,cy * 0.6)
ctx.lineTo(cx * 1.7,cy*1.4)
ctx.stroke();
}
const path = {
wayPoints : null, // holds way points
nextTarget : null, // holds next target waypoint
current : null, // hold previously passed way point
x : 0, // current pos x
y : 0, // current pos y
addWayPoint(x,y,time){
this.wayPoints.push({x,y,time});
},
start(){
if(this.wayPoints.length > 1){
this.current = this.wayPoints.shift();
this.nextTarget = this.wayPoints.shift();
}
},
getNextTarget(){
this.current = this.nextTarget;
if(this.wayPoints.length === 0){ // no more way points
return;
}
this.nextTarget = this.wayPoints.shift(); // get the next target
},
getPos(time){
while(this.nextTarget.time < time && this.wayPoints.length > 0){
this.getNextTarget(); // get targets untill the next target is ahead in time
}
if(this.nextTarget.time < time){
return true; // has arrivecd at target
}
// get time normalised ove time between current and next
var timeN = (time - this.current.time) / (this.nextTarget.time - this.current.time);
this.x = timeN * (this.nextTarget.x - this.current.x) + this.current.x;
this.y = timeN * (this.nextTarget.y - this.current.y) + this.current.y;
return false; // has not arrived
}
}
const planes = {
items : [],
icon : createIcon(drawPlane),
clear(){
planes.items.length = 0;
},
add(x,y){
var p;
planes.items.push(p = {
x,y,
ax : 0, // the direction of the x axis of this plane
ay : 0,
path : Object.assign({},path,{wayPoints : []}),
})
return p; // return the plane
},
update(time){
var i,p;
for(i = 0; i < planes.items.length; i ++){
p = planes.items[i];
if(p.path.getPos(time)){ // target reached
planes.items.splice(i--,1); // remove
}else{
p.dir = Math.atan2(p.y - p.path.y, p.x - p.path.x) + Math.PI; // add 180 because i drew plane wrong way around.
p.ax = Math.cos(p.dir);
p.ay = Math.sin(p.dir);
p.x = p.path.x;
p.y = p.path.y;
}
}
},
draw(){
var i,p;
const w = canvas.width;
const h = canvas.height;
for(i = 0; i < planes.items.length; i ++){
p = planes.items[i];
var x = ((p.x % w) + w) % w;
var y = ((p.y % h) + h) % h;
ctx.setTransform(-p.ax,-p.ay,p.ay,-p.ax,x,y);
ctx.drawImage(planes.icon,-planes.icon.width / 2,-planes.icon.height / 2);
}
}
}
const ctx = canvas.getContext("2d");
function mainLoop(time){
if(canvas.width !== innerWidth || canvas.height !== innerHeight){
canvas.width = innerWidth;
canvas.height = innerHeight;
planes.clear();
doFor(810,()=>{
var p = planes.add(Math.random() * canvas.width, Math.random() * canvas.height);
// now add random number of way points
var timeP = time;
// info to create a random path
var dir = Math.random() * Math.PI * 2;
var x = p.x;
var y = p.y;
doFor(Math.floor(Math.random() * 80 + 12),()=>{
var dist = Math.random() * 5 + 4;
x += Math.cos(dir) * dist;
y += Math.sin(dir) * dist;
dir += (Math.random()-0.5)*0.3;
timeP += Math.random() * 1000 + 500;
p.path.addWayPoint(x,y,timeP);
});
// last waypoin at center of canvas.
p.path.addWayPoint(canvas.width / 2,canvas.height / 2,timeP + 5000);
p.path.start();
})
}
ctx.setTransform(1,0,0,1,0,0);
// clear or render a background map
ctx.clearRect(0,0,canvas.width,canvas.height);
planes.update(time);
planes.draw();
requestAnimationFrame(mainLoop)
}
requestAnimationFrame(mainLoop)
canvas {
position : absolute;
top : 0px;
left : 0px;
}
<canvas id=canvas></canvas>
800 animated points
#Blindman67 is correct, clear and redraw everything, every frame.
I'm here just to say that when dealing with such primitive shapes as arc without too many color variations, it's actually better to use the arc method than drawImage().
The idea is to wrap all your shapes in a single path declaration, using
ctx.beginPath(); // start path declaration
for(i; i<shapes.length; i++){ // loop through our points
ctx.moveTo(pt.x + pt.radius, pt.y); // default is lineTo and we don't want it
// Note the '+ radius', arc starts at 3 o'clock
ctx.arc(pt.x, pt.y, pt.radius, 0, Math.PI*2);
}
ctx.fill(); // a single fill()
This is faster than drawImage, but the main caveat is that it works only for single-colored set of shapes.
I've made an complex plotting app, where I do draw a lot (20K+) of entities, with animated positions. So what I do, is to store two sets of points, one un-sorted (actually sorted by radius), and one
sorted by color. I then do use the sorted-by-color one in my animations loop, and when the animation is complete, I draw only the final frame with the sorted-by-radius (after I filtered the non visible entities). I achieve 60fps on most devices. When I tried with drawImage, I was stuck at about 10fps for 5K points.
Here is a modified version of Blindman67's good answer's snippet, using this single-path approach.
/* All credits to SO user Blindman67 */
const doFor = (count,callback) => {var i=0;while(i < count){callback(i++)}};
const planes = {
items : [],
clear(){
planes.items.length = 0;
},
add(x,y){
planes.items.push({
x,y,
rad: 2,
dir : Math.random() * Math.PI * 2,
speed : Math.random() * 0.2 + 0.1,
dirV : (Math.random() - 0.5) * 0.01, // change in direction
})
},
update(){
var i,p;
for(i = 0; i < planes.items.length; i ++){
p = planes.items[i];
p.dir += p.dirV;
p.x += Math.cos(p.dir) * p.speed;
p.y += Math.sin(p.dir) * p.speed;
}
},
draw(){
var i,p;
const w = canvas.width;
const h = canvas.height;
ctx.beginPath();
ctx.fillStyle = 'red';
for(i = 0; i < planes.items.length; i ++){
p = planes.items[i];
var x = ((p.x % w) + w) % w;
var y = ((p.y % h) + h) % h;
ctx.moveTo(x + p.rad, y)
ctx.arc(x, y, p.rad, 0, Math.PI*2);
}
ctx.fill();
}
}
const ctx = canvas.getContext("2d");
function mainLoop(){
if(canvas.width !== innerWidth || canvas.height !== innerHeight){
canvas.width = innerWidth;
canvas.height = innerHeight;
planes.clear();
doFor(8000,()=>{ planes.add(Math.random() * canvas.width, Math.random() * canvas.height) })
}
ctx.setTransform(1,0,0,1,0,0);
// clear or render a background map
ctx.clearRect(0,0,canvas.width,canvas.height);
planes.update();
planes.draw();
requestAnimationFrame(mainLoop)
}
requestAnimationFrame(mainLoop)
canvas {
position : absolute;
top : 0px;
left : 0px;
z-index: -1;
}
<canvas id=canvas></canvas>
8000 animated points
Not directly related but in case you've got part of your drawings that don't update at the same rate as the rest (e.g if you want to highlight an area of your map...) then you might also consider separating your drawings in different layers, on offscreen canvases. This way you'd have one canvas for the planes, that you'd clear every frame, and other canvas for other layers that you would update at different rate. But that's an other story.
I've got the linear component of collision resolution down relatively well, but I can't quite figure out how to do the same for the angular one. From what I've read, it's something like... torque = point of collision x linear velocity. (cross product) I tried to incorporate an example I found into my code but I actually don't see any rotation at all when objects collide. The other fiddle works perfectly with a rudimentary implementation of the seperating axis theorem and the angular velocity calculations. Here's what I've come up with...
Property definitions (orientation, angular velocity, and angular acceleration):
rotation: 0,
angularVelocity: 0,
angularAcceleration: 0
Calculating the angular velocity in the collision response:
var pivotA = this.vector(bodyA.x, bodyA.y);
bodyA.angularVelocity = 1 * 0.2 * (bodyA.angularVelocity / Math.abs(bodyA.angularVelocity)) * pivotA.subtract(isCircle ? pivotA.add(bodyA.radius) : {
x: pivotA.x + boundsA.width,
y: pivotA.y + boundsA.height
}).vCross(bodyA.velocity);
var pivotB = this.vector(bodyB.x, bodyB.y);
bodyB.angularVelocity = 1 * 0.2 * (bodyB.angularVelocity / Math.abs(bodyB.angularVelocity)) * pivotB.subtract(isCircle ? pivotB.add(bodyB.radius) : {
x: pivotB.x + boundsB.width,
y: pivotB.y + boundsB.height
}).vCross(bodyB.velocity);
Updating the orientation in the update loop:
var torque = 0;
torque += core.objects[o].angularVelocity * -1;
core.objects[o].angularAcceleration = torque / core.objects[o].momentOfInertia();
core.objects[o].angularVelocity += core.objects[o].angularAcceleration;
core.objects[o].rotation += core.objects[o].angularVelocity;
I would post the code that I have for calculating the moments of inertia but there's a seperate one for every object so that would be a bit... lengthy. Nonetheless, here's the one for a circle as an example:
return this.mass * this.radius * this.radius / 2;
Just to show the result, here's my fiddle. As shown, objects do not rotate on collision. (not exactly visible with the circles, but it should work for the zero and seven)
What am I doing wrong?
EDIT: Reason they weren't rotating at all was because of an error with groups in the response function -- it rotates now, just not correctly. However, I've commented that out for now as it messes things up.
Also, I've tried another method for rotation. Here's the code in the response:
_bodyA.angularVelocity = direction.vCross(_bodyA.velocity) / (isCircle ? _bodyA.radius : boundsA.width);
_bodyB.angularVelocity = direction.vCross(_bodyB.velocity) / (isCircle ? _bodyB.radius : boundsB.width);
Note that direction refers to the "collision normal".
Angular and linear acceleration due to force vector
Angular and directional accelerations due to an applied force are two components of the same thing and can not be separated. To get one you need to solve for both.
Define the calculations
From simple physics and standing on shoulders we know the following.
F is force (equivalent to inertia)
Fv is linear force
Fa is angular force
a is acceleration could be linear or rotational depending on where it is used
v is velocity. For angular situations it is the tangential component only
m is mass
r is radius
For linear forces
F = m * v
From which we derive
m = F / v
v = F / m
For rotational force (v is tangential velocity)
F = r * r * m * (v / r) and simplify F = r * m * v
From which we derive
m = F / ( r * v )
v = F / ( r * m )
r = F / ( v * m )
Because the forces we apply are instantaneous we can interchange a acceleration and v velocity to give all the following formulas
Linear
F = m * a
m = F / a
a = F / m
Rotational
F = r * m * a
m = F / ( r * a )
a = F / ( r * m )
r = F / ( a * m )
As we are only interested in the change in velocity for both linear and rotation solutions
a1 = F / m
a2 = F / ( r * m )
Where a1 is acceleration in pixels per frame2 and a2 is acceleration in radians per frame2 ( the frame squared just denotes it is acceleration)
From 1D to 2D
Because this is a 2D solution and all above are 1D we need to use vectors. I for this problem use two forms of the 2D vector. Polar that has a magnitude (length, distance, the like...) and direction. Cartesian which has x and y. What a vector represents depends on how it is used.
The following functions are used as helpers in the solution. They are written in ES6 so for non compliant browsers you will have to adapt them, though I would not ever suggest you use these as they are written for convenience, they are very inefficient and do a lot of redundant calculations.
Converts a vector from polar to cartesian returning a new one
function polarToCart(pVec, retV = {x : 0, y : 0}) {
retV.x = Math.cos(pVec.dir) * pVec.mag;
retV.y = Math.sin(pVec.dir) * pVec.mag;
return retV;
}
Converts a vector from cartesian to polar returning a new one
function cartToPolar(vec, retV = {dir : 0, mag : 0}) {
retV.dir = Math.atan2(vec.y, vec.x);
retV.mag = Math.hypot(vec.x, vec.y);
return retV;
}
Creates a polar vector
function polar(mag = 1, dir = 0) {
return validatePolar({dir : dir,mag : mag});
}
Create a vector as a cartesian
function vector(x = 1, y = 0) {
return {x : x, y : y};
}
True is the arg vec is a vector in polar form
function isPolar(vec) {
if (vec.mag !== undefined && vec.dir !== undefined) {return true;}
return false;
}
Returns true if arg vec is a vector in cartesian form
function isCart(vec) {
if (vec.x !== undefined && vec.y !== undefined) {return true;}
return false;
}
Returns a new vector in polar form also ensures that vec.mag is positive
function asPolar(vec){
if(isCart(vec)){ return cartToPolar(vec); }
if(vec.mag < 0){
vec.mag = - vec.mag;
vec.dir += PI;
}
return { dir : vec.dir, mag : vec.mag };
}
Copy and converts an unknown vec to cart if not already
function asCart(vec){
if(isPolar(vec)){ return polarToCart(vec); }
return { x : vec.x, y : vec.y};
}
Calculations can result in a negative magnitude though this is valid for some calculations this results in the incorrect vector (reversed) this simply validates that the polar vector has a positive magnitude it does not change the vector just the sign and direction
function validatePolar(vec) {
if (isPolar(vec)) {
if (vec.mag < 0) {
vec.mag = - vec.mag;
vec.dir += PI;
}
}
return vec;
}
The Box
Now we can define an object that we can use to play with. A simple box that has position, size, mass, orientation, velocity and rotation
function createBox(x,y,w,h){
var box = {
x : x, // pos
y : y,
r : 0.1, // its rotation AKA orientation or direction in radians
h : h, // its height
w : w, // its width
dx : 0, // delta x in pixels per frame 1/60th second
dy : 0, // delta y
dr : 0.0, // deltat rotation in radians per frame 1/60th second
mass : w * h, // mass in things
update :function(){
this.x += this.dx;
this.y += this.dy;
this.r += this.dr;
},
}
return box;
}
Applying a force to an object
So now we can redefine some terms
F (force) is a vector force the magnitude is the force and it has a direction
var force = polar(100,0); // create a force 100 units to the right (0 radians)
The force is meaningless without a position where it is applied.
Position is a vector that just holds and x and y location
var location = vector(canvas.width/2, canvas.height/2); // defines a point in the middle of the canvas
Directional vector holds the direction and distance between to positional vectors
var l1 = vector(canvas.width/2, canvas.height/2); // defines a point in the middle of the canvas
var l2 = vector(100,100);
var direction = asPolar(vector(l2.x - l1.x, l2.y - l1.y)); // get the direction as polar vector
direction now has the direction from canvas center to point (100,100) and the distance.
The last thing we need to do is extract the components from a force vector along a directional vector. When you apply a force to an object the force is split into two, one is the force along the line to the object center and adds to the object acceleration, the other force is at 90deg to the line to the object center (the tangent) and that is the force that changes rotation.
To get the two components you get the difference in direction between the force vector and the directional vector from where the force is applied to the object center.
var force = polar(100,0); // the force
var forceLoc = vector(50,50); // the location the force is applied
var direction2Center = asPolar(vector(box.x - forceLoc.x, box.y - forceLoc.y)); // get the direction as polar vector
var pheta = direction2Center - force.dir; // get the angle between the force and object center
Now that you have that angle pheta the force can be split into its rotational and linear components with trig.
var F = force.mag; // get the force magnitude
var Fv = Math.cos(pheta) * F; // get the linear force
var Fa = Math.sin(pheta) * F; // get the angular force
Now the forces can be converted back to accelerations for linear a = F/m and angular a = F/(m*r)
accelV = Fv / box.mass; // linear acceleration in pixels
accelA = Fa / (box.mass * direction2Center.mag); // angular acceleration in radians
You then convert the linear force back to a vector that has a direction to the center of the object
var forceV = polar(Fv, direction2Center);
Convert is back to the cartesian so we can add it to the object deltaX and deltaY
forceV = asCart(forceV);
And add the acceleration to the box
box.dx += forceV.x;
box.dy += forceV.y;
Rotational acceleration is just one dimensional so just add it to the delta rotation of the box
box.dr += accelA;
And that is it.
Function to apply force to Box
The function if attached to the box will apply a force vector at a location to the box.
Attach to the box like so
box.applyForce = applyForce; // bind function to the box;
You can then call the function via the box
box.applyForce(force, locationOfForce);
function applyForce(force, loc){ // force is a vector, loc is a coordinate
var toCenter = asPolar(vector(this.x - loc.x, this.y - loc.y)); // get the vector to the center
var pheta = toCenter.dir - force.dir; // get the angle between the force and the line to center
var Fv = Math.cos(pheta) * force.mag; // Split the force into the velocity force along the line to the center
var Fa = Math.sin(pheta) * force.mag; // and the angular force at the tangent to the line to the center
var accel = asPolar(toCenter); // copy the direction to center
accel.mag = Fv / this.mass; // now use F = m * a in the form a = F/m to get acceleration
var deltaV = asCart(accel); // convert acceleration to cartesian
this.dx += deltaV.x // update the box delta V
this.dy += deltaV.y //
var accelA = Fa / (toCenter.mag * this.mass); // for the angular component get the rotation
// acceleration from F=m*a*r in the
// form a = F/(m*r)
this.dr += accelA;// now add that to the box delta r
}
The Demo
The demo is only about the function applyForce the stuff to do with gravity and bouncing are only very bad approximations and should not be used for any physic type of stuff as they do not conserve energy.
Click and drag to apply a force to the object in the direction that the mouse is moved.
const PI90 = Math.PI / 2;
const PI = Math.PI;
const PI2 = Math.PI * 2;
const INSET = 10; // playfeild inset
const ARROW_SIZE = 6
const SCALE_VEC = 10;
const SCALE_FORCE = 0.15;
const LINE_W = 2;
const LIFE = 12;
const FONT_SIZE = 20;
const FONT = "Arial Black";
const WALL_NORMS = [PI90,PI,-PI90,0]; // dirction of the wall normals
var box = createBox(200, 200, 50, 100);
box.applyForce = applyForce; // Add this function to the box
// render / update function
var mouse = (function(){
function preventDefault(e) { e.preventDefault(); }
var i;
var mouse = {
x : 0, y : 0,buttonRaw : 0,
bm : [1, 2, 4, 6, 5, 3], // masks for setting and clearing button raw bits;
mouseEvents : "mousemove,mousedown,mouseup".split(",")
};
function mouseMove(e) {
var t = e.type, m = mouse;
m.x = e.offsetX; m.y = e.offsetY;
if (m.x === undefined) { m.x = e.clientX; m.y = e.clientY; }
if (t === "mousedown") { m.buttonRaw |= m.bm[e.which-1];
} else if (t === "mouseup") { m.buttonRaw &= m.bm[e.which + 2];}
e.preventDefault();
}
mouse.start = function(element = document){
if(mouse.element !== undefined){ mouse.removeMouse();}
mouse.element = element;
mouse.mouseEvents.forEach(n => { element.addEventListener(n, mouseMove); } );
}
mouse.remove = function(){
if(mouse.element !== undefined){
mouse.mouseEvents.forEach(n => { mouse.element.removeEventListener(n, mouseMove); } );
mouse.element = undefined;
}
}
return mouse;
})();
var canvas,ctx;
function createCanvas(){
canvas = document.createElement("canvas");
canvas.style.position = "absolute";
canvas.style.left = "0px";
canvas.style.top = "0px";
canvas.style.zIndex = 1000;
document.body.appendChild(canvas);
}
function resizeCanvas(){
if(canvas === undefined){
createCanvas();
}
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
ctx = canvas.getContext("2d");
if(box){
box.w = canvas.width * 0.10;
box.h = box.w * 2;
box.mass = box.w * box.h;
}
}
window.addEventListener("resize",resizeCanvas);
resizeCanvas();
mouse.start(canvas)
var tempVecs = [];
function addTempVec(v,vec,col,life = LIFE,scale = SCALE_VEC){tempVecs.push({v:v,vec:vec,col:col,scale:scale,life:life,sLife:life});}
function drawTempVecs(){
for(var i = 0; i < tempVecs.length; i ++ ){
var t = tempVecs[i]; t.life -= 1;
if(t.life <= 0){tempVecs.splice(i, 1); i--; continue}
ctx.globalAlpha = (t.life / t.sLife)*0.25;
drawVec(t.v, t.vec ,t.col, t.scale)
}
}
function drawVec(v,vec,col,scale = SCALE_VEC){
vec = asPolar(vec)
ctx.setTransform(1,0,0,1,v.x,v.y);
var d = vec.dir;
var m = vec.mag;
ctx.rotate(d);
ctx.beginPath();
ctx.lineWidth = LINE_W;
ctx.strokeStyle = col;
ctx.moveTo(0,0);
ctx.lineTo(m * scale,0);
ctx.moveTo(m * scale-ARROW_SIZE,-ARROW_SIZE);
ctx.lineTo(m * scale,0);
ctx.lineTo(m * scale-ARROW_SIZE,ARROW_SIZE);
ctx.stroke();
}
function drawText(text,x,y,font,size,col){
ctx.font = size + "px "+font;
ctx.textAlign = "center";
ctx.textBaseline = "middle";
ctx.setTransform(1,0,0,1,x,y);
ctx.globalAlpha = 1;
ctx.fillStyle = col;
ctx.fillText(text,0,0);
}
function createBox(x,y,w,h){
var box = {
x : x, // pos
y : y,
r : 0.1, // its rotation AKA orientation or direction in radians
h : h, // its height, and I will assume that its depth is always equal to its height
w : w, // its width
dx : 0, // delta x in pixels per frame 1/60th second
dy : 0, // delta y
dr : 0.0, // deltat rotation in radians per frame 1/60th second
getDesc : function(){
var vel = Math.hypot(this.dx ,this.dy);
var radius = Math.hypot(this.w,this.h)/2
var rVel = Math.abs(this.dr * radius);
var str = "V " + (vel*60).toFixed(0) + "pps ";
str += Math.abs(this.dr * 60 * 60).toFixed(0) + "rpm ";
str += "Va " + (rVel*60).toFixed(0) + "pps ";
return str;
},
mass : function(){ return (this.w * this.h * this.h)/1000; }, // mass in K things
draw : function(){
ctx.globalAlpha = 1;
ctx.setTransform(1,0,0,1,this.x,this.y);
ctx.rotate(this.r);
ctx.fillStyle = "#444";
ctx.fillRect(-this.w/2, -this.h/2, this.w, this.h)
ctx.strokeRect(-this.w/2, -this.h/2, this.w, this.h)
},
update :function(){
this.x += this.dx;
this.y += this.dy;
this.dy += 0.061; // alittle gravity
this.r += this.dr;
},
getPoint : function(which){
var dx,dy,x,y,xx,yy,velocityA,velocityT,velocity;
dx = Math.cos(this.r);
dy = Math.sin(this.r);
switch(which){
case 0:
x = -this.w /2;
y = -this.h /2;
break;
case 1:
x = this.w /2;
y = -this.h /2;
break;
case 2:
x = this.w /2;
y = this.h /2;
break;
case 3:
x = -this.w /2;
y = this.h /2;
break;
case 4:
x = this.x;
y = this.y;
}
var xx,yy;
xx = x * dx + y * -dy;
yy = x * dy + y * dx;
var details = asPolar(vector(xx, yy))
xx += this.x;
yy += this.y;
velocityA = polar(details.mag * this.dr, details.dir + PI90);
velocityT = vectorAdd(velocity = vector(this.dx, this.dy), velocityA);
return {
velocity : velocity, // only directional
velocityT : velocityT, // total
velocityA : velocityA, // angular only
pos : vector(xx, yy),
radius : details.mag,
}
},
}
box.mass = box.mass(); // Mass remains the same so just set it with its function
return box;
}
// calculations can result in a negative magnitude though this is valide for some
// calculations this results in the incorrect vector (reversed)
// this simply validates that the polat vector has a positive magnitude
// it does not change the vector just the sign and direction
function validatePolar(vec){
if(isPolar(vec)){
if(vec.mag < 0){
vec.mag = - vec.mag;
vec.dir += PI;
}
}
return vec;
}
// converts a vector from polar to cartesian returning a new one
function polarToCart(pVec, retV = {x : 0, y : 0}){
retV.x = Math.cos(pVec.dir) * pVec.mag;
retV.y = Math.sin(pVec.dir) * pVec.mag;
return retV;
}
// converts a vector from cartesian to polar returning a new one
function cartToPolar(vec, retV = {dir : 0, mag : 0}){
retV.dir = Math.atan2(vec.y,vec.x);
retV.mag = Math.hypot(vec.x,vec.y);
return retV;
}
function polar (mag = 1, dir = 0) { return validatePolar({dir : dir, mag : mag}); } // create a polar vector
function vector (x= 1, y= 0) { return {x: x, y: y}; } // create a cartesian vector
function isPolar (vec) { if(vec.mag !== undefined && vec.dir !== undefined) { return true; } return false; }// returns true if polar
function isCart (vec) { if(vec.x !== undefined && vec.y !== undefined) { return true; } return false; }// returns true if cartesian
// copy and converts an unknown vec to polar if not already
function asPolar(vec){
if(isCart(vec)){ return cartToPolar(vec); }
if(vec.mag < 0){
vec.mag = - vec.mag;
vec.dir += PI;
}
return { dir : vec.dir, mag : vec.mag };
}
// copy and converts an unknown vec to cart if not already
function asCart(vec){
if(isPolar(vec)){ return polarToCart(vec); }
return { x : vec.x, y : vec.y};
}
// normalise makes a vector a unit length and returns it as a cartesian
function normalise(vec){
var vp = asPolar(vec);
vap.mag = 1;
return asCart(vp);
}
function vectorAdd(vec1, vec2){
var v1 = asCart(vec1);
var v2 = asCart(vec2);
return vector(v1.x + v2.x, v1.y + v2.y);
}
// This splits the vector (polar or cartesian) into the components along dir and the tangent to that dir
function vectorComponentsForDir(vec,dir){
var v = asPolar(vec); // as polar
var pheta = v.dir - dir;
var Fv = Math.cos(pheta) * v.mag;
var Fa = Math.sin(pheta) * v.mag;
var d1 = dir;
var d2 = dir + PI90;
if(Fv < 0){
d1 += PI;
Fv = -Fv;
}
if(Fa < 0){
d2 += PI;
Fa = -Fa;
}
return {
along : polar(Fv,d1),
tangent : polar(Fa,d2)
};
}
function doCollision(pointDetails, wallIndex){
var vv = asPolar(pointDetails.velocity); // Cartesian V make sure the velocity is in cartesian form
var va = asPolar(pointDetails.velocityA); // Angular V make sure the velocity is in cartesian form
var vvc = vectorComponentsForDir(vv, WALL_NORMS[wallIndex])
var vac = vectorComponentsForDir(va, WALL_NORMS[wallIndex])
vvc.along.mag *= 1.18; // Elastic collision requiers that the two equal forces from the wall
vac.along.mag *= 1.18; // against the box and the box against the wall be summed.
// As the wall can not move the result is that the force is twice
// the force the box applies to the wall (Yes and currently force is in
// velocity form untill the next line)
vvc.along.mag *= box.mass; // convert to force
//vac.along.mag/= pointDetails.radius
vac.along.mag *= box.mass
vvc.along.dir += PI; // force is in the oppisite direction so turn it 180
vac.along.dir += PI; // force is in the oppisite direction so turn it 180
// split the force into components based on the wall normal. One along the norm the
// other along the wall
vvc.tangent.mag *= 0.18; // add friction along the wall
vac.tangent.mag *= 0.18;
vvc.tangent.mag *= box.mass //
vac.tangent.mag *= box.mass
vvc.tangent.dir += PI; // force is in the oppisite direction so turn it 180
vac.tangent.dir += PI; // force is in the oppisite direction so turn it 180
// apply the force out from the wall
box.applyForce(vvc.along, pointDetails.pos)
// apply the force along the wall
box.applyForce(vvc.tangent, pointDetails.pos)
// apply the force out from the wall
box.applyForce(vac.along, pointDetails.pos)
// apply the force along the wall
box.applyForce(vac.tangent, pointDetails.pos)
//addTempVec(pointDetails.pos, vvc.tangent, "red", LIFE, 10)
//addTempVec(pointDetails.pos, vac.tangent, "red", LIFE, 10)
}
function applyForce(force, loc){ // force is a vector, loc is a coordinate
validatePolar(force); // make sure the force is a valid polar
// addTempVec(loc, force,"White", LIFE, SCALE_FORCE) // show the force
var l = asCart(loc); // make sure the location is in cartesian form
var toCenter = asPolar(vector(this.x - l.x, this.y - l.y));
var pheta = toCenter.dir - force.dir;
var Fv = Math.cos(pheta) * force.mag;
var Fa = Math.sin(pheta) * force.mag;
var accel = asPolar(toCenter); // copy the direction to center
accel.mag = Fv / this.mass; // now use F = m * a in the form a = F/m
var deltaV = asCart(accel); // convert it to cartesian
this.dx += deltaV.x // update the box delta V
this.dy += deltaV.y
var accelA = Fa / (toCenter.mag * this.mass); // for the angular component get the rotation
// acceleration
this.dr += accelA;// now add that to the box delta r
}
// make a box
ctx.globalAlpha = 1;
var lx,ly;
function update(){
// clearLog();
ctx.setTransform(1, 0, 0, 1, 0, 0);
ctx.clearRect(0, 0, canvas.width, canvas.height);
ctx.setTransform(1, 0, 0, 1, 0, 0);
ctx.lineWidth = 1;
ctx.strokeStyle = "black";
ctx.fillStyle = "#888";
ctx.fillRect(INSET, INSET, canvas.width - INSET * 2, canvas.height - INSET * 2);
ctx.strokeRect(INSET, INSET, canvas.width - INSET * 2, canvas.height - INSET * 2);
ctx.lineWidth = 2;
ctx.strokeStyle = "black";
box.update();
box.draw();
if(mouse.buttonRaw & 1){
var force = asPolar(vector(mouse.x - lx, mouse.y - ly));
force.mag *= box.mass * 0.1;
box.applyForce(force,vector(mouse.x, mouse.y))
addTempVec(vector(mouse.x, mouse.y), asPolar(vector(mouse.x - lx, mouse.y - ly)), "Cyan", LIFE, 5);
}
lx = mouse.x;
ly = mouse.y;
for(i = 0; i < 4; i++){
var p = box.getPoint(i);
// only do one collision per frame or we will end up adding energy
if(p.pos.x < INSET){
box.x += (INSET) - p.pos.x;
doCollision(p,3)
}else
if( p.pos.x > canvas.width-INSET){
box.x += (canvas.width - INSET) - p.pos.x;
doCollision(p,1)
}else
if(p.pos.y < INSET){
box.y += (INSET) -p.pos.y;
doCollision(p,0)
}else
if( p.pos.y > canvas.height-INSET){
box.y += (canvas.height - INSET) -p.pos.y;
doCollision(p,2)
}
drawVec(p.pos,p.velocity,"blue")
}
drawTempVecs();
ctx.globalAlpha = 1;
drawText(box.getDesc(),canvas.width/2,FONT_SIZE,FONT,FONT_SIZE,"black");
drawText("Click drag to apply force to box",canvas.width/2,FONT_SIZE +17,FONT,14,"black");
requestAnimationFrame(update)
}
update();
I'm creating a Canvas animation, and have managed to position x number of circles in a circular path. Here's a simplified version of the code I'm using:
var total = circles.length,
i = 0,
radius = 500,
angle = 0,
step = (2*Math.PI) / total;
for( i; i < total; i++ ) {
var circle = circles[i].children[0],
cRadius = circle[i].r,
x = Math.round(winWidth/2 + radius * Math.cos( angle ) - cRadius),
y = Math.round(winHeight/2 + radius * Math.sin( angle ) - cRadius);
circle.x = x;
circle.y = y;
angle += step;
}
Which results in this:
What I am trying to achieve is for all the circles to be next to each other with no gap between them (except the first and last). The circles sizes (radius) are generated randomly and shouldn't adjust to fit the circular path:
function getRandomInt(min, max) {
return Math.floor(Math.random() * (max - min + 1)) + min;
}
I expect there to be a gap between the first and last circle.
I'm struggling to get my head around this so any help would be much appreciated :)
Cheers!
Main creation loop :
• take a current radius
• compute the angles it cover ( = atan2(smallRadius/bigRadius) )
• move base angle by this latest angle.
http://jsfiddle.net/dj2v7mbw/9/
function CircledCircle(x, y, radius, margin, subCircleCount, subRadiusMin, subRadiusMax) {
this.x = x;
this.y = y;
this.radius = radius;
this.subCircleCount = subCircleCount;
var circles = this.circles = [];
// build top sub-circles
var halfCount = Math.floor(subCircleCount / 2);
var totalAngle = addCircles(halfCount);
// re-center top circles
var correction = totalAngle / 2 + Math.PI / 2;
for (var i = 0; i < halfCount; i++) this.circles[i].angle -= correction;
// build bottom sub-circles
totalAngle = addCircles(subCircleCount - halfCount);
// re-center bottom circles
var correction = totalAngle / 2 - Math.PI / 2;
for (var i = halfCount; i < subCircleCount; i++) this.circles[i].angle -= correction;
// -- draw this C
this.draw = function (angleShift) {
for (var i = 0; i < this.circles.length; i++) drawDistantCircle(this.circles[i], angleShift);
}
//
function drawDistantCircle(c, angleShift) {
angleShift = angleShift || 0;
var thisX = x + radius * Math.cos(c.angle + angleShift);
var thisY = y + radius * Math.sin(c.angle + angleShift);
ctx.beginPath();
ctx.arc(thisX, thisY, c.r, 0, 2 * Math.PI);
ctx.fillStyle = 'hsl(' + (c.index * 15) + ',75%, 75%)';
ctx.fill();
ctx.stroke();
}
//
function addCircles(cnt) {
var currAngle = 0;
for (var i = 0; i < cnt; i++) {
var thisRadius = getRandomInt(subRadiusMin, subRadiusMax);
var thisAngle = Math.atan2(2 * thisRadius + margin, radius);
var thisCircle = new subCircle(thisRadius, currAngle + thisAngle / 2, i);
currAngle += thisAngle;
circles.push(thisCircle);
}
return currAngle;
}
}
with
function subCircle(radius, angle, index) {
this.r = radius;
this.angle = angle;
this.index = index;
}
function getRandomInt(min, max) {
return Math.floor(Math.random() * (max - min + 1)) + min;
}
use with
var myCircles = new CircledCircle(winWidth / 2, winHeight / 2, 350, 2, 24, 5, 50);
myCircles.draw();
animate with :
var angleShift = 0;
function draw() {
requestAnimationFrame(draw);
ctx.clearRect(0, 0, winWidth, winHeight);
myCircles.draw(angleShift);
angleShift += 0.010;
}
draw();
It's something like this, but you're gonna have to figure out the last circle's size:
http://jsfiddle.net/rudiedirkx/ufvf62yf/2/
The main logic:
var firstStep = 0, rad = 0, step = 0;
firstStep = step = stepSize();
for ( var i=0; i<30; i++ ) {
draw.radCircle(rad, step);
rad += step;
step = stepSize();
rad += step;
}
stepSize() creates a random rad between Math.PI/48 and Math.PI/48 + Math.PI/36 (no special reason, but it looked good). You can fix that to be the right sizes.
draw.radCircle(rad, step) creates a circle at position rad of size step (also in rad).
step is added twice per iteration: once to step from current circle's center to its edge and once to find the next circle's center
firstStep is important because you have to know where to stop drawing (because the first circle crosses into negative angle)
I haven't figured out how to make the last circle the perfect size yet =)
There's also a bit of magic in draw.radCircle():
var r = rRad * Math.PI/3 * 200 * .95;
The 200 is obviously the big circle's radius
The 95% is because the circle's edge length is slightly longer than the (straight) radius of every circle
I have no idea why Math.PI/3 is that... I figured it had to be Math.PI/2, which is 1 rad, but that didn't work at all. 1/3 for some reason does..... Explain that!
If you want to animate these circle sizes and keep them aligned, you'll have a hard time. They're all random now. In an animation, only the very first iteration can be random, and the rest is a big mess of cache and math =)
I am trying to create a grid-based shadow engine using JavaScript. My algorithm shades squares based on whether their position is 'behind' a block, relative to a light source.
This is my algorithm so far: https://jsfiddle.net/jexqpfLf/
var canvas = document.createElement('canvas');
canvas.width = 600;
canvas.height = 400;
document.body.appendChild(canvas);
var ctx = canvas.getContext('2d');
var light_x = 90;
var light_y = 110;
var block_x = 120;
var block_y = 120;
requestAnimationFrame(render);
function render() {
ctx.fillStyle = 'white';
ctx.fillRect(0, 0, canvas.width, canvas.height);
var vec1_x = block_x - light_x;
var vec1_y = block_y - light_y;
var vec1_mag = Math.sqrt(vec1_x * vec1_x + vec1_y * vec1_y);
ctx.fillStyle = 'black';
for (var x = 0; x < canvas.width; x += 10)
for (var y = 0; y < canvas.width; y += 10) {
var vec2_x = x - light_x;
var vec2_y = y - light_y;
var vec2_mag = Math.sqrt(vec2_x * vec2_x + vec2_y * vec2_y);
var dotproduct = vec1_x * vec2_x + vec1_y * vec2_y;
var angle = Math.acos(dotproduct / (vec1_mag * vec2_mag));
if (vec2_mag > vec1_mag && angle < Math.PI / 8 / vec1_mag * 10)
ctx.fillRect(x, y, 10, 10);
}
ctx.fillStyle = 'green';
ctx.fillRect(light_x, light_y, 10, 10);
ctx.fillStyle = 'red';
ctx.fillRect(block_x, block_y, 10, 10);
requestAnimationFrame(render);
}
onkeydown = function (e) {
if (e.which == 65)
light_x -= 10;
if (e.which == 68)
light_x += 10;
if (e.which == 87)
light_y -= 10;
if (e.which == 83)
light_y += 10;
}
Unfortunately, as you can see in the demonstration, I'm finding some angles problematic. Some squares which should be shaded are left unshaded. This happens for some angles and distances (between the light source and the block) but not others. For example, placing the light source at (60, 90) shows these artifacts as well.
I am using the vectors LP (from light to point) and LB (from light to block), taking their dot product and dividing by the product of their magnitudes to find the shading angle, then scaling this angle depending on the distance between the block and light source.
Could these artifacts be due to rounding errors? Or is there a problem with the algorithm itself? Any help would be appreciated :-)
Great question. You're not gonna like this one.
It's a floating point math issue.
What's the value of Math.acos(1.000000000000000)?
0.
Whats the value of Math.acos(1.0000000000000003)?
NaN.
That's annoying, isn't it?
At some values, your dotproduct is 6000 and your (vec1_mag * vec2_mag) is 5999.999999999999, leading to the issue above.
Changing (vec1_mag * vec2_mag) to Math.round(vec1_mag * vec2_mag) will solve your problem.
While we're staring at this fiddle together you should know that there's another bug:
for (var x = 0; x < canvas.width; x += 10) {
for (var y = 0; y < canvas.width; y += 10) {
You use canvas.width here twice. I imagine the second one ought to be canvas.height, so make sure what you wrote there is what you want.
Working fiddle for you!