We Keep Coding

Animating SVG: Move shape in direction of mouse/rotate around fixed point?

After looking through similar questions posted to the forum and not finding something that helped me solve my own problem, I'm posting it.
I'm using SVG.js to generate SVG shapes in a web document. I'd like one of those shapes to ”follow” the mouse/cursor.
By that I mean: The shape has a fixed position/anchor point (at its original center) and it can only move a limited distance (let's say 50px) away from this fixed point.
I want the shape to move in the direction of the cursor, whenever the cursor moves, but never further than a defined distance away from its orignal position. I'm attaching a short animation to illustrate my description:
If the cursor were to disappear, the shape would snap back to its original center.
I know my way around Javascript, HTML and CSS. This type of element-manipulation is new to me and the math is giving my quite the headache, any help would be great.
It looks like I need the shape to basically rotate around its original center, with an angle relative to the cursor? I'm really unsure how to solve this. I have tried using a method to calculate the angle described in this post. My shape moves, but not as intended:
// init
var draw = SVG().addTo('body')
// draw
window.shape = draw.circle(25, 25).stroke({
color: '#000',
width: 2.5
}).fill("#fff");
shape.attr("id", "circle1");
shape.move(50, 50)
// move
var circle = $("#circle1");
var dist = 10;
$(document).mousemove(function(e) {
// angle
var circleCenter = [circle.offset().left + circle.width() / 2, circle.offset().top + circle.height() / 2];
var angle = Math.atan2(e.clientX - circleCenter[0], -(e.clientY - circleCenter[1])) * (180 / Math.PI);
var x = Math.sin(angle) * dist;
var y = (Math.cos(angle) * dist) * -1;
shape.animate().dmove(x, y);
})
<script src="https://cdnjs.cloudflare.com/ajax/libs/svg.js/3.0.16/svg.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
Note: It does not matter to me whether the solution depends on jQuery or not (ideally it doesn't).

After more fiddling around with some solutions to calculating angles and distances, I found the answer.
I'm using a fixed reference point to calculate the angle of the direct line between the center of the shape and the cursor. Then I move the shape relative to this reference point and by a given amount:
// Init canvas
var draw = SVG().addTo('body')
// Draw reference/anchor
var shape_marker_center = draw.circle(3,3).fill("#f00").move(150, 150);;
var grafikCenter = [shape_marker_center.attr("cx"), shape_marker_center.attr("cy")]
// Draw shapes
var shape = draw.circle(25, 25).stroke({color: '#000', width: 2.5 }).fill("none");
shape.attr("id", "circle1").attr({cx: grafikCenter[0], cy:grafikCenter[1]})
var shape2 = draw.circle(50, 50).stroke({color: '#000', width: 2.5 }).fill("none");
shape2.attr("id", "circle2").attr({cx: grafikCenter[0], cy:grafikCenter[1]})
var shape3 = draw.circle(75, 75).stroke({color: '#000', width: 2.5 }).fill("none");
shape3.attr("id", "circle3").attr({cx: grafikCenter[0], cy:grafikCenter[1]})
$(document).mousemove(function(e) {
var pointA = [shape_marker_center.attr("cx"), shape_marker_center.attr("cy")];
var pointB = [e.clientX, e.clientY];
var angle = Math.atan2(pointB[1] - pointA[1], pointB[0] - pointA[0]) * 180 / Math.PI ;
//
var distance_x_1 = Math.cos(angle*Math.PI/180) * 16;
var distance_y_1 = Math.sin(angle*Math.PI/180) * 16;
var distance_x_2 = Math.cos(angle*Math.PI/180) * 8;
var distance_y_2 = Math.sin(angle*Math.PI/180) * 8;
//
shape.center((grafikCenter[0] + distance_x_1), (grafikCenter[1] + distance_y_1));
shape2.center((grafikCenter[0] + (distance_x_2) ), (grafikCenter[1] + (distance_y_2)));
})
svg {
width: 100vw;
height: 100vh;
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/svg.js/3.0.16/svg.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>

Moving object from A to B smoothly across canvas

I am trying to move an object smoothly from point A to point B using HTML canvas and regular javascript.
Point A is a set of coordinates
Point B is in the case the cursor location.
I made a jsfiddle of what I have so far: https://jsfiddle.net/as9fhmw8/
while(projectile.mouseX > projectile.x && projectile.mouseY < projectile.y)
{
ctx.save();
ctx.beginPath();
ctx.translate(projectile.x, projectile.y);
ctx.arc(0,0,5,0,2*Math.PI);
ctx.fillStyle = "blue";
ctx.fill();
ctx.stroke();
ctx.restore();
if(projectile.mouseX > projectile.x && projectile.mouseY < projectile.y)
{
var stepsize = (projectile.mouseX - projectile.x) / (projectile.y - projectile.mouseY);
projectile.x += (stepsize + 1);
}
if(projectile.mouseY < projectile.y)
{
var stepsize = (projectile.y - projectile.mouseY) / (projectile.mouseX - projectile.x);
projectile.y -= (stepsize + 1);
}
}
Essentially what I can't figure out to do is to make the while loop slower (so that it appears animated in stead of just going through every iteration and showing the result).
I also can't figure out how to prevent the Arc from duplicating so that it creates a line that is permanent, instead of appearing to move from point a to point b.

Smooth animation here is really about determining how far to move your object for each iteration of the loop.
There is a little math involved here, but it's not too bad.
Velocity
Velocity in your case is just the speed at which your particles travel in any given direction over a period of time. If you want your particle to travel 200px over the course of 4 seconds, then the velocity would be 50px / second.
With this information, you can easily determine how many pixels to move (animate) a particle given some arbitrary length of time.
pixels = pixelsPerSecond * seconds
This is great to know how many pixels to move, but doesn't translate into individual X and Y coordinates. That's where vectors come in.
Vectors
A vector in mathematics is a measurement of both direction and magnitude. For our purposes, it's like combining our velocity with an angle (47°).
One of the great properties of vectors is it can be broken down into it's individual X and Y components (for 2-Dimensional space).
So if we wanted to move our particle at 50px / second at a 47° angle, we could calculate a vector for that like so:
function Vector(magnitude, angle){
var angleRadians = (angle * Math.PI) / 180;
this.magnitudeX = magnitude * Math.cos(angleRadians);
this.magnitudeY = magnitude * Math.sin(angleRadians);
}
var moveVector = new Vector(50, 47);
The wonderful thing about this is that these values can simply be added to any set of X and Y coordinates to move them based on your velocity calculation.
Mouse Move Vector
Modeling your objects in this way has the added benefit of making things nice and mathematically consistent. The distance between your particle and the mouse is just another vector.
We can back calculate both the distance and angle using a little bit more math. Remember that guy Pythagoras? Turns out he was pretty smart.
function distanceAndAngleBetweenTwoPoints(x1, y1, x2, y2){
var x = x2 - x1,
y = y2 - y1;
return {
// x^2 + y^2 = r^2
distance: Math.sqrt(x * x + y * y),
// convert from radians to degrees
angle: Math.atan2(y, x) * 180 / Math.PI
}
}
var mouseCoords = getMouseCoords();
var data = distanceAndAngleBetweenTwoPoints(particle.x, particle.y, mouse.x, mouse.y);
//Spread movement out over three seconds
var velocity = data.distance / 3;
var toMouseVector = new Vector(velocity, data.angle);
Smoothly Animating
Animating your stuff around the screen in a way that isn't jerky means doing the following:
Run your animation loop as fast as possible
Determine how much time has passed since last time
Move each item based on elapsed time.
Re-paint the screen
For the animation loop, I would use the requestAnimationFrame API instead of setInterval as it will have better overall performance.
Clearing The Screen
Also when you re-paint the screen, just draw a big rectangle over the entire thing in whatever background color you want before re-drawing your items.
ctx.globalCompositeOperation = "source-over";
ctx.fillStyle = "black";
ctx.fillRect(0, 0, canvas.width, canvas.height);
Putting It All Together
Here is a Fiddle demonstrating all these techniques: https://jsfiddle.net/jwcarroll/2r69j1ok/3/

Three.js position objects on curve - rotate towards center of circle

I'm attempting to create a snazzy VR menu so that when the user looks down the menu items are in a column below camera curved around circle so they look the same and are rotated towards camera.
Here is my attempt thus far
And a CodePen with the example
http://codepen.io/bknill/pen/BLOwLj?editors=0010
I'm using some code I found that calculates the position
var radius = 60; // radius of the circle
var height = 60,
angle = 0,
step = (Math.PI /2 ) / menuItems.length;
menuItems.forEach(function(item,index){
var menuItem = createMenuItem(item.title);
menuItem.position.y = - Math.round(height/2 + radius * Math.sin(angle));
menuItem.position.z = Math.round(height/2 + radius * Math.sin(angle));
// menuItem.rotation.x = -Math.round(Math.PI * Math.sin(angle));
angle += step;
menu.add(menuItem);
})
Which is almost right, the next stage is to get them to rotate in a uniform way towards the camera. Using menuItem.lookAt(camera.position) isn't working - they're not uniform rotation.
child.lookAt(camera.position.normalize()) does this
Anyone let me know the clever maths I need to get the rotation of the item so they face the camera and look like they're on a curve?

The simplest way to have an object facing another object is using lookAt.
Be aware this method needs a direction vector, not the point where you want it to look at.
(position you want to look at - position of your object).normalize();
In your case:
var dirToLookAt = new THREE.Vector3();
dirToLookAt.subVectors(menuItem.position, camera.position);
// could be: dirToLookAt.subVectors(camera.position, menuItem.position);
dirToLookAt.normalize();
Operations based on Vector3 documentation.
For more info you can read the last discussion I had about this method.

THREE.js orthographic camera zoom to mouse point

I'm working on an orthographic camera for our THREE.js app. Essentially, this camera will present the scene to the user in 2D (users have the option of switching between the 2D and 3D camera). This camera will allow for panning and zooming to mouse point. I have the panning working, and I have zooming working, but not zooming to mouse point. Here's my code:
import React from 'react';
import T from 'three';
let panDamper = 0.15;
let OrthoCamera = React.createClass({
getInitialState: function () {
return {
distance: 150,
position: { x: 8 * 12, y: 2 * 12, z: 20 * 12 },
};
},
getThreeCameraObject: function () {
return this.camera;
},
applyPan: function (x, y) { // Apply pan by changing the position of the camera
let newPosition = {
x: this.state.position.x + x * -1 * panDamper,
y: this.state.position.y + y * panDamper,
z: this.state.position.z
};
this.setState({position: newPosition});
},
applyDirectedZoom: function(x, y, z) {
let zoomChange = 10;
if(z < 0) zoomChange *= -1;
let newDistance = this.state.distance + zoomChange;
let mouse3D = {
x: ( x / window.innerWidth ) * 2 - 1,
y: -( y / window.innerHeight ) * 2 + 1
};
let newPositionVector = new T.Vector3(mouse3D.x, mouse3D.y, 0.5);
newPositionVector.unproject(this.camera);
newPositionVector.sub(this.camera.position);
let newPosition = {
x: newPositionVector.x,
y: newPositionVector.y,
z: this.state.position.z
};
this.setState({
distance: newDistance,
position: newPosition
});
},
render: function () {
let position = new T.Vector3(this.state.position.x, this.state.position.y, this.state.position.z);
let left = (this.state.distance / -2) * this.props.aspect + this.state.position.x;
let right = (this.state.distance / 2) * this.props.aspect + this.state.position.x;
let top = (this.state.distance / 2) + this.state.position.y;
let bottom = (this.state.distance / -2) + this.state.position.y;
// Using react-three-renderer
// https://github.com/toxicFork/react-three-renderer
return <orthographicCamera
{...(_.pick(this.props, ['near', 'far', 'name']))}
position={position}
left={left}
right={right}
top={top}
bottom={bottom}
ref={(camera) => this.camera = camera}/>
}
});
module.exports = OrthoCamera;
Some zooming towards the mouse point happens but it seems erratic. I want to keep a 2D view, so as I zoom, I also move the camera (rather than having a non-perpendicular target, which kills the 2D effect).
I took cues from this question. As far as I can tell, I am successfully converting to THREE.js coordinates in mouse3D (see the answer to this question).
So, given this setup, how can I smoothly zoom to the mouse point (mouse3D) using the orthographic camera and maintaining a two dimensional view? Thanks in advance.

Assuming you have a camera that is described by a position and a look-at (or pivot) point in world coordinates, zooming at (or away from) a specific point is quite simple at its core.
Your representation seems to be even simpler: just a position/distance pair. I didn't see a rotation component, so I'll assume your camera is meant to be a top-down orthographic one.
In that case, your look-at point (which you won't need) is simply (position.x, position.y - distance, position.z).
In the general case, all you need to do is move both the camera position and the look-at point towards the zoom-at point while preserving the camera normal (i.e. direction). Note that this will work regardless of projection type or camera rotation. EDIT (2020/05/01): When using an orthographic projection, this is not all you need to do (see update at the bottom).
If you think about it, this is exactly what happens when you're zooming at a point in 3D. You keep looking at the same direction, but you move ever closer (without ever reaching) your target.
If you want to zoom by a factor of 1.1 for example, you can imagine scaling the vector connecting your camera position to your zoom-at point by 1/1.1.
You can do that by simply interpolating:
var newPosition = new THREE.Vector3();
newPosition.x = (orgPosition.x - zoomAt.x) / zoomFactor + zoomAt.x;
newPosition.y = (orgPosition.y - zoomAt.y) / zoomFactor + zoomAt.y;
newPosition.z = (orgPosition.z - zoomAt.z) / zoomFactor + zoomAt.z;
As I said above, in your case you won't really need to update a look-at point and then calculate the new distance. Your new distance will simply be:
var newDistance = newPosition.y
That should do it.
It only gets a little bit more sophisticated (mainly in the general case) if you want to set minimum and maximum distance limits both between the position/look-at and position/zoom-at point pairs.
UPDATE (2020/05/01):
I just realized that the above, although correct (except for missing one minor but very important step) is not a complete answer to OP's question. Changing the camera's position in orthographic mode won't of course change the scale of graphics being rendered. For that, the camera's projection matrix will have to be updated (i.e. the left, right, top and bottom parameters of the orthographic projection will have to be changed).
For this reason, many graphics libraries include a scaling factor in their orthographic camera class, which does exactly that. I don't have experience with ThreeJS, but I think that property is called 'zoom'.
So, summing everything up:
var newPosition = new THREE.Vector3();
newPosition.x = (orgPosition.x - zoomAt.x) / zoomFactor + zoomAt.x;
newPosition.y = (orgPosition.y - zoomAt.y) / zoomFactor + zoomAt.y;
newPosition.z = (orgPosition.z - zoomAt.z) / zoomFactor + zoomAt.z;
myCamera.zoom = myCamera.zoom * zoomFactor
myCamera.updateProjectionMatrix()
If you want to use your orthographic camera class code above instead, you will probably have to change the section that computes left, right, top and bottom and add a scaling factor in the calculation. Here's an example:
var aspect = this.viewportWidth / this.viewportHeight
var dX = (this.right - this.left)
var dY = (this.top - this.bottom) / aspect
var left = -dX / (2 * this.scale)
var right = dX / (2 * this.scale)
var bottom = -dY / (2 * this.scale)
var top = dY / (2 * this.scale)
mat4.ortho(this.mProjection, left, right, bottom, top, this.near, this.far)

Rotating One Object Around Another In createJS/easelJS

In easelJS, what is the best way to rotate an object around another? What I'm trying to accomplish is a method to rotate the crosshair around the circle pictured below, just like a planet orbits the sun:
I've been able to rotate objects around their own center point, but am having a difficult time devising a way to rotate one object around the center point of a second object. Any ideas?

Might make sense to wrap content in a Container. Translate the coordinates so the center point is where you want it, and then rotate the container.

To build on what Lanny is suggesting, there may be cases where you don't want to rotate the entire container. An alternative would be to use trigonometric functions and an incrementing angle to calculate the x/y position of the crosshair. You can find the x/y by using an angle (converted to radians) and Math.cos(angleInRadians) for x and Math.sin(angleInRadians) for y, the multiply by the radius of the orbit.
See this working example for reference.
Here's a complete snippet.
var stage = new createjs.Stage("stage");
var angle = 0;
var circle = new createjs.Shape();
circle.graphics.beginFill("#FF0000").drawEllipse(-25, -25, 50, 50).endFill();
circle.x = 100;
circle.y = 100;
var crosshair = new createjs.Shape();
crosshair.graphics.setStrokeStyle(2).beginStroke("#FF0000").moveTo(5, 0).lineTo(5, 10).moveTo(0, 5).lineTo(10, 5).endStroke();
stage.addChild(circle);
stage.addChild(crosshair);
createjs.Ticker.addEventListener("tick", function(){
angle++;
if(angle > 360)
angle = 1;
var rads = angle * Math.PI / 180;
var x = 100 * Math.cos(rads);
var y = 100 * Math.sin(rads);
crosshair.x = x + 100;
crosshair.y = y + 100;
stage.update();
});

Put another point respect to origin point with the same direction
var one_meter = 1 / map_resolution;
// get one meter distance from pointed points
var extra_x = one_meter * Math.cos(temp_rotation);
var extra_y = one_meter * Math.sin(-temp_rotation);
var new_x = mapXY.x + extra_x;
var new_y = mapXY.y + extra_y;
var home_point = new createjs.Shape().set({ x: new_x, y: new_y });
home_point.graphics.beginFill("Blue").drawCircle(0, 0, 10);
stage.addChild(home_point);
stage.update();