I've looked high and low but nothing seems to fit quite what I'm doing. I need to calculate x and y coordinates for a bullets trajectory then plot them on Chart.js.
A bullet fired from (0, 5) will hit a target at (250, 5). The problem lies in graphing it correctly on the trajectory in between (x is yards, y is feet).
I can successfully calculate the trajectory of the bullet and bullet drop without hitting the target, but I'm not able to get the launch angle accounted for so that the bullet hits the target at x distance.
This is mainly where I've gotten my calculations: https://en.wikipedia.org/wiki/Trajectory_of_a_projectile
My app looks like this:
Here's what I have so far:
calcTrajectory() {
// get target distance - passed in
// get launch angle to hit target at that distance
let x = this.distance;
let y = this.height;
let g = 10.733; // gravity in yds
let v = this.velocity / 3; // velocity in yds
let angle = Math.atan(
Math.pow(v, 2) + Math.sqrt(
Math.pow(v, 4) - g * ((g * x * x) + (2 * y * v * v)
))
/
(g * x)
);
// graph x y coords based on target distance, launch angle, and bullet drop
for (let i = 0; i < 10; i++) {
let time = (i * 100) / v;
let bulletY: number = Math.sin(angle - (Math.PI / 2)) * v;
let dropVal = ((10.733 / 2) * Math.pow(time, 2)) * 3;
console.log('Bullet Y:', bulletY);
this.myChart.data.datasets.forEach((dataset) => {
dataset.data.push({
x: (i * 100),
y: parseInt(this.height) + bulletY - dropVal
});
});
// update chart
this.myChart.update();
}
What am I missing?
EDIT: clarified question and added a picture
I had to remove all of the Angular/Typescript stuff, but you should be able to run the below code and paste the output into a graphing program and verify it. What I'm doing is calculating the angle required to travel the distance input, then calculating the x and y vectors of the initial velocity. Then you can just multiply those by a timestep to get points that you can plot. If you want more granular points, just increase the step variable.
const calcTrajectory = (distance, height, velocity)=> {
// get target distance - passed in
// get launch angle to hit target at that distance
let x = distance;
let y = height;
let g = 10.733; // gravity in yds
let v = velocity / 3; // velocity in yds
let angle = Math.asin((x*g)/(v*v));
let step = 100;
let xVelocity = v * Math.cos(angle);
let yVelocity = v * Math.sin(angle)
// graph x y coords based on target distance, launch angle, and bullet drop
let data = {x:[], y:[]}
for (let i = 0; i < 100; i++) {
let time = (i / step);
data.x.push(time*xVelocity)
data.y.push(time* yVelocity)
yVelocity -= (g/step)
}
console.log(data);
}
calcTrajectory(250, 0, 2024.43)
So I built some time ago a little Breakout clone, and I wanted to upgrade it a little bit, mostly for the collisions. When I first made it I had a basic "collision" detection between my ball and my brick, which in fact considered the ball as another rectangle. But this created an issue with the edge collisions, so I thought I would change it. The thing is, I found some answers to my problem:
for example this image
and the last comment of this thread : circle/rect collision reaction but i could not find how to compute the final velocity vector.
So far I have :
- Found the closest point on the rectangle,
- created the normal and tangent vectors,
And now what I need is to somehow "divide the velocity vector into a normal component and a tangent component; negate the normal component and add the normal and tangent components to get the new Velocity vector" I'm sorry if this seems terribly easy but I could not get my mind around that ...
code :
function collision(rect, circle){
var NearestX = Max(rect.x, Min(circle.pos.x, rect.x + rect.w));
var NearestY = Max(rect.y, Min(circle.pos.y, rect.y + rect.w));
var dist = createVector(circle.pos.x - NearestX, circle.pos.y - NearestY);
var dnormal = createVector(- dist.y, dist.x);
//change current circle vel according to the collision response
}
Thanks !
EDIT: Also found this but I didn't know if it is applicable at all points of the rectangle or only the corners.
Best explained with a couple of diagrams:
Have angle of incidence = angle of reflection. Call this value θ.
Have θ = normal angle - incoming angle.
atan2 is the function for computing the angle of a vector from the positive x-axis.
Then the code below immediately follows:
function collision(rect, circle){
var NearestX = Max(rect.x, Min(circle.pos.x, rect.x + rect.w));
var NearestY = Max(rect.y, Min(circle.pos.y, rect.y + rect.h));
var dist = createVector(circle.pos.x - NearestX, circle.pos.y - NearestY);
var dnormal = createVector(- dist.y, dist.x);
var normal_angle = atan2(dnormal.y, dnormal.x);
var incoming_angle = atan2(circle.vel.y, circle.vel.x);
var theta = normal_angle - incoming_angle;
circle.vel = circle.vel.rotate(2*theta);
}
Another way of doing it is to get the velocity along the tangent and then subtracting twice this value from the circle velocity.
Then the code becomes
function collision(rect, circle){
var NearestX = Max(rect.x, Min(circle.pos.x, rect.x + rect.w));
var NearestY = Max(rect.y, Min(circle.pos.y, rect.y + rect.h));
var dist = createVector(circle.pos.x - NearestX, circle.pos.y - NearestY);
var tangent_vel = dist.normalize().dot(circle.vel);
circle.vel = circle.vel.sub(tangent_vel.mult(2));
}
Both of the code snippets above do basically the same thing in about the same time (probably). Just pick whichever one you best understand.
Also, as #arbuthnott pointed out, there's a copy-paste error in that NearestY should use rect.h instead of rect.w.
Edit: I forgot the positional resolution. This is the process of moving two physics objects apart so that they're no longer intersecting. In this case, since the block is static, we only need to move the ball.
function collision(rect, circle){
var NearestX = Max(rect.x, Min(circle.pos.x, rect.x + rect.w));
var NearestY = Max(rect.y, Min(circle.pos.y, rect.y + rect.h));
var dist = createVector(circle.pos.x - NearestX, circle.pos.y - NearestY);
if (circle.vel.dot(dist) < 0) { //if circle is moving toward the rect
//update circle.vel using one of the above methods
}
var penetrationDepth = circle.r - dist.mag();
var penetrationVector = dist.normalise().mult(penetrationDepth);
circle.pos = circle.pos.sub(penetrationVector);
}
Bat and Ball collision
The best way to handle ball and rectangle collision is to exploit the symmetry of the system.
Ball as a point.
First the ball, it has a radius r that defines all the points r distance from the center. But we can turn the ball into a point and add to the rectangle the radius. The ball is now just a single point moving over time, which is a line.
The rectangle has grown on all sides by radius. The diagram shows how this works.
The green rectangle is the original rectangle. The balls A,B are not touching the rectangle, while the balls C,D are touching. The balls A,D represent a special case, but is easy to solve as you will see.
All motion as a line.
So now we have a larger rectangle and a ball as a point moving over time (a line), but the rectangle is also moving, which means over time the edges will sweep out areas which is too complicated for my brain, so once again we can use symmetry, this time in relative movement.
From the bat's point of view it is stationary while the ball is moving, and from the ball, it is still while the bat is moving. They both see each other move in the opposite directions.
As the ball is now a point, making changes to its movement will only change the line it travels along. So we can now fix the bat in space and subtract its movement from the ball. And as the bat is now fixed we can move its center point to the origin, (0,0) and move the ball in the opposite direction.
At this point we make an important assumption. The ball and bat are always in a state that they are not touching, when we move the ball and/or bat then they may touch. If they do make contact we calculate a new trajectory so that they are not touching.
Two possible collisions
There are now two possible collision cases, one where the ball hits the side of the bat, and one where the ball hits the corner of the bat.
The next images show the bat at the origin and the ball relative to the bat in both motion and position. It is travelling along the red line from A to B then bounces off to C
Ball hits edge
Ball hits corner
As there is symmetry here as well which side or corner is hit does not make any difference. In fact we can mirror the whole problem depending on which size the ball is from the center of the bat. So if the ball is left of the bat then mirror its position and motion in the x direction, and the same for the y direction (you must keep track of this mirror via a semaphore so you can reverse it once the solution is found).
Code
The example does what is described above in the function doBatBall(bat, ball) The ball has some gravity and will bounce off of the sides of the canvas. The bat is moved via the mouse. The bats movement will be transferred to the ball, but the bat will not feel any force from the ball.
const ctx = canvas.getContext("2d");
const mouse = {x : 0, y : 0, button : false}
function mouseEvents(e){
mouse.x = e.pageX;
mouse.y = e.pageY;
mouse.button = e.type === "mousedown" ? true : e.type === "mouseup" ? false : mouse.button;
}
["down","up","move"].forEach(name => document.addEventListener("mouse" + name, mouseEvents));
// short cut vars
var w = canvas.width;
var h = canvas.height;
var cw = w / 2; // center
var ch = h / 2;
const gravity = 1;
// constants and helpers
const PI2 = Math.PI * 2;
const setStyle = (ctx,style) => { Object.keys(style).forEach(key=> ctx[key] = style[key] ) };
// the ball
const ball = {
r : 50,
x : 50,
y : 50,
dx : 0.2,
dy : 0.2,
maxSpeed : 8,
style : {
lineWidth : 12,
strokeStyle : "green",
},
draw(ctx){
setStyle(ctx,this.style);
ctx.beginPath();
ctx.arc(this.x,this.y,this.r-this.style.lineWidth * 0.45,0,PI2);
ctx.stroke();
},
update(){
this.dy += gravity;
var speed = Math.sqrt(this.dx * this.dx + this.dy * this.dy);
var x = this.x + this.dx;
var y = this.y + this.dy;
if(y > canvas.height - this.r){
y = (canvas.height - this.r) - (y - (canvas.height - this.r));
this.dy = -this.dy;
}
if(y < this.r){
y = this.r - (y - this.r);
this.dy = -this.dy;
}
if(x > canvas.width - this.r){
x = (canvas.width - this.r) - (x - (canvas.width - this.r));
this.dx = -this.dx;
}
if(x < this.r){
x = this.r - (x - this.r);
this.dx = -this.dx;
}
this.x = x;
this.y = y;
if(speed > this.maxSpeed){ // if over speed then slow the ball down gradualy
var reduceSpeed = this.maxSpeed + (speed-this.maxSpeed) * 0.9; // reduce speed if over max speed
this.dx = (this.dx / speed) * reduceSpeed;
this.dy = (this.dy / speed) * reduceSpeed;
}
}
}
const ballShadow = { // this is used to do calcs that may be dumped
r : 50,
x : 50,
y : 50,
dx : 0.2,
dy : 0.2,
}
// Creates the bat
const bat = {
x : 100,
y : 250,
dx : 0,
dy : 0,
width : 140,
height : 10,
style : {
lineWidth : 2,
strokeStyle : "black",
},
draw(ctx){
setStyle(ctx,this.style);
ctx.strokeRect(this.x - this.width / 2,this.y - this.height / 2, this.width, this.height);
},
update(){
this.dx = mouse.x - this.x;
this.dy = mouse.y - this.y;
var x = this.x + this.dx;
var y = this.y + this.dy;
x < this.width / 2 && (x = this.width / 2);
y < this.height / 2 && (y = this.height / 2);
x > canvas.width - this.width / 2 && (x = canvas.width - this.width / 2);
y > canvas.height - this.height / 2 && (y = canvas.height - this.height / 2);
this.dx = x - this.x;
this.dy = y - this.y;
this.x = x;
this.y = y;
}
}
//=============================================================================
// THE FUNCTION THAT DOES THE BALL BAT sim.
// the ball and bat are at new position
function doBatBall(bat,ball){
var mirrorX = 1;
var mirrorY = 1;
const s = ballShadow; // alias
s.x = ball.x;
s.y = ball.y;
s.dx = ball.dx;
s.dy = ball.dy;
s.x -= s.dx;
s.y -= s.dy;
// get the bat half width height
const batW2 = bat.width / 2;
const batH2 = bat.height / 2;
// and bat size plus radius of ball
var batH = batH2 + ball.r;
var batW = batW2 + ball.r;
// set ball position relative to bats last pos
s.x -= bat.x;
s.y -= bat.y;
// set ball delta relative to bat
s.dx -= bat.dx;
s.dy -= bat.dy;
// mirror x and or y if needed
if(s.x < 0){
mirrorX = -1;
s.x = -s.x;
s.dx = -s.dx;
}
if(s.y < 0){
mirrorY = -1;
s.y = -s.y;
s.dy = -s.dy;
}
// bat now only has a bottom, right sides and bottom right corner
var distY = (batH - s.y); // distance from bottom
var distX = (batW - s.x); // distance from right
if(s.dx > 0 && s.dy > 0){ return }// ball moving away so no hit
var ballSpeed = Math.sqrt(s.dx * s.dx + s.dy * s.dy); // get ball speed relative to bat
// get x location of intercept for bottom of bat
var bottomX = s.x +(s.dx / s.dy) * distY;
// get y location of intercept for right of bat
var rightY = s.y +(s.dy / s.dx) * distX;
// get distance to bottom and right intercepts
var distB = Math.hypot(bottomX - s.x, batH - s.y);
var distR = Math.hypot(batW - s.x, rightY - s.y);
var hit = false;
if(s.dy < 0 && bottomX <= batW2 && distB <= ballSpeed && distB < distR){ // if hit is on bottom and bottom hit is closest
hit = true;
s.y = batH - s.dy * ((ballSpeed - distB) / ballSpeed);
s.dy = -s.dy;
}
if(! hit && s.dx < 0 && rightY <= batH2 && distR <= ballSpeed && distR <= distB){ // if hit is on right and right hit is closest
hit = true;
s.x = batW - s.dx * ((ballSpeed - distR) / ballSpeed);;
s.dx = -s.dx;
}
if(!hit){ // if no hit may have intercepted the corner.
// find the distance that the corner is from the line segment from the balls pos to the next pos
const u = ((batW2 - s.x) * s.dx + (batH2 - s.y) * s.dy)/(ballSpeed * ballSpeed);
// get the closest point on the line to the corner
var cpx = s.x + s.dx * u;
var cpy = s.y + s.dy * u;
// get ball radius squared
const radSqr = ball.r * ball.r;
// get the distance of that point from the corner squared
const dist = (cpx - batW2) * (cpx - batW2) + (cpy - batH2) * (cpy - batH2);
// is that distance greater than ball radius
if(dist > radSqr){ return } // no hit
// solves the triangle from center to closest point on balls trajectory
var d = Math.sqrt(radSqr - dist) / ballSpeed;
// intercept point is closest to line start
cpx -= s.dx * d;
cpy -= s.dy * d;
// get the distance from the ball current pos to the intercept point
d = Math.hypot(cpx - s.x,cpy - s.y);
// is the distance greater than the ball speed then its a miss
if(d > ballSpeed){ return } // no hit return
s.x = cpx; // position of contact
s.y = cpy;
// find the normalised tangent at intercept point
const ty = (cpx - batW2) / ball.r;
const tx = -(cpy - batH2) / ball.r;
// calculate the reflection vector
const bsx = s.dx / ballSpeed; // normalise ball speed
const bsy = s.dy / ballSpeed;
const dot = (bsx * tx + bsy * ty) * 2;
// get the distance the ball travels past the intercept
d = ballSpeed - d;
// the reflected vector is the balls new delta (this delta is normalised)
s.dx = (tx * dot - bsx);
s.dy = (ty * dot - bsy);
// move the ball the remaining distance away from corner
s.x += s.dx * d;
s.y += s.dy * d;
// set the ball delta to the balls speed
s.dx *= ballSpeed;
s.dy *= ballSpeed;
hit = true;
}
// if the ball hit the bat restore absolute position
if(hit){
// reverse mirror
s.x *= mirrorX;
s.dx *= mirrorX;
s.y *= mirrorY;
s.dy *= mirrorY;
// remove bat relative position
s.x += bat.x;
s.y += bat.y;
// remove bat relative delta
s.dx += bat.dx;
s.dy += bat.dy;
// set the balls new position and delta
ball.x = s.x;
ball.y = s.y;
ball.dx = s.dx;
ball.dy = s.dy;
}
}
// main update function
function update(timer){
if(w !== innerWidth || h !== innerHeight){
cw = (w = canvas.width = innerWidth) / 2;
ch = (h = canvas.height = innerHeight) / 2;
}
ctx.setTransform(1,0,0,1,0,0); // reset transform
ctx.globalAlpha = 1; // reset alpha
ctx.clearRect(0,0,w,h);
// move bat and ball
bat.update();
ball.update();
// check for bal bat contact and change ball position and trajectory if needed
doBatBall(bat,ball);
// draw ball and bat
bat.draw(ctx);
ball.draw(ctx);
requestAnimationFrame(update);
}
requestAnimationFrame(update);
canvas { position : absolute; top : 0px; left : 0px; }
body {font-family : arial; }
Use the mouse to move the bat and hit the ball.
<canvas id="canvas"></canvas>
Flaws with this method.
It is possible to trap the ball with the bat such that there is no valid solution, such as pressing the ball down onto the bottom of the screen. At some point the balls diameter is greater than the space between the wall and the bat. When this happens the solution will fail and the ball will pass through the bat.
In the demo there is every effort made to not loss energy, but over time floating point errors will accumulate, this can lead to a loss of energy if the sim is run without some input.
As the bat has infinite momentum it is easy to transfer a lot of energy to the ball, to prevent the ball accumulating to much momentum I have added a max speed to the ball. if the ball moves quicker than the max speed it is gradually slowed down until at or under the max speed.
On occasion if you move the bat away from the ball at the same speed, the extra acceleration due to gravity can result in the ball not being pushed away from the bat correctly.
Correction of an idea shared above, with adjusting velocity after collision using tangental velocity.
bounciness - constant defined to represent lost force after collision
nv = vector # normalized vector from center of cricle to collision point (normal)
pv = [-vector[1], vector[0]] # normalized vector perpendicular to nv (tangental)
n = dot_product(nv, circle.vel) # normal vector length
t = dot_product(pv, circle.vel) # tangental_vector length
new_v = sum_vectors(multiply_vector(t*bounciness, pv), multiply_vector(-n*self.bounciness, nv)) # new velocity vector
circle.velocity = new_v
Im trying to make an particle move towards where on canvas was clicked however the formula returns NaN. Why is this and how can I fix this?
step 1: Particle gets placed at player.x, player.y properly.
step 2: At first tick the particle goes to the upper left point of the canvas without x,y position.
Screenie of particle props
example at jsfiddle
Particle Object
function Shuriken(mouseX, mouseY) {
this.rot = 0;
this.vel = 2;
this.angle = 0;
this.x = player.x || WIDTH / 2;
this.y = player.y || HEIGHT / 2;
this.mouseX = mouseX || WIDTH /2;
this.mouseY = mouseY || HEIGHT /2
this.width = shurikenImg.width;
this.height = shurikenImg.height;
}
update on tick
Shuriken.prototype.move = function() {
this.angle = Math.atan2(this.mouseY, this.x) * (180 / Math.PI);
this.x += this.vel * Math.cos(this.angle);
this.y += this.vel * Math.sin(this.angle);
}
You convert angle from radians into degrees. Nicer to debug (because degrees are still taught in school) but alas, the sin and cos in the next lines expect their arguments to be in radians again. Granted, the functions ought still to work; but the values you get are no longer what you expect.
this.vel is undefined in the jsfiddle. This is most likely what lead to the observed NaN.
This is a wrong calculation:
this.x = this.vel * Math.cos(this.angle);
this.y = this.vel * Math.sin(this.angle);
You don't want the x and y positions calculated this way. Add or subtract the (adjusted) velocity from the x/y coordinates.
Trying to get two balls to collide and bounce back at appropriate angles.
When the balls collide however they get stuck together and I have no idea what I'm doing wrong here.
I'm calling this checkCollision() function within my animate function
Obviously cx is ball1 xpos, cx2 is ball2 xpos. Same for cy.
function checkCollision () {
var dx = cx2 - cx; // distance between x
var dy = cy2 - cy; // distance between y
var distance = Math.sqrt(dx * dx + dy * dy);
if (distance < (radius1 + radius2)) {
// Collision detected. Find the normal.
var normalX = dx / distance;
var normalY = dy / distance;
//find the middle point of the distance
var midpointX = (cx + cx2)/2;
var midpointY = (cy + cy2)/2;
//bounce back
cx = midpointX - radius1*normalX;
cy = midpointY - radius1*normalY;
cx2 = midpointX - radius2*normalX;
cy2 = midpointY - radius2*normalY;
var dVector = (vx - vx2) * normalX;
dVector += (vy - vy2) * normalY;
var dvx = dVector * normalX;
var dvy = dVector * normalY;
vx -= dvx;
vy -= dvy;
vx2 += dvx;
vy2 += dvy;
}
...
I've never done much/any vector work. Is there any easier way to do this?
How would I write this with angles instead?
You need to use some basic maths to detect the intersection between two circles.
A similar problem is described here:
algorithm to detect if a Circles intersect with any other circle in the same plane
There is a C# sample that could be easily adapted to Javascript.
I am using time based movement, but its still super choppy. this code shoots in arrow in the air then calculates the difference in movement to determine to rotation of the arrow. It works most of the time, but sometimes it just jitters.
for(i=0;i<this.arrows.length;i++){
a = this.arrows[i];
point0 = [a.x,a.y];
x_speed = e.delta/1000*a.speed * Math.cos(a.angle * Math.PI / 180);
y_speed = e.delta/1000*a.speed * Math.sin(a.angle * Math.PI / 180);
a.x += x_speed;
a.y += y_speed;
a.y += a.velocity;
a.velocity += e.delta/1000*this.gravity;
alert(e.delta);
ang = Math.atan2(point0[1]-a.y,point0[0]-a.x);
ang = (ang * (180/Math.PI))+180;
a.rotation = ang;
}
1) I'm surprised you are using a.angle, ang and a.rotation. I guess ang is a var declared before the for loop, but isn't there an issue here ?
2) You might use radians, not degrees, to avoid conversions.
3) There's also an issue with speed vs velocity : you don't update speed (linear speed) when you change velocity (speed on Y).
•• Anyway there's a simpler way of proceeding : compute speed/position just like for a regular point moving, then use the speed vector to compute where the end of the arrow is.
It works fine in this fiddle : http://jsbin.com/dexaroriwixo/1/
update :
var i=0, a=null, delta_ms = 1e-3 * e.delta;
for(i=0;i<this.arrows.length;i++){
a = this.arrows[i];
a.x += delta_ms*a.speedX;
a.y += delta_ms*a.speedY;
a.speedY += delta_ms*this.gravity;
a.speedNorm = Math.sqrt(sq(a.speedX)+sq(a.speedY));
}
to draw :
Arrow.prototype.draw = function(ctx) {
ctx.beginPath();
ctx.moveTo(this.x, this.y);
ctx.lineTo(this.x+ this.length*this.speedX/this.speedNorm,
this.y+ this.length*this.speedY/this.speedNorm );
ctx.strokeStyle = '#F00';
ctx.stroke();
}
to 'launch' an arrow,
Arrow.prototype.launch(initialSpeed, angle) {
this.speedX = initialSpeed * Math.cos(angle);
this.speedY = initialSpeed * Math.sin(angle);
}