Good day, I am trying to create a simple 2D solar system model in javascript, but am having some trouble understanding how to go about calculating where planets will be for the next frame, aswell as a few other bits which I'll go into detail with soon.
After watching this very nice video and a whole bunch of his others, I made a quick MS paint image to try and simplify my situation.
With the second scene, you can see that the new position is calulated using the velocity, gravitational pull, and the angle between these two 'directions'?
I cannot get my head around how to figure this all out.
Below is a JS fiddle of my code. You'll notice I'm trying my best to use real NASA given data to keep it accurate.
You'll want to look specifically at lines 138 which is where all the calculations for its next move are made.
https://jsfiddle.net/c8eru7mk/9/
attraction: function(p2) {
// Distance to other body
var dx = p2.position.x - this.position.x;
var dy = p2.position.y - this.position.y;
var d = Math.sqrt(dx ** 2 + dy ** 2); // Possibly correct
// Force of attracrtion
this.f = G * (this.mass * p2.mass) / (d ** 2); // Possibly Correct
// Direction of force, If you read it hard enough you should be able to hear my screams of pain
// Not sure if this is correct, most likely not.
var theta = Math.atan2(dy, dx);
var fx = Math.cos(theta) * this.f;
var fy = Math.sin(theta) * this.f;
this.velocity.x += fx / this.mass;
this.velocity.y += fy / this.mass;
this.position.x += this.velocity.x;
this.position.y += this.velocity.y;
}
The problems I'm currently facing are
If I am to use NASA values, the distance between planets is so big, they won't fit on the screen, and I can't simply scale the distances down by multiplying them by 0.0002 or whatever, as that'll mess with the gravitational constant, and the simulation will be completely off.
I have no idea how to caluclate the next position and my brain has imploded several times this past week trying to attempt it several times.
I have no idea on how to check if my configuration data of planets is wrong, or if the simulation is wrong, so I'm pretty much just guessing.
This is also my first time actually coding anything more complex than a button in javascript too, so feedback on code layout and whatnot is welcome!
Many thanks
Using NASA values is not a problem when using separate coordinates for drawing. Using an appropriate linear transfomration from real coordinates to screen coordinatees for displaying does not influence the physical values and computations.
For simulating the motion of a planet with iterative updates one can assume that the gravitational force and the velocity are constant for a small portion of time dt. This factor dt is missing in your conversions from accelration to velocity and from velocity to distance. Choosing an appropriate value for dt may need some experiments. If the value is too big the approximation will be too far off from reality. If the value is too small you may not see any movement or rounding errors may influence the result.
For the beginning let us assume that the sun is always at (0,0). Also for a start let us ignore the forces between the planets. Then here are the necessary formulas for a first not too bad approximation:
scalar acceleration of a planet at position (x,y) by the gravitational force of the sun (with mass M): a = G*M/(d*d) where d=sqrt(x*x+y*y). Note that this is indepent of the planet's mass.
acceleration vector: ax = -a*x/d, ay = -a*y/d (the vector (-x,-y) is pointing towards the sun and must be brought the length a)
change of the planet's velocity (vx,vy): vx += ax*dt, vy += ay*dt
change of the planet's position: x += vx*dt, y += vy*dt
Related
I am designing a web script to automatically create a Java file to perform autonomous actions for a robotics team based on nodes created by the player. It also features a simulation to check collision (I could use an algorithm to do this but sometimes we want it to hit the walls). The robot takes relative degrees, but atan2 gives radians on the unit circle. If I use atan, it just doesn't work right. I've tried this:
function findDegrees(node1, node2){
return Math.atan((node2.y - node1.y) / (node2.x - node1.x)) * 180 / Math.PI;
}
But it just doesn't work. This piece of code writes the data too the output. (Also, I'm following the pattern: Drive, then turn towards next node).
let theta = currentAngle - findDegrees(nextNode, twoNodes);
currentAngle += theta;
if (theta && typeof theta !== 'undefined'){
middle += `${INDENTSPACE}turn(${theta}, 1.0);\n`;
}
The way I change the x and y of the robot simulation is this:
turn(degrees, speed){
this.theta -= degrees;
}
But sometimes it goes the other way. How do I get the robot to rotate at a relative angle to the current angle where directly forward is 0°? (If you want the full code here it is.)
I'm working through a tutorial to make the old arcade game Breakout - you have a paddle at the bottom of the screen and the goal is to deflect a moving ball into a series of blocks at the top of the screen.
The code to calculate the rebound effect is:
ball.dx = ball.speed * Math.sin(angle);
ball.dy = - ball.speed * Math.cos(angle);
The yellow circle represents the ball:
I understand sine and cosine as ratios of the hypotenuse; I just still can't seem to grasp how they are used to calculate the rebound angle here exactly. Can anyone explain how the resulting numbers, given an angle and a speed value, produce the directionality of the ball on rebound? I feel there's a simple conceptual piece of the puzzle I'm missing.
This is vector adding - the X and Y vector added give you the new speed value.
To easier understand how sin and cos work here, take the case of angel = 0 deg. The ball falls straight down, and should bounce back up:
ball.dx = ball.speed * Math.sin(0); // 0
ball.dy = - ball.speed * Math.cos(0); // 1
So there's no movement left or right, speed is the same but the vertical direction is reversed because of the minus sign.
Using sin and cos here takes care of having a constant speed, as well, as these always sum up to 1.
Hope that's a bit more clarifying than confusing, but I did some similar code tasks that got easily solved with basic vector operations.
I'm trying to detect collision between two circles like this:
var circle1 = {radius: 20, x: 5, y: 5}; //moving
var circle2 = {radius: 12, x: 10, y: 5}; //not moving
var dx = circle1.x - circle2.x;
var dy = circle1.y - circle2.y;
var distance = Math.sqrt(dx * dx + dy * dy);
if (distance < circle1.radius + circle2.radius) {
// collision detected
}else{
circle1.x += 1 * Math.cos(circle1.angle);
circle1.y += 1 * Math.sin(circle1.angle);
}
Now when collision is detected I want to slide the circle1 from on the circle2 (circle1 is moving) like this:
--circle1---------------------------------circle2-------------------------
I could do this by updating the angle of circle1 and Moving it toward the new angle when collision is detected.
Now My question is that how can I detect whether to update/increase the angle or update/decrease the angle based on which part of circle2 circle1 is colliding with ?? (circle one comes from all angles)
I would appreciate any help
This will depend a bit on how you are using these circles, and how many will ever exist in a single system, but if you are trying to simulate the effect of two bodies colliding under gravity where one roles around to the edge then falls off (or similar under-thrust scenario), then you should apply a constant acceleration or velocity to the moving object and after you compute it's movement phase, you do a displacement phase where you take the angle to the object you are colliding with and move it back far enough in that direction to reach circle1.radius + circle2.radius.
[edit] To get that redirection after falling though (not sure if you intended this or if it's just your sketch), there is probably going to be another force at play. Most likely it will involve a "stickiness" applied between the bodies. Basically, on a collision, you need to make sure that on the next movement cycle, you apply Normal Movement, then movement towards the other body, then the repulsion to make sure they don't overlap. This way it will stick to the big circle until gravity pulls way at enough of a direct angle to break the connection.
[edit2] If you want to make this smoother and achieve a natural curve as you fall away you can use an acceleration under friction formula. So, instead of this:
circle1.x += 1 * Math.cos(circle1.angle);
circle1.y += 1 * Math.sin(circle1.angle);
You want to create velocity properties for your object that are acted on by acceleration and friction until they balance out to a fixed terminal velocity. Think:
// constants - adjust these to get the speed and smoothness you desire
var accelerationX = 1;
var accelerationY = 0;
var friction = 0.8;
// part of physics loop
circle1.velX += (accelerationX * Math.cos(circle1.angle)) - (friction * circle1.velX);
circle1.velY += (accelerationY * Math.sin(circle1.angle)) - (friction * circle1.velX);
circle1.x += circle1.velX;
circle1.y += circle1.velY;
This way, when things hit they will slow down (or stop), then speed back up when they start moving again. The acceleration as it gets back up to speed will achieve a more natural arc as it falls away.
You could get the tangent of the point of contact between both circles, which would indicate you how much to change your angle compared to the destination point (or any horizontal plane).
I am currently working moving different cars around a race track. I am using the formula listed in
Canvas move object in circle
arccos (1- ( d ⁄ r ) 2 ⁄ 2 )
to vary the speed of the cars around the ends of the track and it works very well. What I don't understand is how the formula is derived. I have been working on trying to derive it from the second derivative of the arcsin or arccos but I can't get out the formula (so am guessing I'm walking the wrong path). Anyways, I am never comfortable using code I don't understand, so I would appreciate it if someone could shed some light on it for me.
As detailed in the linked question, the movement of an object along a circle can be parametrized with a single angle theta which in loose terms describes how many "revolutions" the object has already made. Now, the question is for which angle theta the object is at Euclidean distance d from the initial (current) position A:
In other words, if you fix the time step delta of your simulation, the problem can be restated as to how one should adjust (increment) the angle so that the object displaces within the time interval delta to distance d.
From the law of cosines, one gets:
d^2 = r^2 + r^2 - 2*r*r*cos(theta) = 2*r^2*(1 - cos(theta))
Thus:
cos(theta) = 1 - 1/2*(d/r)^2
theta = arccos(1 - 1/2*(d/r)^2)
I am currently working on a game using javascript and processing.js and I am having trouble trying to figure out how to move stuff diagonally. In this game, there is an object in the center that shoots other objects around it. Now I have no problem moving the bullet only vertically or only horizontally, however I am having difficulty implementing a diagonal motion for the bullet algorithm.
In terms of attempts, I tried putting on my math thinking cap and used the y=mx+b formula for motion along a straight line, but this is what my code ends up looking like:
ellipse(shuriken.xPos, shuriken.yPos, shuriken.width, shuriken.height); //this is what I want to move diagonally
if(abs(shuriken.slope) > 0.65) {
if(shuriken.targetY < shuriken.OrigYPos) {
shuriken.yPos -= 4;
} else {
shuriken.yPos += 4;
}
shuriken.xPos = (shuriken.yPos - shuriken.intercept)/shuriken.slope;
} else {
if(shuriken.targetX < shuriken.OrigXPos) {
shuriken.xPos -= 4;
} else {
shuriken.xPos += 4;
}
shuriken.yPos = shuriken.slope * shuriken.xPos + shuriken.intercept;
}
The above code is very bad and hacky as the speed varies with the slope of the line.
I tried implementing a trigonometry relationship but still in vain.
Any help/advice will be greatly appreciated!
Think of it this way: you want the shuriken to move s pixels. If the motion is horizontal, it should move s pixels horizontally; if vertical, s pixels vertically. However, if it's anything else, it will be a combination of pixels horizontally/vertically. What's the correct combination? Well, what shape do you get if you project s distance in any direction from a given point? That's right, a circle with radius s. Let's represent the direction in terms of an angle, a. So we have this picture:
How do we get the x and the y? If you notice, we have a triangle. If you recall your trigonometry, this is precisely what the sine, cosine, and tangent functions are for. I learned their definitions via the mnemonic SOHCAHTOA. That is: Sin (a) = Opposite/Hypotenuse, Cos(a) = Adjacent/Hypotenuse, Tan(a) = Opposite/Adjacent. In this case, opposite of angle a is y, and adjacent of angle a is x. Thus we have:
cos(a) = x / s
sin(a) = y / s
Solving for x and y:
x = s * cos(a)
y = s * sin(a)
So, given the angle a, and that you want to move your shuriken s pixels, you want to move it s * cos(a) horizontally and s * sin(a) vertically.
Just be sure you pass a in radians, not degrees, to javascript's Math.sin and Math.cos functions:
radians = degrees * pi / 180.0
This may be why your trigonometric solution didn't work as this has bitten me a bunch in the past.
If you know the angle and speed you are trying to move at, you can treat it as a polar coordinate, then convert to cartesian coordinates to get an x,y vector you would need to move the object by to go in that direction and speed.
If you don't know the angle, you could also come up with the vector by taking the difference in X and difference in Y (this I know you can do as you are able to calculate the slope between the 2 points). Then take the resulting vector and divide by the length of the vector to get a unit vector, which you can then scale to your speed to get a final vector in which you can move your object by.
(This is what probably what kennypu means by sticking with vectors?)