Im creating a simple particle experiment on canvas. Now i want them to "run away" from mouse coursor over canvas. detecting the distance from the mouse is not a problem, but how to code their behaviour?
each particle is created as following:
var particle = {
x: Math.floor(Math.random() * width),
y: Math.floor(Math.random() * height),
xVel: Math.random() * 10 - 5,
yVel: Math.random() * 10 - 5,
}
so i assume i should also save the direction somehow, and if the distance from pointer is < x, reverse the direction? maybe also save old speed, and decrease it slowly while moving away?
how to detect the direction?
Velocity (xVel, yVel, together) is a 2D vector. And so is the distance between the mouse and the particles. A vector contains both direction and magnitude. So you want a vector that is the difference between the mouse position and the particle position.
var posRelativeToMouse = {
x: particle.x - mousPosX,
y: particle.y - mousPosY
};
So small numbers of x and y mean the the particle is close to the mouse, and big mean it's far away.
Next we need to figure out how these numbers should affect the velocity of the particle. So we need 2 things.
What direction do we push them in?
We already have this, mostly. posRelativeToMouse is a vector that has the direction we want. We just normalize it, which means to set the length of the vector to 1. To do that, we divide each component by the current length of the vector. The length of this vector is always the distance to from the particle to the mouse.
var distance = Math.sqrt(
posRelativeToMouse.x * posRelativeToMouse.x +
posRelativeToMouse.y * posRelativeToMouse.y
);
var forceDirection = {
x: posRelativeToMouse.x / distance,
y: posRelativeToMouse.y / distance,
};
How hard do we push the particles?
This is an inverse of the distance. Close means a big push, far means a little push. So lets reuse our distance we calculated above.
// distance past which the force is zero
var maxDistance = 1000;
// convert (0...maxDistance) range into a (1...0).
// Close is near 1, far is near 0
// for example:
// 250 => 0.75
// 100 => 0.9
// 10 => 0.99
var force = (maxDistance - distance) / maxDistance;
// if we went below zero, set it to zero.
if (force < 0) force = 0;
Ok we have a direction, and we have the force. All that's left is to apply this to the particle velocity.
particle.xVel += forceDirection.x * force * timeElapsedSinceLastFrame;
particle.yVel += forceDirection.y * force * timeElapsedSinceLastFrame;
And assuming you are animating your position each frame by that xVel/yVel, you should now have particles being pushed away by the mouse.
you can obtain a vector v by subtracting the position of particle from position of mouse,
then you can find the magnitude of this vector my taking sqrt(x^2 + y^2)
by dividing v by magnitude, you obtain a unit vector in the direction you want your particles to go.
for instance.
suppose I have 10 particles in a list U, each has an x and y field.
I can obtain it's vector from each particle v by setting v = (xpart - mousepart, ypart - mousepart)
then you need to find the magnitude vmag by taking sqrt(vx^2 + vy^2)
then you obtain vunit = (vx / vmag, vy / vmag)
This is the vector "away from the mouse".
the rest can be left to detemining speed you want to move at, and ensuring you bounce of walls and such.
I have a similar project at github open source:
https://github.com/dmitrymakhnin/JavaParticleSystem/blob/master/Main.java
Related
I'm working on a 2D rendering system in 3D space, for practice. The sprites are 2D, but they're rendered in 3D space. The "camera" can move in 3D space and turn 360 degrees horizontally. I'm having trouble figuring out the right formula to calculate, based on the position/rotation of the camera and the position of the assets, where they should exist on the screen.
What I have is like this:
chunk.assets.forEach(asset => {
let x = Math.round(
asset.coords.x * Math.cos(angle) - asset.coords.y * Math.sin(angle)
);
let y = Math.round(
asset.coords.y * Math.cos(angle) + asset.coords.x * Math.sin(angle)
);
if (!depthMap[y]) {
depthMap[y] = [];
}
depthMap[y].push(asset);
});
But this does not take into account the camera's (player's) position (stored at player.coords.x, player.coords.y), only the angle the camera/player is facing (angle). So right now the camera can't move. Note: Depth map is just storing the assets in order so the renderer knows which order to render the sprites so things appear in the right order based on which is closer to the player/camera.
How can I incorporate the camera's position into this algorithm?
Some assumptions:
If the camera and the sprite are at the same position, the sprite will be rendered at 0|0.
Wether the camera moves left or the sprite moves right does not matter.
From that we can conclude that only the relative position matters, and that can be easily calculated (by subtracting both positions).
let x = Math.round(
(asset.coords.x - player.coords.x) * Math.cos(angle) - (asset.coords.y - player coords.y) * Math.sin(angle)
);
let y = Math.round(
(asset.coords.y - player.coords.y) * Math.cos(angle) + (asset.coords.x - player.coords.x) * Math.sin(angle)
);
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/
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.
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)
I'm sorry to say that Math really isn't my strong suit. Normally I can get by, but this has got me totally stumped.
I'm trying to code up a quiz results screen in HTML/CSS/Javascript.
On my interface, I have a semicircle (the right hemisphere of a target).
I have a range of 'scores' (integers out of 100 - so 50, 80, 90 etc.).
I need to plot these points on the semicircle to be n% away from the centre, where n is the value of each score - the higher the score, the closer to the centre of the target the point will appear.
I know how wide my semicircle is, and have already handled the conversion of the % values so that the higher ones appear closer to the centre while the lower ones appear further out.
What I can't wrap my head around is plotting these points on a line that travels out from the centre point (x = 0, y = target height/2) of the target at a random angle (so the points don't overlap).
Any suggestions are gratefully received!
Do you have an example of what you want this to look like? It sounds like you want to divide up the circle into N slices where N is the number of points you need to display, then plot the points along each of those radii. So you might have something like:
Edit: code was rotating about the origin, not the circle specified
var scores = [];
//...
//assume scores is an array of distances from the center of the circle
var points = [];
var interval = 2 * Math.PI / N;
var angle;
for (var i = 0; i < N; i++) {
angle = interval * i;
//assume (cx, cy) are the coordinates of the center of your circle
points.push({
x: scores[i] * Math.cos(angle) + cx,
y: scores[i] * Math.sin(angle) + cy
});
}
Then you can plot points however you see fit.
After much headscratching, I managed to arrive at this solution (with the help of a colleague who's much, much better at this kind of thing than me):
(arr_result is an array containing IDs and scores - scores are percentages of 100)
for (var i = 0; i < arr_result.length; i++){
var angle = angleArray[i]; // this is an array of angles (randomised) - points around the edge of the semicircle
var radius = 150; // width of the semicircle
var deadZone = 25 // to make matters complicated, the circle has a 'dead zone' in the centre which we want to discount
var maxScore = 100
var score = parseInt(arr_result[i]['score'], 10)
var alpha = angle * Math.PI
var distance = (maxScore-score)/maxScore*(radius-deadZone) + deadZone
var x = distance * Math.sin(alpha)
var y = radius + distance * Math.cos(alpha)
$('#marker_' + arr_result[i]['id'], templateCode).css({ // target a specific marker and move it using jQuery
'left' : pointX,
'top': pointY
});
}
I've omitted the code for generating the array of angles and randomising that array - that's only needed for presentational purposes so the markers don't overlap.
I also do some weird things with the co-ordinates before I move the markers (again, this has been omitted) as I want the point to be at the bottom-centre of the marker rather than the top-left.