Develop Reference

Unity2D: move object along path - unevenly distributed waypoints - constant speed needed

I am currently facing a problem I cannot wrap my head around. In my 2D game which in the end should become some kind of virtual model railway, I can create a path, consisting of different railtypes. Each rail has it's own waypoints. Now the issue is as follows:
Straight rails don't need many waypoints, since they only need two to be defined; The start and the end point. Curves on the other hand need a lot more waypoints, so the objects movement on them is not all jaggy and unsmooth. The problem I am facing is, that the waypoints then are so unevenly distributed on the whole railway, it makes the speed which the object moves along the path very uneven.
I also already know the issue: The points are so cramped in the curve sections that the distribution looks like this:
See this picture for an example with red Gizmo.Spheres as waypoints
Now when I move an object along that said path, I do it like this:
wagon.transform.position = Vector2.MoveTowards(wagon.transform.position, wagon.GetNextPosition(), wagon.GetSpeed());
The third parameter of the method Vector2.MoveTowards() is the maxDistanceDelta, so it can only move that amount into the direction of wagon.GetNextPosition(), which is constantly updated.
The twist is, that the densly packed points result in a way shorter distance than the maxDistanceDelta. So in those parts of the railway, the object moves way slower then wagon.GetSpeed() per frame.
I already have a solution to this, which sadly I cannot use: I took every waypoint and distributed them evenly on the path. I don't want that; I want the path to stay as is, but the speed to the eye to be uniform.
Thanks in advance for your help!
PS: I already looked in similar threads, but none of those solutions seems to work for me :( Namely:
This thread
And this one

I would comment this but unfortunately I don't have enough reputation, so here it is:
The best idea I can think of is to create 2 waypoints for your curve (at the start and finish) and use a parabolic function to define the movement between them. So in other words, your train follows a parabola instead of moving towards waypoints directly.
I found a useful answer on a unity forum about parabolic trajectories which you may find useful for your project (It is the first answer beneath the question at the time of writing).

How are you generating those waypoints?
Could you use bezier curves instead?
If yes, there it's typical to run into exactly this issue and solutions have been found. Not solutions with absolute accuracy, but usually sufficient for games (aka visualizations that in the end only need to be as accurate as the pixels you see).
There is this outstanding video about the topic: https://www.youtube.com/watch?v=aVwxzDHniEw

Use c# to animate instead of Animator in Unity

Well I know animator system in Unity is very useful for many things but I find myself having my own state machine in the code and somehow the state machine that the animator provides is not accurate due to blend time maybe I dont know, so I find often my character being in state 2 in the animator state machine and state 0 in my own state machine and its crazy as I cant seem to make it match in limit cases when its about to end the action. So I would like to know if there is a way to just say with code "play this animation from frame A to frame B" and loop it or not loop, that would be much better for me, of course I will lose all the blend features but really I will be better, all I can fin in the docs refer to using the animator so far. Thanks a lot for any help regarding this =)
Edit: Forgot to add that I found Animation.Play but apparently this only play animation saved on separate files like when we use the Animation timeline to record a certain motion, but I have a character with a lot of frames there and I dont think it serves in this case (or in my tests it never finds the specified animation at least, maybe i miss somethnig)

before anything, you can your own state machine with Animator. in fact, you don't need to two different state machine for your purposes. (Watch this video here)
and about your question, I found a good answer here: Link
From what I've seen you can either do AnimationState.normalizedTime
which returns the progress of an animation on a scale of 0 to 1. So if
you have a 30 frame animation and you want frame 15, you can do if
(normalizedTime == 0.5)* Or the better and more reliable option is to
use AnimationEvents that fire on specific frames.
*You won't really be able to do this if we're dealing in floats--You can only get the approximate value or you'll have to check greater
then or equal to 0.4 AND less then or equal to 0.6 because the
animation could go faster than the current frame rate or the
normalized time value could be 0.50000001 because of the nature of
float values.

Vector direction for gravity in a circular orbit

I am currently working on a project in C# where i play around with planetary gravitation, which i know is a hardcore topic to graps to it's fullest but i like challenges. I've been reading up on Newtons laws and Keplers Laws, but one thing i cannot figure out is how to get the correct gravitational direction.
In my example i only have 2 bodies. A Satellite and a Planet. This is to make is simplify it, so i can grasp it - but my plan is to have multiple objects that dynamically effect each other, and hopefully end up with a somewhat realistic multi-body system.
When you have an orbit, then the satellite has a gravitational force, and that is ofcourse in the direction of the planet, but that direction isn't a constant. To explain my problem better i'll try using an example:
let's say we have a satellite moving at a speed of 50 m/s and accelerates towards the planet at a speed of 10 m/s/s, in a radius of 100 m. (all theoretical numbers) If we then say that the framerate is at 1, then after one second the object will be 50 units forward and 10 units down.
As the satellite moves multiple units in a frame and about 50% of the radius, the gravitational direcion have shifted alot, during this frame, but the applied force have only been "downwards". this creates a big margin of error, especially if the object is moving a big percentage of the radius.
In our example we'd probably needed our graviational direction to be based upon the average between our current position and the position at the end of this frame.
How would one go about calculating this?
I have a basis understanding of trigonometry, but mainly with focus on triangles. Assume i am stupid, because compared to any of you, i probably am.
(I made a previous question but ended up deleting it as it created some hostility and was basicly not that well phrased, and was ALL to general - it wasn't really a specific question. i hope this is better. if not, then please inform me, i am here to learn :) )
Just for reference, this is the function i have right now for movement:
foreach (ExtTerBody OtherObject in UniverseController.CurrentUniverse.ExterTerBodies.Where(x => x != this))
{
double massOther = OtherObject.Mass;
double R = Vector2Math.Distance(Position, OtherObject.Position);
double V = (massOther) / Math.Pow(R,2) * UniverseController.DeltaTime;
Vector2 NonNormTwo = (OtherObject.Position - Position).Normalized() * V;
Vector2 NonNormDir = Velocity + NonNormTwo;
Velocity = NonNormDir;
Position += Velocity * Time.DeltaTime;
}
If i have phrased myself badly, please ask me to rephrase parts - English isn't my native language, and specific subjects can be hard to phrase, when you don't know the correct technical terms. :)
I have a hunch that this is covered in keplers second law, but if it is, then i'm not sure how to use it, as i don't understand his laws to the fullest.
Thank you for your time - it means alot!
(also if anyone see multi mistakes in my function, then please point them out!)

I am currently working on a project in C# where i play around with planetary gravitation
This is a fun way to learn simulation techniques, programming and physics at the same time.
One thing I cannot figure out is how to get the correct gravitational direction.
I assume that you are not trying to simulate relativistic gravitation. The Earth isn't in orbit around the Sun, the Earth is in orbit around where the sun was eight minutes ago. Correcting for the fact that gravitation is not instantaneous can be difficult. (UPDATE: According to commentary this is incorrect. What do I know; I stopped taking physics after second year Newtonian dynamics and have only the vaguest understanding of tensor calculus.)
You'll do best at this early stage to assume that the gravitational force is instantaneous and that planets are points with all their mass at the center. The gravitational force vector is a straight line from one point to another.
Let's say we have a satellite moving at a speed of 50 m/s ... If we then say that the framerate is one frame per second then after one second the object will be 50 units right and 10 units down.
Let's make that more clear. Force is equal to mass times acceleration. You work out the force between the bodies. You know their masses, so you now know the acceleration of each body. Each body has a position and a velocity. The acceleration changes the velocity. The velocity changes the position. So if the particle starts off having a velocity of 50 m/s to the left and 0 m/s down, and then you apply a force that accelerates it by 10 m/s/s down, then we can work out the change to the velocity, and then the change to the position. As you note, at the end of that second the position and the velocity will have both changed by a huge amount compared to their existing magnitudes.
As the satellite moves multiple units in a frame and about 50% of the radius, the gravitational direcion have shifted alot, during this frame, but the applied force have only been "downwards". this creates a big margin of error, especially if the object is moving a big percentage of the radius.
Correct. The problem is that the frame rate is enormously too low to correctly model the interaction you're describing. You need to be running the simulation so that you're looking at tenths, hundredths or thousanths of seconds if the objects are changing direction that rapidly. The size of the time step is usually called the "delta t" of the simulation, and yours is way too large.
For planetary bodies, what you're doing now is like trying to model the earth by simulating its position every few months and assuming it moves in a straight line in the meanwhile. You need to actually simulate its position every few minutes, not every few months.
In our example we'd probably needed our graviational direction to be based upon the average between our current position and the position at the end of this frame.
You could do that but it would be easier to simply decrease the "delta t" for the computation. Then the difference between the directions at the beginning and the end of the frame is much smaller.
Once you've got that sorted out then there are more techniques you can use. For example, you could detect when the position changes too much between frames and go back and redo the computations with a smaller time step. If the positions change hardly at all then increase the time step.
Once you've got that sorted, there are lots of more advanced techniques you can use in physics simulations, but I would start by getting basic time stepping really solid first. The more advanced techniques are essentially variations on your idea of "do a smarter interpolation of the change over the time step" -- you are on the right track here, but you should walk before you run.

I'll start with a technique that is almost as simple as the Euler-Cromer integration you've been using but is markedly more accurate. This is the leapfrog technique. The idea is very simple: position and velocity are kept at half time steps from one another.
The initial state has position and velocity at time t0. To get that half step offset, you'll need a special case for the very first step, where velocity is advanced half a time step using the acceleration at the start of the interval and then position is advanced by a full step. After this first time special case, the code works just like your Euler-Cromer integrator.
In pseudo code, the algorithm looks like
void calculate_accel (orbiting_body_collection, central_body) {
foreach (orbiting_body : orbiting_body_collection) {
delta_pos = central_body.pos - orbiting_body.pos;
orbiting_body.acc =
(central_body.mu / pow(delta_pos.magnitude(),3)) * delta_pos;
}
}
void leapfrog_step (orbiting_body_collection, central_body, delta_t) {
static bool initialized = false;
calculate_accel (orbiting_body_collection, central_body);
if (! initialized) {
initialized = true;
foreach orbiting_body {
orbiting_body.vel += orbiting_body.acc*delta_t/2.0;
orbiting_body.pos += orbiting_body.vel*delta_t;
}
}
else {
foreach orbiting_body {
orbiting_body.vel += orbiting_body.acc*delta_t;
orbiting_body.pos += orbiting_body.vel*delta_t;
}
}
}
Note that I've added acceleration as a field of each orbiting body. This was a temporary step to keep the algorithm similar to yours. Note also that I moved the calculation of acceleration to it's own separate function. That is not a temporary step. It is the first essential step to advancing to even more advanced integration techniques.
The next essential step is to undo that temporary addition of the acceleration. The accelerations properly belong to the integrator, not the body. On the other hand, the calculation of accelerations belongs to the problem space, not the integrator. You might want to add relativistic corrections, or solar radiation pressure, or planet to planet gravitational interactions. The integrator should be unaware of what goes into those accelerations are calculated. The function calculate_accels is a black box called by the integrator.
Different integrators have very different concepts of when accelerations need to be calculated. Some store a history of recent accelerations, some need an additional workspace to compute an average acceleration of some sort. Some do the same with velocities (keep a history, have some velocity workspace). Some more advanced integration techniques use a number of techniques internally, switching from one to another to provide the best balance between accuracy and CPU usage. If you want to simulate the solar system, you need an extremely accurate integrator. (And you need to move far, far away from floats. Even doubles aren't good enough for a high precision solar system integration. With floats, there's not much point going past RK4, and maybe not even leapfrog.)
Properly separating what belongs to whom (the integrator versus the problem space) makes it possible to refine the problem domain (add relativity, etc.) and makes it possible to easily switch integration techniques so you can evaluate one technique versus another.

So i found a solution, it might not be the smartest, but it works, and it's pretty came to mind after reading both Eric's answer and also reading the comment made by marcus, you could say that it's a combination of the two:
This is the new code:
foreach (ExtTerBody OtherObject in UniverseController.CurrentUniverse.ExterTerBodies.Where(x => x != this))
{
double massOther = OtherObject.Mass;
double R = Vector2Math.Distance(Position, OtherObject.Position);
double V = (massOther) / Math.Pow(R,2) * Time.DeltaTime;
float VRmod = (float)Math.Round(V/(R*0.001), 0, MidpointRounding.AwayFromZero);
if(V > R*0.01f)
{
for (int x = 0; x < VRmod; x++)
{
EulerMovement(OtherObject, Time.DeltaTime / VRmod);
}
}
else
EulerMovement(OtherObject, Time.DeltaTime);
}
public void EulerMovement(ExtTerBody OtherObject, float deltaTime)
{
double massOther = OtherObject.Mass;
double R = Vector2Math.Distance(Position, OtherObject.Position);
double V = (massOther) / Math.Pow(R, 2) * deltaTime;
Vector2 NonNormTwo = (OtherObject.Position - Position).Normalized() * V;
Vector2 NonNormDir = Velocity + NonNormTwo;
Velocity = NonNormDir;
//Debug.WriteLine("Velocity=" + Velocity);
Position += Velocity * deltaTime;
}
To explain it:
I came to the conclusion that if the problem was that the satellite had too much velocity in one frame, then why not seperate it into multiple frames? So this is what "it" does now.
When the velocity of the satellite is more than 1% of the current radius, it seperates the calculation into multiple bites, making it more precise.. This will ofcourse lower the framerate when working with high velocities, but it's okay with a project like this.
Different solutions are still very welcome. I might tweak the trigger-amounts, but the most important thing is that it works, then i can worry about making it more smooth!
Thank's everybody that took a look, and everyone who helped be find the conclusion myself! :) It's awesome that people can help like this!

Sight range, player position update

I'm coding a server for a multi-player RPG, and I'm currently struggling with implementing a sight range. Since some maps are rather large, I have to limit what the client sees. My approach:
If I get new coordinates from the client, I save them as the destination, together with a move start time. Once every x ms I go through all creatures in the world, and update their current position, after saving the position they were at the last time I've updated them. Basically I calculate the new position, based on move start time and speed, and write those in the current position variables, while saving the new start time. Once this update is done, I'm going through all creatures which moved, aka those who have a different position than at the last update. In a sub-loop I go through all creatures/clients again, to check if I have to notify them about a (dis)appearing creature. At the moment I'm running this update every 100ms.
This approach is working, but I have a feeling it's not the best way to do this. And I'm not sure what will happen once I have a few thousand creatures (players, monster, etc) in the world, which have to be updated and checked.
Since I weren't able to find resources about this particular problem, I'm asking here.
Is this approach okay? Will I run into problems soon? What's the standard to do this? What's the best way?

Eric Lippert had a really good series of posts on shadowcasting that might be helpful in approaching/solving this.

You may want to consider using quadtrees to split the game world into sections based on the areas that player characters can see. Then you don't need to loop over every creature in the game all the time; you only need to loop over the ones within the section that the player character in question is located in, and any adjacent ones in case something crossed the boundary.
I haven't done this sort of coding personally myself, but I did work with someone who did this in a space combat game for which I was developing a GUI!

Stay Away from target

I have an array which is filled with all the objects with the tag Enemy. When one enemy comes close to an other enemy, it has to stay away from that enemy or go around it.
This is what I have now:
foreach(Transform enemy in enemies){
if(enemy == this.transform) continue;
enemyPos = enemy;
float enemyDistance = Vector3.Distance(enemy.transform.position, transform.position);
if(enemyDistance < 8){
transform.RotateAround (enemyPos.position, Vector3.up, 360 * Time.deltaTime);
}
}
If enemies come close enough to each other, they will circle around each other. Also tried to use 2 cube triggers for when an enemy object touches one of the cubes, the cubed enemy wil rotate away from it. Also tried different angles.
But no luck :(
I am still trying to find a solution. But if you have a better idea about this, your help is much appreceated :)
Thanks in advance!!!

You have several moving objects, and some of them may stand in the way of other objects. I would propose that you defer moving of all those objects that have a moving obstacle in front of them. When all free-moving objects are moved then try to move all other, by repeating the procedure, because in the process some objects might become free. You essentially loop through list of not-yet-moved objects until there is no change in the list.
If you don't find any new free-moving objects then deal with the rest as you like. I would suggest that you try find alternative route only for one of them, and then repeat the procedure above. It might be that when one object is unstuck then all others are unstuck as well. You may repeat this second procedure for the rest of stuck objects.

The following article could help you.
In short, your agent are "repulsing" each other when they are under the given distance. This is the "separation" concept in the flock. What is really interesting is that you can have a rotation that depends on the distance (ie another agent very near mean that you have to turn hard) and that you can interact with more than one agent.
in the same site, this can help you search the player. Combien the two method, and you have agents that try to catch the player while avoiding other agents.
regards
Guillaume