I'm having a hard time to understand the need of ccpNormalize, the cocos2d reference says it multiplies the CGPoint to 1. I can't just google it that doens't explain it instead of showing in code.
is it that obvious that I can't find it?
feeling stupid here, please help
The idea of normalising a vector is to have magnitude of 1, this is important if you only care about the direction of your vector.
For example maybe you want to keep all your sprite moving at constant speed regardless of any collisions and so you may want to normalise their velocity after the collision and then multiply by you relevant constant speed.
If you are more interested in reading about the subject try http://en.wikipedia.org/wiki/Normalized_vector
Related
http://pastebin.com/ccck8LjE
Hello i've written this code to try and simulate the moon earth sun system. I get a circular orbit for the earth but the moon goes mad.
Is there a better way to try and do this whilst still using a euler/leapfrog method?
I didn't take the effort to carefully review your code or test its behavior, but it is well known that the Euler method gains energy in such simulations, so "trapezoidal" is generally used instead.
https://en.wikipedia.org/wiki/Trapezoidal_rule
If I understand correctly, your method is second order in the relationship between position and velocity (I assume with the intent of avoiding that energy gain) but it appears to be first order in the relationship between acceleration and velocity.
You might be able to keep the leapfrog design (rather than trapezoidal) but in trying to do so, you should do a better job of making the extra state explicit to eliminate the use of second derivative.
Edit: I reread the Wikipedia page on leapfrog and reread your code and it is clear you are not using leapfrog (as I said earlier because you only apply it to position\velocity not to velocity\acceleration). Note that page also shows you how to simplify the equations of leapfrog for the situation (that you have) in which acceleration depends on position and not on velocity:
https://en.wikipedia.org/wiki/Leapfrog_integration
Maybe you could try to use Runge Kutta methods if you want to keep using explicit integration : https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
RK4 is usually enough.
Because this is a complex question that usually results in much confusion (I've asked variations on this question previously, but never asked the question the right way and never got an answer), I'm going to try to make this as clear as possible.
Facts:
I'm using Unity.
I'm can get the Forward, Up and Right vectors easily from any Quaternion rotation.
I can't simply record my own Euler angles, modify them and apply the rotation through a new Quaternion because the object is controlled by physics.
I don't understand maths very well at all unless it's written in code (or pseudo-code), so this would be most beneficial to me.
A C++ style answer would be easiest for me to understand, but I can work out pretty much any kind of code.
I'm NOT trying to get anyone to write the code for me! I'm only asking for the answer in code or pseudo-code because I never learned to read normal maths squiggles; I'm a programmer, not a mathematician.
Unity uses a left-handed coordinate system. X = right, Y = up, Z = forward.
What I'm trying to do:
I'm trying to play an animation on a humanoid bone structure and, using torque (rotational force), push the physics ragdoll into approximately the same pose as the bone structure.
The problem:
I can work fully in Quaternions right up to the point where I need to apply the torque to the rigidbodies. The AddTorque function effectively works in Euler angles, which means I can't use the Quaternions. I can easily extract Euler angles from the Quaternions, but they are unreliable and cause the ragdoll to spaz out severely.
What I need:
I need to calculate reliable 3D Euler angles (as in, ones that don't flip from + to - "randomly") from Forward, Up and Right vectors. I realise this is a bit complicated, but that's why I ask here: I lack the knowledge and experience to work out this problem myself.
Given that the vectors themselves are reliable, I see no reason why it would not be possible to work out reliable Euler angles from them. Also, I don't know what order of rotation I would want or need for the Euler angles, but I believe that would be fairly easy to modify later.
Any help would be much appreciated!
First, I'd like to say that I solved my problem entirely due to #Tobias's efforts. Many, many thanks! All this time I've been approaching the problem from the wrong end. I assumed that I needed to use AddTorque in a particular way (with Euler angles) and worked from there, but #Tobias (and #JarkkoL a little later) pointed out that I needed to use AddTorque differently.
So this is what I did, in UnityScript (effectively JavaScript):
var quat0:Quaternion;
var quat1:Quaternion;
var quat10:Quaternion;
quat0=transform.rotation;
quat1=target.transform.rotation;
quat10=quat1*Quaternion.Inverse(quat0);
rigidbody.AddTorque(quat10.x,quat10.y,quat10.z,ForceMode.Force);
And, against all expectations, this WORKS!! It just... works! Sure, it takes a long time for the rigidbody cube to settle down, but that's because I need a PID controller. Or maybe quat10 needs normalising, not sure. I'll work it out :)
I had no idea you could actually use that part of a quat by itself.
First off, I think you would have better luck in Unity forums for Unity specific questions (: That said, I think you are misinterpreting the AddTorque() interface if this one is what you are using: http://docs.unity3d.com/ScriptReference/Rigidbody.AddTorque.html
Instead of passing Euler angles you pass a vector to the function that's the axis of rotation. I'm not familiar with Unity, but I believe the length of the vector specifies how much torque to add. Euler angles are inherently bad representation for rotations so you should always assume (unless otherwise documented) that well established API's work with quaternions, axis/angle pairs or matrices when it comes to rotations. Euler angles are more of a convenience representation for end users.
So I have an iterative closest point (ICP) algorithm that has been written and will fit a model to a point cloud. As a quick tutorial for those not in the know ICP is a simple algorithm that fits points to a model ultimately providing a homogeneous transform matrix between the model and points.
Here is a quick picture tutorial.
Step 1. Find the closest point in the model set to your data set:
Step 2: Using a bunch of fun maths (sometimes based on gradiant descent or SVD) pull the clouds closer together and repeat untill a pose is formed:
![Figure 2][2]
Now that bit is simple and working, what i would like help with is:
How do I tell if the pose that I have is a good one?
So currently I have two ideas, but they are kind of hacky:
How many points are in the ICP Algorithm. Ie, if I am fitting to almost no points, I assume that the pose will be bad:
But what if the pose is actually good? It could be, even with few points. I dont want to reject good poses:
So what we see here is that low points can actually make a very good position if they are in the right place.
So the other metric investigated was the ratio of the supplied points to the used points. Here's an example
Now we exlude points that are too far away because they will be outliers, now this means we need a good starting position for the ICP to work, but i am ok with that. Now in the above example the assurance will say NO, this is a bad pose, and it would be right because the ratio of points vs points included is:
2/11 < SOME_THRESHOLD
So thats good, but it will fail in the case shown above where the triangle is upside down. It will say that the upside down triangle is good because all of the points are used by ICP.
You don't need to be an expert on ICP to answer this question, i am looking for good ideas. Using knowledge of the points how can we classify whether it is a good pose solution or not?
Using both of these solutions together in tandem is a good suggestion but its a pretty lame solution if you ask me, very dumb to just threshold it.
What are some good ideas for how to do this?
PS. If you want to add some code, please go for it. I am working in c++.
PPS. Someone help me with tagging this question I am not sure where it should fall.
One possible approach might be comparing poses by their shapes and their orientation.
Shapes comparison can be done with Hausdorff distance up to isometry, that is poses are of the same shape if
d(I(actual_pose), calculated_pose) < d_threshold
where d_threshold should be found from experiments. As isometric modifications of X I would consider rotations by different angles - seems to be sufficient in this case.
Is poses have the same shape, we should compare their orientation. To compare orientation we could use somewhat simplified Freksa model. For each pose we should calculate values
{x_y min, x_y max, x_z min, x_z max, y_z min, y_z max}
and then make sure that each difference between corresponding values for poses does not break another_threshold, derived from experiments as well.
Hopefully this makes some sense, or at least you can draw something useful for your purpose from this.
ICP attempts to minimize the distance between your point-cloud and a model, yes? Wouldn't it make the most sense to evaluate it based on what that distance actually is after execution?
I'm assuming it tries to minimize the sum of squared distances between each point you try to fit and the closest model point. So if you want a metric for quality, why not just normalize that sum, dividing by the number of points it's fitting. Yes, outliers will disrupt it somewhat but they're also going to disrupt your fit somewhat.
It seems like any calculation you can come up with that provides more insight than whatever ICP is minimizing would be more useful incorporated into the algorithm itself, so it can minimize that too. =)
Update
I think I didn't quite understand the algorithm. It seems that it iteratively selects a subset of points, transforms them to minimize error, and then repeats those two steps? In that case your ideal solution selects as many points as possible while keeping error as small as possible.
You said combining the two terms seemed like a weak solution, but it sounds to me like an exact description of what you want, and it captures the two major features of the algorithm (yes?). Evaluating using something like error + B * (selected / total) seems spiritually similar to how regularization is used to address the overfitting problem with gradient descent (and similar) ML algorithms. Selecting a good value for B would take some experimentation.
Looking at your examples, it seems that one of the things that determines whether the match is good or not, is the quality of the points. Could you use/calculate a weighting factor in calculating your metric?
For example, you could weight down points which are co-linear / co-planar, or spatially close, as they probably define the same feature. That would perhaps allow your upside-down triangle to be rejected (as the points are in a line, and that not a great indicator of the overall pose) but the corner-case would be ok, as they roughly define the hull.
Alternatively, maybe the weighting should be on how distributed the points are around the pose, again trying to ensure you have good coverage, rather than matching small indistinct features.
I been reading about RK4 for physics implementation in a game, so I read in some pages and all people recommend me this page:
http://gafferongames.com/game-physics/fix-your-timestep/
This page shows clearly how this one works, but I can't figure out how to implement in my game, maybe I don't understand that good but I find some things that are not really clearly to me.
In my game, the player decides when change direction in the X-Axis but I can't figure out how with this RK4 implementation change the direction of the object, in the example the point goes side to side but I don't understand how I can control when he goes right or left.
So if anyone can give a little bit of clarity in this implementation and my problem which I do not understand I will be really grateful.
Thanks beforehand
I've got a point in 2d image for example the red Dot in the given picture and a set of n points blue dot (x1,y1)...(xn,yn) and I want to find nearest point to (x0,y0) in a way better than trying all points. Like to have best possible solution. Would appreciate if you share any similar class if you have.
There are many approaches to this, the most common probably being using some form of space partitioning to speed up the search so that it is not O(n). For details, see Nearest neighbor search on Wikipedia.
Most solutions that we could suggest would depend on a little bit more knowledge, I am going to go out on a limb and say that unless you already know that you are short on time. I.e. there are tens of thousands of blue dots or you have to do thousands of these calculations in a short time. "Linear Search" will serve you well enough.
Don't bother calculating the actual distance, save yourself calculating the square root and use this as the "distance".
Most other methods use more complex data structures to sort the points in respect to their geometric arrangement. But are a lot harder to implement.