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svg.js animated rotation of elements gives unexpected results (visible "jiggling")

I am using svg.js to create an animation of a bicyle rider. Semi-complete version here: https://pedalfuriously.neocities.org/. I'm running in to a bit of a problem with moving and rotating svg elements during animation created with requestAnimationFrame (rather than the svg.js built in animation).
If you take a look at the link, and use the cadence slider to make the rider pedal very fast, and then flip the slider quickly all the way back to zero, you can see that his lower leg "jiggles" in a disconnected way. What's really doing my head in is that the postion of the legs are determined in each frame based on an absolute relation to the rotation of the cranks (rather than taking some delta time value to determine movement over that frame).
I think I've been able to confirm what aspect of my code is causing the problem. Here is a minimal example that doesn't exhibit the exact behaviour, but I think illustrates the kind of thing I think is responsible:
var draw = SVG("drawing").viewbox(0, 0, 400, 400)
var origin = {
x: 70,
y: 70
}
var length = 60
var blueLine = draw.group()
blueLine.line(0, 0, 0 + length, 0).move(origin.x, origin.y)
.stroke({
color: "#00f",
width: 4
})
blueLine.angle = 0
var greenLine = draw.group()
greenLine.line(0, 0, 0 + length, 0).move(origin.x, origin.y)
.stroke({
color: "#0f0",
width: 4
})
greenLine.angle = 0
var previous = 0
var dt = 0
var step = function(timestamp) {
dt = timestamp - previous
previous = timestamp
blueLine.angle += 0.18 * dt
blueLine.rotate(blueLine.angle, origin.x, origin.y)
var endX = Math.cos(toRad(blueLine.angle)) * length
var endY = Math.sin(toRad(blueLine.angle)) * length
// Comment out this line, and rotation works fine
greenLine.move(endX, endY)
greenLine.angle = blueLine.angle - 10
// Comment out this line, and movement works fine
greenLine.rotate(greenLine.angle, origin.x, origin.y)
// But they don't work together. If I both move and rotate
// the green line, it goes in this crazy huge arc, rather
// than rotating neatly around the end of the blue line
// as expected.
window.requestAnimationFrame(step)
}
window.requestAnimationFrame(step)
function toRad(deg) {
return deg * (Math.PI / 180)
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/svg.js/2.6.4/svg.js"></script>
<div id="drawing"></div>
Something else I noticed with my actual code is that if I move the position of the legs, it changes the severity of the problem, or even stops it altogether. If the hips are positioned all the way near the front of the bicycle, the problem is not nearly as bad. Also, if I disable rotation on the lower legs, there is no jiggling. In some positions, the lower leg will just rotate out of the screen instantly on load, even before any motion has been started.
I'm hoping for some guidance on wether I'm misunderstanding the way manipulating elements works, either in svg.js in particular, or SVG in general.
Thank you kind vector graphics experts!
Here is the actual code for the legs. The step() function would probably be the most relevant. Not sure if it will be helpful:
Rider.Leg = function(foot, front, xOffset, yOffset) {
var upper = front ? SVGE.upperLeg : SVGE.upperLegBack
var lower = front ? SVGE.lowerLeg : SVGE.lowerLegBack
this.foot = foot
this.draw = foot.draw
this.geo = {
upper: {
x: this.foot.pedal.gear.x + 150,
y: this.foot.pedal.gear.y - 750,
length: 396
},
lower: {
length: 390
}
}
this.upper = this.draw.group().svg(upper).move(this.geo.upper.x, this.geo.upper.y)
.transform({ scale: 0.95, cx: 0, cy: 0 })
this.lower = this.draw.group().svg(lower).move(this.geo.upper.x, this.geo.upper.y)
}
// Step function does not take in a time argument. Positioning of legs is based only on
// the absolute position of other elements, none of which jiggle.
Rider.Leg.prototype.step = function () {
var angle = this.pedalAngle() - Math.PI
var ha = this.scaleneAngle(this.geo.lower.length, this.geo.upper.length, this.pedalDistance())
var ka = this.scaleneAngle(this.pedalDistance(), this.geo.lower.length, this.geo.upper.length)
var x = this.geo.upper.length * Math.cos(ha + angle)
var y = this.geo.upper.length * Math.sin(ha + angle)
this.upper.rotate(Drive.toDeg(angle + ha), 0, 0)
this.lower.move(this.geo.upper.x + x, + this.geo.upper.y + y)
this.lower.rotate(Drive.toDeg(angle + ha + ka - Math.PI), 0, 0)
}
// Gets the distance between the hip joint and the pedal
Rider.Leg.prototype.pedalDistance = function () {
var pos = this.foot.getPos()
var xDist = this.geo.upper.x - pos.x
var yDist = this.geo.upper.y - pos.y
return Math.hypot(xDist, yDist)
}
// Gets the angle between the hip joint and the pedal
Rider.Leg.prototype.pedalAngle = function () {
var pos = this.foot.getPos()
var xDist = this.geo.upper.x - pos.x
var yDist = this.geo.upper.y - pos.y
return Math.atan2(yDist, xDist)
}
Rider.Leg.prototype.scaleneAngle = function (a, b, c) {
return Math.acos(((b * b) + (c * c) - (a * a)) / (2 * b * c))
}

When you call move() on a group it is internally represented as a translation. svg.js figures out crazy ways to translate the object to the new place without changing any other transformations. That often does not work out. Especially not, when you rotate.
Thats why you should avoid these absolute transformations and go with relative ones. Just call untransform before every move and go from zero. Then you can do:
greenLine.transform({x:endX, y:endY, relative: true})
To move the line by a certain amount. That should work way better.

d3.js version 4 - rect zoom - cannot get the transformation right

d3.js verison 4:
I have a line chart, which should have a rectangle zoom.
I used this example: http://bl.ocks.org/jasondavies/3689931
I don't want to apply the rectangle data to the scales, like in the example
Instead I want to apply this to my normal zoom Element.
For that I have the math:
.on("mouseup.zoomRect", function() {
d3.select(window).on("mousemove.zoomRect", null).on("mouseup.zoomRect", null);
d3.select("body").classed("noselect", false);
var m = d3.mouse(e);
m[0] = Math.max(0, Math.min(width, m[0]));
m[1] = Math.max(0, Math.min(height, m[1]));
if (m[0] !== origin[0] && m[1] !== origin[1]) {
//different code here
//I have the scale factor
var zoomRectWidth = Math.abs(m[0] - origin[0]);
scaleFactor = width / zoomRectWidth;
//Getting the translation
var translateX = Math.min(m[0], origin[0]);
//Apply to __zoom Element
var t = d3.zoomTransform(e.node());
e.transition()
.duration(that.chart.animationDuration)
.call(that.chart.zoomX.transform, t
.translate(translateX, 0)
.scale(scaleFactor)
.translate(-translateX, 0)
);
}
rect.remove();
refresh();
}, true);
So I actually get the scaleFactor right and it zooms in smoothly.
Only problem is, that I don't seem to get the translation correct.
So it zooms in to the wrong position.

So, now I got it right:
All transformations by earlier zooms need to be undone.
so that k = 1, x = 0, y = 0;
This is the d3.zoomIdentity.
From that point the current zoom needs to be applied and afterwards the translation.
After that the old transform needs to be applied, first translate and then scale
var t = d3.zoomTransform(e.node());
//store x translation
var x = t.x;
//store scaling factor
var k = t.k;
//apply first rect zoom scale and then translation
//then old translate and old zoom scale
e.transition()
.call(that.chart.zoomX.transform, d3.zoomIdentity
.scale(scaleFactor)
.translate(-translateX, 0)
.translate(x)
.scale(k)
);
Working Fiddle only for X-Axis here: https://jsfiddle.net/9j4kqq1v/3/
Working fiddle for X and Y-axis here: https://jsfiddle.net/9j4kqq1v/5/

Realistic mouse movement coordinates in javascript?

In javascript, is there a way I can create a variable and a function that "simulates" smooth mouse movement? i.e., say the function simulates a user starts from lower left corner of the browser window, and then moves mouse in a random direction slowly...
The function would return x and y value of the next position the mouse would move each time it is called (would probably use something like setInterval to keep calling it to get the next mouse position). Movement should be restricted to the width and height of the screen, assuming the mouse never going off of it.
What I don't want is the mouse to be skipping super fast all over the place. I like smooth movements/positions being returned.

A "realistic mouse movement" doesn't mean anything without context :
Every mouse user have different behaviors with this device, and they won't even do the same gestures given what they have on their screen.
If you take an FPS game, the movements will in majority be in a small vertical range, along the whole horizontal screen.
Here is a "drip painting" I made by recording my mouse movements while playing some FPS game.
If we take the google home page however, I don't even use the mouse. The input is already focused, and I just use my keyboard.
On some infinite scrolling websites, my mouse can stay at the same position for dozens of minutes and just go to a link at some point.
I think that to get the more realistic mouse movements possible, you would have to record all your users' gestures, and repro them.
Also, a good strategy could be to get the coordinates of the elements that will attract user's cursor the more likely (like the "close" link under SO's question) and make movements go to those elements' coordinates.
Anyway, here I made a snippet which uses Math.random() and requestAnimationFrame() in order to make an object move smoothly, with some times of pausing, and variable speeds.
// Canvas is here only to show the output of function
var canvas = document.createElement('canvas');
var ctx = canvas.getContext('2d');
document.body.appendChild(canvas);
var maxX = canvas.width = window.innerWidth;
var maxY = canvas.height = window.innerHeight;
window.onresize = function(){
maxX = canvas.width = window.innerWidth;
maxY = canvas.height = window.innerHeight;
}
gc.onclick = function(){
var coords = mouse.getCoords();
out.innerHTML = 'x : '+coords.x+'<br>y : '+coords.y;
}
var Mouse = function() {
var that = {},
size = 15,
border = size / 2,
maxSpeed = 50, // pixels per frame
maxTimePause = 5000; // ms
that.draw = function() {
if (that.paused)
return;
that.update();
// just for the example
ctx.clearRect(0, 0, canvas.width, canvas.height);
if(show.checked){
ctx.drawImage(that.img, that.x - border, that.y - border, size, size)
}
// use requestAnimationFrame for smooth update
requestAnimationFrame(that.draw);
}
that.update = function() {
// take a random position, in the same direction
that.x += Math.random() * that.speedX;
that.y += Math.random() * that.speedY;
// if we're out of bounds or the interval has passed
if (that.x <= border || that.x >= maxX - border || that.y <= 0 || that.y >= maxY - border || ++that.i > that.interval)
that.reset();
}
that.reset = function() {
that.i = 0; // reset the counter
that.interval = Math.random() * 50; // reset the interval
that.speedX = (Math.random() * (maxSpeed)) - (maxSpeed / 2); // reset the horizontal direction
that.speedY = (Math.random() * (maxSpeed)) - (maxSpeed / 2); // reset the vertical direction
// we're in one of the corner, and random returned farther out of bounds
if (that.x <= border && that.speedX < 0 || that.x >= maxX - border && that.speedX > 0)
// change the direction
that.speedX *= -1;
if (that.y <= border && that.speedY < 0 || that.y >= maxY - border && that.speedY > 0)
that.speedY *= -1;
// check if the interval was complete
if (that.x > border && that.x < maxX - border && that.y > border && that.y < maxY - border) {
if (Math.random() > .5) {
// set a pause and remove it after some time
that.paused = true;
setTimeout(function() {
that.paused = false;
that.draw();
}, (Math.random() * maxTimePause));
}
}
}
that.init = function() {
that.x = 0;
that.y = 0;
that.img = new Image();
that.img.src ="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAeCAYAAAA7MK6iAAABJUlEQVRIic2WXbHEIAyFI6ESKgEJkVIJlYCTSqiESIiESqiEb19gL9Od3f5R5mbmPPHwBTgnIPJfChiAGbCkCQgtG7BpmgAWIALaDDyOI2bGuq40BasqIoKZATgwNAWHEEjHbkBsBhYRVJUYIwBNwVlFaVOwiDDPMylmQ1OwquY7d0CBrglYkuEeidoeOKt61I6Cq0ftKFhqR+0MOKuo2BQsInnndvnOr4JvR+0qWO5G7Q44K0XtOXDf96jqh9z9WXAy1FJ8l0qd+zbtvU7lWs7wIzkuh8SvpqqDi3zGndPQauDkzvdESm8xZvbh4mVZ7k8ud/+aR0C3YPk7mVvgkCZPVrdZV3dHVem6bju1roMPNmbAmq8kG+/ynD7ZwNsAVVz9dL0AhBrZq7F+CSQAAAAASUVORK5CYII=";
that.reset();
}
that.getCoords = function(){
return {x: that.x, y:that.y};
}
that.init()
return that;
}
var mouse = new Mouse()
mouse.draw();
html,body {margin: 0}
canvas {position: absolute; top:0; left:0;z-index:-1}
#out{font-size: 0.8em}
<label for="show">Display cursor</label><input name="show" type="checkbox" id="show" checked="true"/><br>
<button id="gc">get cursor Coords</button>
<p id="out"></p>

Last I heard the browser's mouse position cannot be altered with JavaScript, so the question really has no answer "as is". The mouse position can be locked though. I'm not certain whether it would be possible to implement a custom cursor that allows setting the position. This would include hiding and perhaps locking the stock cursor.

Having something smoothly follow the cursor is quite straight forward. You may be able to reverse this process to achieve what you need. Here's a code snippet which simply calculates the distance between the cursor and a div every frame and then moves the div 10% of that distance towards the cursor:
http://jsfiddle.net/hpp0qb0d/
var p = document.getElementById('nextmove')
var lastX,lastY,cursorX,cursorY;
window.addEventListener('mousemove', function(e){
cursorX = e.pageX;
cursorY = e.pageY;
})
setInterval(function(){
var newX = p.offsetLeft + (cursorX - lastX)/10
var newY = p.offsetTop + (cursorY - lastY)/10
p.style.left = newX+'px'
p.style.top = newY+'px'
lastX = p.offsetLeft
lastY = p.offsetTop
},20)

KineticJS and pinch and zoom

I would like to achieve this effect outlined here: http://www.html5canvastutorials.com/labs/html5-canvas-multi-touch-scale-stage-with-kineticjs/
But on a Layer in KineticJS
I have already got it working to a degree (using basically the same code as in the link), but it seems the Layer scales around the 0,0 origin point and I cannot see any doco about changing the transform origin?
How can I effectively pinch and zoom a Layer such that it scales around it center point?

I made a plugin for this kind of behavior: https://github.com/eduplus/pinchlayer
It is probably a little outdated now with the recent changes, but the logic in layerTouchMove function is most likely still sound. Here:
var touch1 = event.touches[0];
var touch2 = event.touches[1];
if (touch1 && touch2) {
self.setDraggable(false);
if (self.trans != undefined) { self.trans.stop(); }
if (self.startDistance === undefined) {
self.startDistance = self.getDistance(touch1, touch2);
self.touchPosition.x = (touch1.clientX + touch2.clientX) / 2;
self.touchPosition.y = (touch1.clientY + touch2.clientY) / 2;
self.layerPosition.x = (Math.abs(self.getX()) + self.touchPosition.x) / self.startScale;
self.layerPosition.y = (Math.abs(self.getY()) + self.touchPosition.y) / self.startScale;
}
else {
var dist = self.getDistance(touch1, touch2);
var scale = (dist / self.startDistance) * self.startScale;
if (scale < self.minScale) { scale = self.minScale; }
if (scale > self.maxScale) { scale = self.maxScale; }
self.setScale(scale, scale);
var x = (self.layerPosition.x * scale) - self.touchPosition.x;
var y = (self.layerPosition.y * scale) - self.touchPosition.y;
var pos = self.checkBounds({ x: -x, y: -y });
self.setPosition(pos.x, pos.y);
self.draw();
}
Basically it will record the starting point and the distance (how long the pinch is) and then scale and set the layer position accordingly. Hope this helps.

Zoom Canvas to Mouse Cursor

I'm programming a HTML5 < canvas > project that involves zooming in and out of images using the scroll wheel.
I want to zoom towards the cursor like google maps does but I'm completely lost on how to calculate the movements.
What I have: image x and y (top-left corner); image width and height; cursor x and y relative to the center of the canvas.

In short, you want to translate() the canvas context by your offset, scale() it to zoom in or out, and then translate() back by the opposite of the mouse offset. Note that you need to transform the cursor position from screen space into the transformed canvas context.
ctx.translate(pt.x,pt.y);
ctx.scale(factor,factor);
ctx.translate(-pt.x,-pt.y);
Demo: http://phrogz.net/tmp/canvas_zoom_to_cursor.html
I've put up a full working example on my website for you to examine, supporting dragging, click to zoom in, shift-click to out, or scroll wheel up/down.
The only (current) issue is that Safari zooms too fast compared to Chrome or Firefox.

I hope, these JS libraries will help you:
(HTML5, JS)
Loupe
http://www.netzgesta.de/loupe/
CanvasZoom
https://github.com/akademy/CanvasZoom
Scroller
https://github.com/zynga/scroller
As for me, I'm using loupe. It's awesome!
For you the best case - scroller.

I recently needed to archive same results as Phrogz had already done but instead of using context.scale(), I calculated each object size based on ratio.
This is what I came up with. Logic behind it is very simple. Before scaling, I calculate point distance from edge in percentages and later adjust viewport to correct place.
It took me quite a while to come up with it, hope it saves someones time.
$(function () {
var canvas = $('canvas.main').get(0)
var canvasContext = canvas.getContext('2d')
var ratio = 1
var vpx = 0
var vpy = 0
var vpw = window.innerWidth
var vph = window.innerHeight
var orig_width = 4000
var orig_height = 4000
var width = 4000
var height = 4000
$(window).on('resize', function () {
$(canvas).prop({
width: window.innerWidth,
height: window.innerHeight,
})
}).trigger('resize')
$(canvas).on('wheel', function (ev) {
ev.preventDefault() // for stackoverflow
var step
if (ev.originalEvent.wheelDelta) {
step = (ev.originalEvent.wheelDelta > 0) ? 0.05 : -0.05
}
if (ev.originalEvent.deltaY) {
step = (ev.originalEvent.deltaY > 0) ? 0.05 : -0.05
}
if (!step) return false // yea..
var new_ratio = ratio + step
var min_ratio = Math.max(vpw / orig_width, vph / orig_height)
var max_ratio = 3.0
if (new_ratio < min_ratio) {
new_ratio = min_ratio
}
if (new_ratio > max_ratio) {
new_ratio = max_ratio
}
// zoom center point
var targetX = ev.originalEvent.clientX || (vpw / 2)
var targetY = ev.originalEvent.clientY || (vph / 2)
// percentages from side
var pX = ((vpx * -1) + targetX) * 100 / width
var pY = ((vpy * -1) + targetY) * 100 / height
// update ratio and dimentsions
ratio = new_ratio
width = orig_width * new_ratio
height = orig_height * new_ratio
// translate view back to center point
var x = ((width * pX / 100) - targetX)
var y = ((height * pY / 100) - targetY)
// don't let viewport go over edges
if (x < 0) {
x = 0
}
if (x + vpw > width) {
x = width - vpw
}
if (y < 0) {
y = 0
}
if (y + vph > height) {
y = height - vph
}
vpx = x * -1
vpy = y * -1
})
var is_down, is_drag, last_drag
$(canvas).on('mousedown', function (ev) {
is_down = true
is_drag = false
last_drag = { x: ev.clientX, y: ev.clientY }
})
$(canvas).on('mousemove', function (ev) {
is_drag = true
if (is_down) {
var x = vpx - (last_drag.x - ev.clientX)
var y = vpy - (last_drag.y - ev.clientY)
if (x <= 0 && vpw < x + width) {
vpx = x
}
if (y <= 0 && vph < y + height) {
vpy = y
}
last_drag = { x: ev.clientX, y: ev.clientY }
}
})
$(canvas).on('mouseup', function (ev) {
is_down = false
last_drag = null
var was_click = !is_drag
is_drag = false
if (was_click) {
}
})
$(canvas).css({ position: 'absolute', top: 0, left: 0 }).appendTo(document.body)
function animate () {
window.requestAnimationFrame(animate)
canvasContext.clearRect(0, 0, canvas.width, canvas.height)
canvasContext.lineWidth = 1
canvasContext.strokeStyle = '#ccc'
var step = 100 * ratio
for (var x = vpx; x < width + vpx; x += step) {
canvasContext.beginPath()
canvasContext.moveTo(x, vpy)
canvasContext.lineTo(x, vpy + height)
canvasContext.stroke()
}
for (var y = vpy; y < height + vpy; y += step) {
canvasContext.beginPath()
canvasContext.moveTo(vpx, y)
canvasContext.lineTo(vpx + width, y)
canvasContext.stroke()
}
canvasContext.strokeRect(vpx, vpy, width, height)
canvasContext.beginPath()
canvasContext.moveTo(vpx, vpy)
canvasContext.lineTo(vpx + width, vpy + height)
canvasContext.stroke()
canvasContext.beginPath()
canvasContext.moveTo(vpx + width, vpy)
canvasContext.lineTo(vpx, vpy + height)
canvasContext.stroke()
canvasContext.restore()
}
animate()
})
<!DOCTYPE html>
<html>
<head>
<title></title>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
</head>
<body>
<canvas class="main"></canvas>
</body>
</html>

I took #Phrogz's answer as a basis and made a small library that enables canvas with dragging, zooming and rotating.
Here is the example.
var canvas = document.getElementById('canvas')
//assuming that #param draw is a function where you do your main drawing.
var control = new CanvasManipulation(canvas, draw)
control.init()
control.layout()
//now you can drag, zoom and rotate in canvas
You can find more detailed examples and documentation on the project's page

Faster
Using ctx.setTransform gives you more performance than multiple matrix calls ctx.translate, ctx.scale, ctx.translate.
No need for complex transformation inversions as and expensive DOM matrix calls tp converts point between zoomed and screen coordinate systems.
Flexible
Flexibility as you don't need to use ctx.save and ctx.restore if you are rendering content at using different transforms. Returning to the transform with ctx.setTransform rather than the potentially frame rate wreaking ctx.restorecall
Easy to invert the transform and get the world coordinates of a (screen) pixel position and the other way round.
Examples
Using mouse and mouse wheel to zoom in and out at mouse position
An example using this method to scale page content at a point (mouse) via CSS transform CSS Demo at bottom of answer also has a copy of the demo from the next example.
And an example of this method used to scale canvas content at a point using setTransform
How
Given a scale and pixel position you can get the new scale as follow...
const origin = {x:0, y:0}; // canvas origin
var scale = 1; // current scale
function scaleAt(x, y, scaleBy) { // at pixel coords x, y scale by scaleBy
scale *= scaleBy;
origin.x = x - (x - origin.x) * scaleBy;
origin.y = y - (y - origin.y) * scaleBy;
}
To position the canvas and draw content
ctx.setTransform(scale, 0, 0, scale, origin.x, origin.y);
ctx.drawImage(img, 0, 0);
To use if you have the mouse coordinates
const zoomBy = 1.1; // zoom in amount
scaleAt(mouse.x, mouse.y, zoomBy); // will zoom in at mouse x, y
scaleAt(mouse.x, mouse.y, 1 / zoomBy); // will zoom out by same amount at mouse x,y
To restore the default transform
ctx.setTransform(1,0,0,1,0,0);
The inversions
To get the coordinates of a point in the zoomed coordinate system and the screen position of a point in the zoomed coordinate system
Screen to world
function toWorld(x, y) { // convert to world coordinates
x = (x - origin.x) / scale;
y = (y - origin.y) / scale;
return {x, y};
}
World to screen
function toScreen(x, y) {
x = x * scale + origin.x;
y = y * scale + origin.y;
return {x, y};
}