Deconstructing Google maps smarty pins animation - math

Question

Updates
Updated fiddle to simplify what is going on:
added four buttons to move the stick, each button increments the value by 30 in the direction
plotted x and y axis
red line is the stick, with bottom end coordinates at (ax,ay) and top end coordinates at (bx,by)
green line is (presumably) previous position of the stick, with bottom end coordinates at (ax, ay) and top end coordinates at (bx0, by0)
So, after having my ninja moments. I'm still nowhere near understanding the sorcery behind unknownFunctionA and unknownFunctionB
For the sake of everyone (all two of you) here is what I've sort of learnt so far
function unknownFunctionB(e) {
var t = e.b.x - e.a.x
, n = e.b.y - e.a.y
, a = t * t + n * n;
if (a > 0) {
if (a == e.lengthSq)
return;
var o = Math.sqrt(a)
, i = (o - e.length) / o
, s = .5;
e.b.x -= t * i * .5 * s,
e.b.y -= n * i * .5 * s
}
}
In the unknownFunctionB above, variable o is length of the red sitck.
Still don't understand
What is variable i and how is (bx,by) calculated? essentially:
bx = bx - (bx - ax) * 0.5 * 0.5
by = by - (by - ay) * 0.5 * 0.5
In unknownFunctionA what are those magic numbers 1.825 and 0.825?
Below is irrelevant
I'm trying to deconstruct marker drag animation used on smartypins
I've managed to get the relevant code for marker move animation but I'm struggling to learn how it all works, especially 2 functions (that I've named unknownFunctionA and unknownFunctionB)
Heres the StickModel class used on smartypins website, unminified to best of my knowledge
function unknownFunctionA(e) {
var t = 1.825
, n = .825
, a = t * e.x - n * e.x0
, o = t * e.y - n * e.y0 - 5;
e.x0 = e.x,
e.y0 = e.y,
e.x = a,
e.y = o;
}
function unknownFunctionB(e) {
var t = e.b.x - e.a.x
, n = e.b.y - e.a.y
, a = t * t + n * n;
if (a > 0) {
if (a == e.lengthSq)
return;
var o = Math.sqrt(a)
, i = (o - e.length) / o
, s = .5;
e.b.x -= t * i * .5 * s,
e.b.y -= n * i * .5 * s
}
}
function StickModel() {
this._props = function(e) {
return {
length: e,
lengthSq: e * e,
a: {
x: 0,
y: 0
},
b: {
x: 0,
y: 0 - e,
x0: 0,
y0: 0 - e
},
angle: 0
}
}
(60)
}
var radianToDegrees = 180 / Math.PI;
StickModel.prototype = {
pos: {
x: 0,
y: 0
},
angle: function() {
return this._props.angle
},
reset: function(e, t) {
var n = e - this._props.a.x
, a = t - this._props.a.y;
this._props.a.x += n,
this._props.a.y += a,
this._props.b.x += n,
this._props.b.y += a,
this._props.b.x0 += n,
this._props.b.y0 += a
},
move: function(e, t) {
this._props.a.x = e,
this._props.a.y = t
},
update: function() {
unknownFunctionA(this._props.b),
unknownFunctionB(this._props),
this.pos.x = this._props.a.x,
this.pos.y = this._props.a.y;
var e = this._props.b.x - this._props.a.x
, t = this._props.b.y - this._props.a.y
, o = Math.atan2(t, e);
this._props.angle = o * radianToDegrees;
}
}
StickModel.prototype.constructor = StickModel;
Fiddle link with sample implementation on canvas: http://jsfiddle.net/vff1w82w/3/
Again, Everything works as expected, I'm just really curious to learn the following:
What could be the ideal names for unknownFunctionA and unknownFunctionB and an explanation of their functionality
What are those magic numbers in unknownFunctionA (1.825 and .825) and .5 in unknownFunctionB.
Variable o in unknownFunctionB appears to be hypotenuse. If that's the case, then what exactly is i = (o - e.length) / o in other words, i = (hypotenuse - stickLength) / hypotenuse?

Answer 1

First thing I'd recommend is renaming all those variables and methods until they start making sense. I also removed unused code.
oscillator
adds wobble to the Stick model by creating new position values for the Stick that follows the mouse
Exaggerates its movement by multiplying its new position by 1.825 and also subtracting the position of an "echo" of its previous position multiplied by 0.825. Sort of looking for a middle point between them. Helium makes the stick sit upright.
overshooter minus undershooter must equal 1 or you will have orientation problems with your stick. overshooter values above 2.1 tend to make it never settle.
seekerUpdate
updates the seeker according to mouse positions.
The distance_to_cover variable measures the length of the total movement. You were right: hypothenuse (variable o).
The ratio variable calculates the ratio of the distance that can be covered subtracting the size of the stick. The ratio is then used to limit the adjustment of the update on the seeker in both directions (x and y). That's how much of the update should be applied to prevent overshooting the target.
easing slows down the correct updates.
There are lots of interesting info related to vectors on the book The nature of code.
function oscillator(seeker) {
var overshooter = 1.825;
var undershooter = .825;
var helium = -5;
var new_seeker_x = overshooter * seeker.x - undershooter * seeker.echo_x;
var new_seeker_y = overshooter * seeker.y - undershooter * seeker.echo_y + helium;
seeker.echo_x = seeker.x;
seeker.echo_y = seeker.y;
seeker.x = new_seeker_x;
seeker.y = new_seeker_y;
}
function seekerUpdate(stick) {
var dX = stick.seeker.x - stick.mouse_pos.x;
var dY = stick.seeker.y - stick.mouse_pos.y;
var distance_to_cover = Math.sqrt(dX * dX + dY * dY);
var ratio = (distance_to_cover - stick.length) / distance_to_cover;
var easing = .25;
stick.seeker.x -= dX * ratio * easing;
stick.seeker.y -= dY * ratio * easing;
}
function StickModel() {
this._props = function(length) {
return {
length: length,
lengthSq: length * length,
mouse_pos: {
x: 0,
y: 0
},
seeker: {
x: 0,
y: 0 - length,
echo_x: 0,
echo_y: 0 - length
}
}
}(60)
}
StickModel.prototype = {
move: function(x, y) {
this._props.mouse_pos.x = x;
this._props.mouse_pos.y = y;
},
update: function() {
oscillator(this._props.seeker);
seekerUpdate(this._props);
}
};
StickModel.prototype.constructor = StickModel;
// Canvas to draw stick model coordinates
var canvas = document.getElementById('myCanvas');
var context = canvas.getContext('2d');
canvas.width = window.outerWidth;
canvas.height = window.outerHeight;
var canvasCenterX = Math.floor(canvas.width / 2);
var canvasCenterY = Math.floor(canvas.height / 2);
context.translate(canvasCenterX, canvasCenterY);
var stickModel = new StickModel();
draw();
setInterval(function() {
stickModel.update();
draw();
}, 16);
$(window).mousemove(function(e) {
var mouseX = (e.pageX - canvasCenterX);
var mouseY = (e.pageY - canvasCenterY);
stickModel.move(mouseX, mouseY);
stickModel.update();
draw();
});
function draw() {
context.clearRect(-canvas.width, -canvas.height, canvas.width * 2, canvas.height * 2);
// red line from (ax, ay) to (bx, by)
context.beginPath();
context.strokeStyle = "#ff0000";
context.moveTo(stickModel._props.mouse_pos.x, stickModel._props.mouse_pos.y);
context.lineTo(stickModel._props.seeker.x, stickModel._props.seeker.y);
context.fillText('mouse_pos x:' + stickModel._props.mouse_pos.x + ' y: ' + stickModel._props.mouse_pos.y, stickModel._props.mouse_pos.x, stickModel._props.mouse_pos.y);
context.fillText('seeker x:' + stickModel._props.seeker.x + ' y: ' + stickModel._props.seeker.y, stickModel._props.seeker.x - 30, stickModel._props.seeker.y);
context.lineWidth = 1;
context.stroke();
context.closePath();
// green line from (ax, ay) to (bx0, by0)
context.beginPath();
context.strokeStyle = "#00ff00";
context.moveTo(stickModel._props.mouse_pos.x, stickModel._props.mouse_pos.y);
context.lineTo(stickModel._props.seeker.echo_x, stickModel._props.seeker.echo_y);
context.fillText('echo x:' + stickModel._props.seeker.echo_x + ' y: ' + stickModel._props.seeker.echo_y, stickModel._props.seeker.echo_x, stickModel._props.seeker.echo_y - 20);
context.lineWidth = 1;
context.stroke();
context.closePath();
// blue line from (bx0, by0) to (bx, by)
context.beginPath();
context.strokeStyle = "#0000ff";
context.moveTo(stickModel._props.seeker.echo_x, stickModel._props.seeker.echo_y);
context.lineTo(stickModel._props.seeker.x, stickModel._props.seeker.y);
context.stroke();
context.closePath();
}
body {
margin: 0px;
padding: 0px;
}
canvas {
display: block;
}
p {
position: absolute;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.0/jquery.min.js"></script>
<p>Move your mouse to see the stick (colored red) follow</p>
<canvas id="myCanvas"></canvas>