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Fix Fish-eye effect 2.5D Raycaster game

I'm working on a simple raycaster game for fun. I have two canvases, (id's canvas1 and canvas2), one for the 2D view of the world, and the other for the 2.5D raycasted view. The raycasted view looks sort of distorted, like a fish eye effect. Another problem (less important) is that the view doesn't really look like your average 3D world, even with the effect of fish eye distortion. Looking for some good FOV + height values/settings.
Here's my code:
const canvas1 = document.querySelector("#canvas1");
const canvas2 = document.querySelector("#canvas2");
const ctx1 = canvas1.getContext("2d");
const ctx2 = canvas2.getContext("2d");
let width1 = 256;
let height1 = 256;
let width2 = 720;
let height2 = 360;
const columns = 100;
let columnWidth = width2 / columns;
canvas1.width = width1;
canvas1.height = height1;
canvas2.width = width2;
canvas2.height = height2;
let deltaTime = 0;
let lastFrame = Date.now();
const moveSpeed = 70;
const rotationSpeed = 175;
const FOV = 65;
const rayCastStep = 0.5;
let rayCastWidth = FOV / columns;
let map = [
["##########"],
["#...#....#"],
["#...#....#"],
["### #....#"],
["#...#....#"],
["# ###....#"],
["#...#### #"],
["#........#"],
["#........#"],
["##########"]
];
const player = {
x: 45,
y: 165,
heading: 270
}
const keyMap = {
w: false,
a: false,
s: false,
d: false
}
const willCollide = ({ xC, yC }, { x, y, w, h }) => {
boundingBox = {
left: x - w / 2,
right: x + w / 2,
top: y - h / 2,
bottom: y + h / 2
}
return xC > boundingBox.left && xC < boundingBox.right && yC > boundingBox.top && yC < boundingBox.bottom;
}
const handlePlayerMovement = () => {
if (keyMap.w) {
let dx = Math.cos(player.heading * Math.PI / 180);
let dy = Math.sin(player.heading * Math.PI / 180);
xCheck = player.x + dx * moveSpeed * deltaTime;
yCheck = player.y + dy * moveSpeed * deltaTime;
let canMove = true;
for (let y = 0; y < map.length; y++) {
for (let x = 0; x < map[y][0].length; x++) {
if (map[y][0][x] == "#" && willCollide({ xC: xCheck, yC: yCheck }, { x: x * 20 + 10, y: y * 20 + 10, w: 20, h: 20})) {
canMove = false;
}
}
}
if (canMove) {
player.x = xCheck;
player.y = yCheck;
}
}
if (keyMap.s) {
let dx = Math.cos((player.heading * Math.PI / 180) + Math.PI);
let dy = Math.sin((player.heading * Math.PI / 180) + Math.PI);
xCheck = player.x + dx * moveSpeed * deltaTime;
yCheck = player.y + dy * moveSpeed * deltaTime;
let canMove = true;
for (let y = 0; y < map.length; y++) {
for (let x = 0; x < map[y][0].length; x++) {
if (map[y][0][x] == "#" && willCollide({ xC: xCheck, yC: yCheck }, { x: x * 20 + 10, y: y * 20 + 10, w: 20, h: 20})) {
canMove = false;
}
}
}
if (canMove) {
player.x = xCheck;
player.y = yCheck;
}
}
if (keyMap.a) {
player.heading -= rotationSpeed * deltaTime;
}
if (keyMap.d) {
player.heading += rotationSpeed * deltaTime;
}
}
const generateColumns = () => {
let distances = Array(columns).fill(0);
for (let i = 0; i < columns; i++) {
let collided = false;
let rayX = player.x;
let rayY = player.y;
let angle = (player.heading - FOV / 2) + (i / columns) * FOV;
let dx = rayCastStep * Math.cos(angle * Math.PI / 180 + Math.PI);
let dy = rayCastStep * Math.sin(angle * Math.PI / 180 + Math.PI);
while (!collided) {
rayX -= dx;
rayY -= dy;
for (let y = 0; y < map.length; y++) {
for (let x = 0; x < map[y][0].length; x++) {
if (map[y][0][x] == "#" && willCollide({ xC: rayX, yC: rayY }, { x: x * 20 + 10, y: y * 20 + 10, w: 20, h: 20 })) {
collided = true;
let deltaX = player.x - rayX;
let deltaY = player.y - rayY;
let dist = Math.sqrt(deltaX * deltaX + deltaY * deltaY);
let h = Math.max(height2 - height2 * (dist / 200), 0);
distances[i] = {
fill: h / height2,
h: h
}
}
}
}
}
ctx1.strokeStyle = "#fff";
ctx1.beginPath();
ctx1.moveTo(player.x * (256 / map[0][0].length) / 20, player.y * (256 / map.length) / 20);
ctx1.lineTo(rayX * (256 / map[0][0].length) / 20, rayY * (256 / map.length) / 20)
ctx1.stroke();
}
return distances;
}
const update = () => {
ctx1.fillStyle = "#000";
ctx1.fillRect(0, 0, width1, height1);
ctx2.fillStyle = "#000";
ctx2.fillRect(0, 0, width2, height2 / 2);
ctx2.fillStyle = "#fff";
ctx2.fillRect(0, height2 - height2 / 2, width2, height2 / 2);
handlePlayerMovement();
for (let y = 0; y < map.length; y++) {
for (let x = 0; x < map[y][0].length; x++) {
ctx1.fillStyle = "#fff";
if (map[y][0][x] == "#") ctx1.fillRect(x * (256 / map[y][0].length), y * (256 / map.length), (256 / map[y][0].length), (256 / map.length));
ctx1.fillStyle = "#666";
ctx1.fillRect(0, y * (256 / map.length), 256, 1);
ctx1.fillRect(x * (256 / map[y][0].length), 0, 1, 256);
}
}
ctx1.fillStyle = "#0f0";
ctx1.beginPath();
ctx1.ellipse(player.x * (256 / map[0][0].length) / 20, player.y * (256 / map.length) / 20, 2, 2, 0, 0, 2 * Math.PI);
ctx1.fill();
let cols = generateColumns();
for (let i = 0; i < columns; i++) {
ctx2.fillStyle = `rgb(0, ${cols[i].fill * 255}, 0)`;
ctx2.fillRect(Math.round(columnWidth * i), height2 / 2 - cols[i].h / 2, columnWidth + 1, cols[i].h);
}
deltaTime = (Date.now() / 1000 - lastFrame / 1000);
lastFrame = Date.now();
requestAnimationFrame(update);
}
update();
window.onkeydown = (e) => {
if (Object.keys(keyMap).includes(e.key.toLowerCase())) keyMap[e.key.toLowerCase()] = true;
}
window.onkeyup = (e) => {
if (Object.keys(keyMap).includes(e.key.toLowerCase())) keyMap[e.key.toLowerCase()] = false;
}
Any help is appreciated. Thanks!

adding custom animation in canvas html5

this might be somewhat difficult but i wil still ask, so i made a starfield ,now what i want to do is to have my stars( a pair each) connected to eachother by a line ,now this line will expand as the stars move forward and disappear when the stars move out of the canvas .any help would be appreciated here this is difficult i have the logic but i seem unable to follow the correct way to implement it
function randomRange(minVal, maxVal) {
return Math.floor(Math.random() * (maxVal - minVal - 1)) + minVal;
}
function initStars() {
for (var i = 0; i < stars.length; i++) {
stars[i] = {
x: randomRange(-25, 25),
y: randomRange(-25, 25),
z: randomRange(1, MAX_DEPTH)
}
}
}
function degToRad(deg) {
radians = (deg * Math.PI / 180) - Math.PI / 2;
return radians;
}
function animate() {
var halfWidth = canvas.width / 2;
var halfHeight = canvas.height / 2;
ctx.fillStyle = "rgb(0,0,0)";
ctx.fillRect(0, 0, canvas.width, canvas.height);
for (var i = 0; i < stars.length; i++) {
stars[i].z -= 0.2;
if (stars[i].z <= 0) {
stars[i].x = randomRange(-25, 25);
stars[i].y = randomRange(-25, 25);
stars[i].z = MAX_DEPTH;
}
var k = 128.0 / stars[i].z;
var px = stars[i].x * k + halfWidth;
var py = stars[i].y * k + halfHeight;
if (px >= 0 && px <= 1500 && py >= 0 && py <= 1500) {
var size = (1 - stars[i].z / 32.0) * 5;
var shade = parseInt((1 - stars[i].z / 32.0) * 750);
ctx.fillStyle = "rgb(" + shade + "," + shade + "," + shade + ")";
ctx.beginPath();
ctx.arc(px, py, size, degToRad(0), degToRad(360));
ctx.fill();
}
}
}
function animate() {
var halfWidth = canvas.width / 2;
var halfHeight = canvas.height / 2;
ctx.fillStyle = "rgb(0,0,0)";
ctx.fillRect(0, 0, canvas.width, canvas.height);
for (var i = 0; i < stars.length; i++) {
stars[i].z -= 0.2;
if (stars[i].z <= 0) {
stars[i].x = randomRange(-25, 25);
stars[i].y = randomRange(-25, 25);
stars[i].z = MAX_DEPTH;
}
var k = 128.0 / stars[i].z;
var px = stars[i].x * k + halfWidth;
var py = stars[i].y * k + halfHeight;
if (px >= 0 && px <= 1500 && py >= 0 && py <= 1500) {
var size = (1 - stars[i].z / 32.0) * 5;
var shade = parseInt((1 - stars[i].z / 32.0) * 750);
ctx.fillStyle = "rgb(" + shade + "," + shade + "," + shade + ")";
ctx.beginPath();
ctx.arc(px, py, size, degToRad(0), degToRad(360));
ctx.fill();
}
}
}
<!DOCTYPE html5>
<html>
<head>
<title>stars</title>
<script src="convergis.js"></script>
<script>
MAX_DEPTH = 32;
var canvas, ctx;
var stars = new Array(500);
window.onload = function() {
canvas = document.getElementById("tutorial");
if( canvas && canvas.getContext ) {
ctx = canvas.getContext("2d");
initStars();
setInterval(animate,17);
}
}
</script>
</head>
<body>
<canvas id='tutorial' width='1500' height='1500'>
</canvas>
</body>
</html>

You could just say you want a lightspeed effect!
One way very cheap way to do it is to paint the background with some transparency. You can also render a set of points close together in order to make the illusion of the effect.
The good way to do it is shaders since they will allow you to add glow and some other nice image trickery that will make it look better. Here is a good example: https://www.shadertoy.com/view/Xdl3D2
Below I used the canvas api lineTo and even with a fixed line width, it's a pretty good final result.
var MAX_DEPTH = 64;
var LINELENGTH = 0.1;
var stars = new Array(500);
var canvas = document.getElementById("tutorial");
canvas.width = innerWidth;
canvas.height = innerHeight;
var ctx = canvas.getContext("2d");
initStars();
setInterval(animate,17);
function randomRange(minVal, maxVal) {
return Math.floor(Math.random() * (maxVal - minVal - 1)) + minVal;
}
function initStars() {
for (var i = 0; i < stars.length; i++) {
stars[i] = {
x: randomRange(-25, 25),
y: randomRange(-25, 25),
z: randomRange(1, MAX_DEPTH)
}
}
}
function degToRad(deg) {
radians = (deg * Math.PI / 180) - Math.PI / 2;
return radians;
}
function animate() {
var halfWidth = canvas.width / 2;
var halfHeight = canvas.height / 2;
ctx.fillStyle = "rgba(0,0,0,1)";
ctx.fillRect(0, 0, canvas.width, canvas.height);
for (var i = 0; i < stars.length; i++) {
stars[i].z -= 0.5;
if (stars[i].z <= 0) {
stars[i].x = randomRange(-25, 25);
stars[i].y = randomRange(-25, 25);
stars[i].z = MAX_DEPTH;
}
var k = 254.0 / stars[i].z;
var px = stars[i].x * k + halfWidth;
var py = stars[i].y * k + halfHeight;
if (px >= 0 && px <= 1500 && py >= 0 && py <= 1500) {
var size = (1 - stars[i].z / 32.0) * 2;
var shade = parseInt((1 - stars[i].z / 32.0) * 750);
ctx.strokeStyle = "rgb(" + shade + "," + shade + "," + shade + ")";
ctx.lineWidth = size;
ctx.beginPath();
ctx.moveTo(px,py);
var ox = size * (px - halfWidth) * LINELENGTH;
var oy = size * (py - halfHeight) * LINELENGTH;
ctx.lineTo(px + ox, py + oy);
ctx.stroke();
}
}
}
<canvas id='tutorial' width='1500' height='1500'></canvas>

In round range slider, how can i change background color of the changed path?

I have got this function but i am unable to get the path to which the slider when dragged should change the background color of the circle...
$(document).ready(function () {
$("#circle").append('<canvas id="slideColorTracker" class="slideColor"></canvas>');
var canvas = document.getElementById("slideColorTracker");
var context = canvas.getContext('2d');
var $circle = $("#circle"),
$handler = $("#handler"),
$p = $("#test").val(),
handlerW2 = $handler.width() / 2,
radius = ($circle.width()/2)+10,
offset = $circle.offset(),
elementPos = { x: offset.left, y: offset.top },
mHold = 0,
PI = Math.PI / 180
$handler.mousedown(function () {
mHold = 1;
var dim = $("#slideColorTracker");
if ($(".slideColor").length > 1) {
$("#slideColorTracker").remove();
}
});
$(document).mousemove(function (e){
move(e);
}).mouseup(function () { mHold = 0 });
function move(e) {
if (mHold) {
debugger
var deg = 180;
var startAngle = 4.72;
var mousePos = { x: e.pageX - elementPos.x, y: e.pageY - elementPos.y }
var atan = Math.atan2(mousePos.x - radius, mousePos.y - radius);
var deg = -atan / PI + 180;
var percentage = (deg * 100 / 360) | 0;
var endAngle = percentage;
var X = Math.round(radius * Math.sin(deg * PI)),
Y = Math.round(radius * -Math.cos(deg * PI));
var cw = X + radius - handlerW2 - 10; //context.canvas.width /2;
var ch = Y + radius - handlerW2 - 10;
$handler.css({
left: X + radius - handlerW2 - 10,
top: Y + radius - handlerW2 - 10,
})
context.beginPath();
context.arc(($circle.width() / 2), ($circle.height() / 2), radius+20, startAngle, endAngle, false);
context.lineWidth = 15;
context.strokeStyle = 'black';
context.stroke();
$("#test").val(percentage);
$circle.css({ borderColor: "hsl(200,70%," + (percentage * 70 / 100 + 30) + "%)" });
}
}
});
I do not want to use any plugin!
Any help will be much appreciated, since i am new to jquery!

Your $handler does not drag for me unless I change it to this:
$handler.css({
left: mousePos.x,
top: mousePos.y,
position:'absolute'
})
When dragged passed $cirlce.width / 2 it does stroke it correctly.

How do I draw an arrow between two points in d3v4?

I have created a custom path renderer that draws an arrow between the nodes in my d3 graph as shown in the snippet. I have one last issue I am getting stuck on,
How would I rotate the arrow portion so that it is pointing from the direction of the curve instead of the direction of the source?
var w2 = 6,
ar2 = w2 * 2,
ah = w2 * 3,
baseHeight = 30;
// Arrow function
function CurvedArrow(context, index) {
this._context = context;
this._index = index;
}
CurvedArrow.prototype = {
areaStart: function() {
this._line = 0;
},
areaEnd: function() {
this._line = NaN;
},
lineStart: function() {
this._point = 0;
},
lineEnd: function() {
if (this._line || (this._line !== 0 && this._point === 1)) {
this._context.closePath();
}
this._line = 1 - this._line;
},
point: function(x, y) {
x = +x, y = +y; // jshint ignore:line
switch (this._point) {
case 0:
this._point = 1;
this._p1x = x;
this._p1y = y;
break;
case 1:
this._point = 2; // jshint ignore:line
default:
var p1x = this._p1x,
p1y = this._p1y,
p2x = x,
p2y = y,
dx = p2x - p1x,
dy = p2y - p1y,
px = dy,
py = -dx,
pr = Math.sqrt(px * px + py * py),
nx = px / pr,
ny = py / pr,
dr = Math.sqrt(dx * dx + dy * dy),
wx = dx / dr,
wy = dy / dr,
ahx = wx * ah,
ahy = wy * ah,
awx = nx * ar2,
awy = ny * ar2,
phx = nx * w2,
phy = ny * w2,
//Curve figures
alpha = Math.floor((this._index - 1) / 2),
direction = p1y < p2y ? -1 : 1,
height = (baseHeight + alpha * 3 * ar2) * direction,
// r5
//r7 r6|\
// ------------ \
// ____________ /r4
//r1 r2|/
// r3
r1x = p1x - phx,
r1y = p1y - phy,
r2x = p2x - phx - ahx,
r2y = p2y - phy - ahy,
r3x = p2x - awx - ahx,
r3y = p2y - awy - ahy,
r4x = p2x,
r4y = p2y,
r5x = p2x + awx - ahx,
r5y = p2y + awy - ahy,
r6x = p2x + phx - ahx,
r6y = p2y + phy - ahy,
r7x = p1x + phx,
r7y = p1y + phy,
//Curve 1
c1mx = (r2x + r1x) / 2,
c1my = (r2y + r1y) / 2,
m1b = (c1mx - r1x) / (r1y - c1my),
den1 = Math.sqrt(1 + Math.pow(m1b, 2)),
mp1x = c1mx + height * (1 / den1),
mp1y = c1my + height * (m1b / den1),
//Curve 2
c2mx = (r7x + r6x) / 2,
c2my = (r7y + r6y) / 2,
m2b = (c2mx - r6x) / (r6y - c2my),
den2 = Math.sqrt(1 + Math.pow(m2b, 2)),
mp2x = c2mx + height * (1 / den2),
mp2y = c2my + height * (m2b / den2);
this._context.moveTo(r1x, r1y);
this._context.quadraticCurveTo(mp1x, mp1y, r2x, r2y);
this._context.lineTo(r3x, r3y);
this._context.lineTo(r4x, r4y);
this._context.lineTo(r5x, r5y);
this._context.lineTo(r6x, r6y);
this._context.quadraticCurveTo(mp2x, mp2y, r7x, r7y);
break;
}
}
};
var w = 600,
h = 220;
var t0 = Date.now();
var points = [{
R: 100,
r: 3,
speed: 2,
phi0: 190
}];
var path = d3.line()
.curve(function(ctx) {
return new CurvedArrow(ctx, 1);
});
var svg = d3.select("svg");
var container = svg.append("g")
.attr("transform", "translate(" + w / 2 + "," + h / 2 + ")")
container.selectAll("g.planet").data(points).enter().append("g")
.attr("class", "planet").each(function(d, i) {
d3.select(this).append("circle").attr("r", d.r).attr("cx", d.R)
.attr("cy", 0).attr("class", "planet");
});
container.append("path");
var planet = d3.select('.planet circle');
d3.timer(function() {
var delta = (Date.now() - t0);
planet.attr("transform", function(d) {
return "rotate(" + d.phi0 + delta * d.speed / 50 + ")";
});
var g = document.createElementNS("http://www.w3.org/2000/svg", "g");
g.setAttributeNS(null, "transform", planet.attr('transform'));
var matrix = g.transform.baseVal.consolidate().matrix;
svg.selectAll("path").attr('d', function(d) {
return path([
[0, 0],
[matrix.a * 100, matrix.b * 100]
])
});
});
path {
stroke: #11a;
fill: #eee;
}
<script src="https://d3js.org/d3.v4.min.js"></script>
<svg width="600" height="220"></svg>

I ended up doing what #Mark suggested in the comments, I calculate the point that is the height of the curve away along the normal midway between the two points, then calculate the unit vectors from the start point to the mid point and again from the midpoint to the end. I can then use those to get all the required points.
var arrowRadius = 6,
arrowPointRadius = arrowRadius * 2,
arrowPointHeight = arrowRadius * 3,
baseHeight = 30;
// Arrow function
function CurvedArrow(context, index) {
this._context = context;
this._index = index;
}
CurvedArrow.prototype = {
areaStart: function() {
this._line = 0;
},
areaEnd: function() {
this._line = NaN;
},
lineStart: function() {
this._point = 0;
},
lineEnd: function() {
if (this._line || (this._line !== 0 && this._point === 1)) {
this._context.closePath();
}
this._line = 1 - this._line;
},
point: function(x, y) {
x = +x, y = +y; // jshint ignore:line
switch (this._point) {
case 0:
this._point = 1;
this._p1x = x;
this._p1y = y;
break;
case 1:
this._point = 2; // jshint ignore:line
default:
var p1x = this._p1x,
p1y = this._p1y,
p2x = x,
p2y = y,
//Curve figures
// mp1
// |
// | height
// |
// p1 ----------------------- p2
//
alpha = Math.floor((this._index - 1) / 2),
direction = p1y < p2y ? -1 : 1,
height = (baseHeight + alpha * 3 * arrowPointRadius) * direction,
c1mx = (p2x + p1x) / 2,
c1my = (p2y + p1y) / 2,
m1b = (c1mx - p1x) / (p1y - c1my),
den1 = Math.sqrt(1 + Math.pow(m1b, 2)),
// Perpendicular point from the midpoint.
mp1x = c1mx + height * (1 / den1),
mp1y = c1my + height * (m1b / den1),
// Arrow figures
dx = p2x - mp1x,
dy = p2y - mp1y,
dr = Math.sqrt(dx * dx + dy * dy),
// Normal unit vectors
nx = dy / dr,
wy = nx,
wx = dx / dr,
ny = -wx,
ahx = wx * arrowPointHeight,
ahy = wy * arrowPointHeight,
awx = nx * arrowPointRadius,
awy = ny * arrowPointRadius,
phx = nx * arrowRadius,
phy = ny * arrowRadius,
// Start arrow offset.
sdx = mp1x - p1x,
sdy = mp1y - p1y,
spr = Math.sqrt(sdy * sdy + sdx * sdx),
snx = sdy / spr,
sny = -sdx / spr,
sphx = snx * arrowRadius,
sphy = sny * arrowRadius,
// r5
//r7 r6|\
// ------------ \
// ____________ /r4
//r1 r2|/
// r3
r1x = p1x - sphx,
r1y = p1y - sphy,
r2x = p2x - phx - ahx,
r2y = p2y - phy - ahy,
r3x = p2x - awx - ahx,
r3y = p2y - awy - ahy,
r4x = p2x,
r4y = p2y,
r5x = p2x + awx - ahx,
r5y = p2y + awy - ahy,
r6x = p2x + phx - ahx,
r6y = p2y + phy - ahy,
r7x = p1x + sphx,
r7y = p1y + sphy,
mpc1x = mp1x - phx,
mpc1y = mp1y - phy,
mpc2x = mp1x + phx,
mpc2y = mp1y + phy;
this._context.moveTo(r1x, r1y);
this._context.quadraticCurveTo(mpc1x, mpc1y, r2x, r2y);
this._context.lineTo(r3x, r3y);
this._context.lineTo(r4x, r4y);
this._context.lineTo(r5x, r5y);
this._context.lineTo(r6x, r6y);
this._context.quadraticCurveTo(mpc2x, mpc2y, r7x, r7y);
this._context.closePath();
break;
}
}
};
var w = 600,
h = 220;
var t0 = Date.now();
var points = [{
R: 100,
r: 3,
speed: 2,
phi0: 190
}];
var path = d3.line()
.curve(function(ctx) {
return new CurvedArrow(ctx, 1);
});
var svg = d3.select("svg");
var container = svg.append("g")
.attr("transform", "translate(" + w / 2 + "," + h / 2 + ")")
container.selectAll("g.planet").data(points).enter().append("g")
.attr("class", "planet").each(function(d, i) {
d3.select(this).append("circle").attr("r", d.r).attr("cx", d.R)
.attr("cy", 0).attr("class", "planet");
});
container.append("path");
var planet = d3.select('.planet circle');
d3.timer(function() {
var delta = (Date.now() - t0);
planet.attr("transform", function(d) {
return "rotate(" + d.phi0 + delta * d.speed / 50 + ")";
});
var g = document.createElementNS("http://www.w3.org/2000/svg", "g");
g.setAttributeNS(null, "transform", planet.attr('transform'));
var matrix = g.transform.baseVal.consolidate().matrix;
svg.selectAll("path").attr('d', function(d) {
return path([
[0, 0],
[matrix.a * 100, matrix.b * 100]
])
});
});
path {
stroke: #11a;
fill: #eee;
}
<script src="https://d3js.org/d3.v4.min.js"></script>
<svg width="600" height="220"></svg>

Creating Falling Snow using HTML 5 and JS

I visited the Stack Exchange Winter Bash website and I love the falling snow! My question is, how can I recreate a similar effect that looks as nice. I attempted to reverse engineer the code to see if I could figure it out but alas no luck there. The JS is over my head. I did a bit of googling and came across some examples but they were not as elegant as the SE site or did not look very good.
Can anyone provide some instructions on how to replicate what the SE Winter Bash site creates or a place where I might learn how to do this?
Edit: I would like to replicate the effect as close as possible, IE: falling snow with snowflakes, and being able to move the mouse and cause the snow to move or swirl with the mouse moments.

Great question, I actually wrote a snow plugin a while ago that I continually update see it in action. Also a link to the pure js source
I noticed you tagged the question html5 and canvas, however you can do it without using either, and just standard elements with images or different background colors.
Here's two really simple ones I put together just now for you to mess with. The key in my opinion is using sin to get the nice wavy effect as the flakes fall. The first one uses the canvas element, the 2nd one uses regular dom elements.
Since I'm absolutely addicted to canvas here's a canvas version that performs quite nicely in my opinion.
Canvas version
Full Screen
(function() {
var requestAnimationFrame = window.requestAnimationFrame || window.mozRequestAnimationFrame || window.webkitRequestAnimationFrame || window.msRequestAnimationFrame ||
function(callback) {
window.setTimeout(callback, 1000 / 60);
};
window.requestAnimationFrame = requestAnimationFrame;
})();
var flakes = [],
canvas = document.getElementById("canvas"),
ctx = canvas.getContext("2d"),
flakeCount = 200,
mX = -100,
mY = -100
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
function snow() {
ctx.clearRect(0, 0, canvas.width, canvas.height);
for (var i = 0; i < flakeCount; i++) {
var flake = flakes[i],
x = mX,
y = mY,
minDist = 150,
x2 = flake.x,
y2 = flake.y;
var dist = Math.sqrt((x2 - x) * (x2 - x) + (y2 - y) * (y2 - y)),
dx = x2 - x,
dy = y2 - y;
if (dist < minDist) {
var force = minDist / (dist * dist),
xcomp = (x - x2) / dist,
ycomp = (y - y2) / dist,
deltaV = force / 2;
flake.velX -= deltaV * xcomp;
flake.velY -= deltaV * ycomp;
} else {
flake.velX *= .98;
if (flake.velY <= flake.speed) {
flake.velY = flake.speed
}
flake.velX += Math.cos(flake.step += .05) * flake.stepSize;
}
ctx.fillStyle = "rgba(255,255,255," + flake.opacity + ")";
flake.y += flake.velY;
flake.x += flake.velX;
if (flake.y >= canvas.height || flake.y <= 0) {
reset(flake);
}
if (flake.x >= canvas.width || flake.x <= 0) {
reset(flake);
}
ctx.beginPath();
ctx.arc(flake.x, flake.y, flake.size, 0, Math.PI * 2);
ctx.fill();
}
requestAnimationFrame(snow);
};
function reset(flake) {
flake.x = Math.floor(Math.random() * canvas.width);
flake.y = 0;
flake.size = (Math.random() * 3) + 2;
flake.speed = (Math.random() * 1) + 0.5;
flake.velY = flake.speed;
flake.velX = 0;
flake.opacity = (Math.random() * 0.5) + 0.3;
}
function init() {
for (var i = 0; i < flakeCount; i++) {
var x = Math.floor(Math.random() * canvas.width),
y = Math.floor(Math.random() * canvas.height),
size = (Math.random() * 3) + 2,
speed = (Math.random() * 1) + 0.5,
opacity = (Math.random() * 0.5) + 0.3;
flakes.push({
speed: speed,
velY: speed,
velX: 0,
x: x,
y: y,
size: size,
stepSize: (Math.random()) / 30,
step: 0,
angle: 180,
opacity: opacity
});
}
snow();
};
canvas.addEventListener("mousemove", function(e) {
mX = e.clientX,
mY = e.clientY
});
init();​
Standard element version
var flakes = [],
bodyHeight = getDocHeight(),
bodyWidth = document.body.offsetWidth;
function snow() {
for (var i = 0; i < 50; i++) {
var flake = flakes[i];
flake.y += flake.velY;
if (flake.y > bodyHeight - (flake.size + 6)) {
flake.y = 0;
}
flake.el.style.top = flake.y + 'px';
flake.el.style.left = ~~flake.x + 'px';
flake.step += flake.stepSize;
flake.velX = Math.cos(flake.step);
flake.x += flake.velX;
if (flake.x > bodyWidth - 40 || flake.x < 30) {
flake.y = 0;
}
}
setTimeout(snow, 10);
};
function init() {
var docFrag = document.createDocumentFragment();
for (var i = 0; i < 50; i++) {
var flake = document.createElement("div"),
x = Math.floor(Math.random() * bodyWidth),
y = Math.floor(Math.random() * bodyHeight),
size = (Math.random() * 5) + 2,
speed = (Math.random() * 1) + 0.5;
flake.style.width = size + 'px';
flake.style.height = size + 'px';
flake.style.background = "#fff";
flake.style.left = x + 'px';
flake.style.top = y;
flake.classList.add("flake");
flakes.push({
el: flake,
speed: speed,
velY: speed,
velX: 0,
x: x,
y: y,
size: 2,
stepSize: (Math.random() * 5) / 100,
step: 0
});
docFrag.appendChild(flake);
}
document.body.appendChild(docFrag);
snow();
};
document.addEventListener("mousemove", function(e) {
var x = e.clientX,
y = e.clientY,
minDist = 150;
for (var i = 0; i < flakes.length; i++) {
var x2 = flakes[i].x,
y2 = flakes[i].y;
var dist = Math.sqrt((x2 - x) * (x2 - x) + (y2 - y) * (y2 - y));
if (dist < minDist) {
rad = Math.atan2(y2, x2), angle = rad / Math.PI * 180;
flakes[i].velX = (x2 / dist) * 0.2;
flakes[i].velY = (y2 / dist) * 0.2;
flakes[i].x += flakes[i].velX;
flakes[i].y += flakes[i].velY;
} else {
flakes[i].velY *= 0.9;
flakes[i].velX
if (flakes[i].velY <= flakes[i].speed) {
flakes[i].velY = flakes[i].speed;
}
}
}
});
init();
function getDocHeight() {
return Math.max(
Math.max(document.body.scrollHeight, document.documentElement.scrollHeight), Math.max(document.body.offsetHeight, document.documentElement.offsetHeight), Math.max(document.body.clientHeight, document.documentElement.clientHeight));
}​

I've created a pure HTML 5 and js snowfall.
Check it out on my code pen here: https://codepen.io/onlintool24/pen/GRMOBVo
// Amount of Snowflakes
var snowMax = 35;
// Snowflake Colours
var snowColor = ["#DDD", "#EEE"];
// Snow Entity
var snowEntity = "•";
// Falling Velocity
var snowSpeed = 0.75;
// Minimum Flake Size
var snowMinSize = 8;
// Maximum Flake Size
var snowMaxSize = 24;
// Refresh Rate (in milliseconds)
var snowRefresh = 50;
// Additional Styles
var snowStyles = "cursor: default; -webkit-user-select: none; -moz-user-select: none; -ms-user-select: none; -o-user-select: none; user-select: none;";
/*
// End of Configuration
// ----------------------------------------
// Do not modify the code below this line
*/
var snow = [],
pos = [],
coords = [],
lefr = [],
marginBottom,
marginRight;
function randomise(range) {
rand = Math.floor(range * Math.random());
return rand;
}
function initSnow() {
var snowSize = snowMaxSize - snowMinSize;
marginBottom = document.body.scrollHeight - 5;
marginRight = document.body.clientWidth - 15;
for (i = 0; i <= snowMax; i++) {
coords[i] = 0;
lefr[i] = Math.random() * 15;
pos[i] = 0.03 + Math.random() / 10;
snow[i] = document.getElementById("flake" + i);
snow[i].style.fontFamily = "inherit";
snow[i].size = randomise(snowSize) + snowMinSize;
snow[i].style.fontSize = snow[i].size + "px";
snow[i].style.color = snowColor[randomise(snowColor.length)];
snow[i].style.zIndex = 1000;
snow[i].sink = snowSpeed * snow[i].size / 5;
snow[i].posX = randomise(marginRight - snow[i].size);
snow[i].posY = randomise(2 * marginBottom - marginBottom - 2 * snow[i].size);
snow[i].style.left = snow[i].posX + "px";
snow[i].style.top = snow[i].posY + "px";
}
moveSnow();
}
function resize() {
marginBottom = document.body.scrollHeight - 5;
marginRight = document.body.clientWidth - 15;
}
function moveSnow() {
for (i = 0; i <= snowMax; i++) {
coords[i] += pos[i];
snow[i].posY += snow[i].sink;
snow[i].style.left = snow[i].posX + lefr[i] * Math.sin(coords[i]) + "px";
snow[i].style.top = snow[i].posY + "px";
if (snow[i].posY >= marginBottom - 2 * snow[i].size || parseInt(snow[i].style.left) > (marginRight - 3 * lefr[i])) {
snow[i].posX = randomise(marginRight - snow[i].size);
snow[i].posY = 0;
}
}
setTimeout("moveSnow()", snowRefresh);
}
for (i = 0; i <= snowMax; i++) {
document.write("<span id='flake" + i + "' style='" + snowStyles + "position:absolute;top:-" + snowMaxSize + "'>" + snowEntity + "</span>");
}
window.addEventListener('resize', resize);
window.addEventListener('load', initSnow);
body{
background: skyblue;
height:100%;
width:100%;
display:block;
position:relative;
}
<span id="flake0" style="cursor: default; user-select: none; position: absolute; font-family: inherit; font-size: 19px; color: rgb(221, 221, 221); z-index: 1000; left: 226px; top: 561px;">•</span>

The falling snow is simple: Create a canvas, create a bunch of snowflakes, draw them.
You can create a snowflake class like so:
function Snowflake() {
this.x = Math.random()*canvas.width;
this.y = -16;
this.speed = Math.random()*3+1;
this.direction = Math.random()*360;
this.maxSpeed = 4;
}
Or something like that. Then you have a timer that, each step, adjusts each snowflake's direction by a small amount, and then calculates its new X and Y by factoring in the Speed and Direction.
It's hard to explain, but actually quite basic.