I want to do a project, which will consist in detecting possible collision of the pool balls, using opencv, webcam and C++ programming language. For now I just want to prediction collision of 2 balls on minibilard table. I detect them by change rgb to hsv and then use thereshold, in future i will probably use another method for detect a random amount of balls, but it's not so important now.
So, for now I can detect two balls, i know their position, radius, now I'm thinking how to predict whether there will be a collision between them, if we if we assume that they will move in straight lines. I think that I should check their position in every frame update (and i have to know a time between frames in my webcamera) and by that, i I will be able to determine the value of speed, acceleration and direction of the ball. So, if i will know those parameters for for both balls, I will be able to determine where can they collide, and then, using parametric equastion I will be able to check, if they will be on collision point on the same time.
I wonder if this is the right approach to the problem, maybe there is a simpler and more effective method to do this?
Thanks for any kind of help.
Karol
This sounds like you are on track for a good project...
Calculating acceleration seems, from what I briefly read here, reasonably difficult though. So as a preliminary step, you could just assume a constant velocity. So take the difference between a balls position last frame and current frame as a vector and add it on to the current frames position to find where it will be next frame. Doing this for both balls will allow you to check for a collision.
You can check for a collision by comparing the distance between the balls centers using Pythagoras to the sum of their radii. If the sum of their radii will be greater than the distances between their centers, you have a collision.
Obviously, calculating one frame ahead is not very useful, but if you assume a constant velocity or manage to calculate their acceleration, there is no reason to why you can't calculate 30 or 100 frames in the future with this method.
I recently made a billiards ball simulation in javascript which you could take a quick look at here if you want to see how this could work.
Related
I have a physics engine that uses AABB testing to detect object collisions and an animation system that does not use linear interpolation. Because of this, my collisions act erratically at times, especially at high speeds. Here is a glaringly obvious problem in my system...
For the sake of demonstration, assume a frame in our animation system lasts 1 second and we are given the following scenario at frame 0.
At frame 1, the collision of the objects will not bet detected, because c1 will have traveled past c2 on the next draw.
Although I'm not using it, I have a bit of a grasp on how linear interpolation works because I have used linear extrapolation in this project in a different context. I'm wondering if linear interpolation will solve the problems I'm experiencing, or if I will need other methods as well.
There is a part of me that is confused about how linear interpolation is used in the context of animation. The idea is that we can achieve smooth animation at low frame rates. In the above scenario, we cannot simply just set c1 to be centered at x=3 in frame 1. In reality, they would have collided somewhere between frame 0 and frame 1. Does linear interpolation automatically take care of this and allow for precise AABB testing? If not, what will it solve and what other methods should I look into to achieve smooth and precise collision detection and animation?
The phenomenon you are experiencing is called tunnelling, and is a problem inherent to discrete collision detection architectures. You are correct in feeling that linear interpolation may have something to do with the solution as it can allow you to, within a margin of error (usually), predict the path of an object between frames, but this is just one piece of a much larger solution. The terminology I've seen associated with these types of solutions is "Continuous Collision Detection". The topic is large and gets quite complex, and there are books that discuss it, such as Real Time Collision Detection and other online resources.
So to answer your question: no, linear interpolation on its own won't solve your problems*. Unless you're only dealing with circles or spheres.
What to Start Thinking About
The way the solutions look and behave are dependant on your design decisions and are generally large. So just to point in the direction of the solution, the fundamental idea of continuous collision detection is to figure out: How far between the early frame and the later frame does the collision happen, and in what position and rotation are the two objects at this point. Then you must calculate the configuration the objects will be in at the later frame time in response to this. Things get very interesting addressing these problems for anything other than circles in two dimensions.
I haven't implemented this but I've seen described a solution where you march the two candidates forward between the frames, advancing their position with linear interpolation and their orientation with spherical linear interpolation and checking with discrete algorithms whether they're intersecting (Gilbert-Johnson-Keerthi Algorithm). From here you continue to apply discrete algorithms to get the smallest penetration depth (Expanding Polytope Algorithm) and pass that and the remaining time between the frames, along to a solver to get how the objects look at your later frame time. This doesn't give an analytic answer but I don't have knowledge of an analytic answer for generalized 2 or 3D cases.
If you don't want to go down this path, your best weapon in the fight against complexity is assumptions: If you can assume your high velocity objects can be represented as a point things get easier, if you can assume the orientation of the objects doesn't matter (circles, spheres) things get easier, and it keeps going and going. The topic is beyond interesting and I'm still on the path of learning it, but it has provided some of the most satisfying moments in my programming period. I hope these ideas get you on that path as well.
Edit: Since you specified you're working on a billiard game.
First we'll check whether discrete or continuous is needed
Is any amount of tunnelling acceptable in this game? Not in billiards
no.
What is the speed at which we will see tunnelling? Using a 0.0285m
radius for the ball (standard American) and a 0.01s physics step, we
get 2.85m/s as the minimum speed that collisions start giving bad
response. I'm not familiar with the speed of billiard balls but that
number feels too low.
So just checking on every frame if two of the balls are intersecting is not enough, but we don't need to go completely continuous. If we use interpolation to subdivide each frame we can increase the velocity needed to create incorrect behaviour: With 2 subdivisions we get 5.7m/s, which is still low; 3 subdivisions gives us 8.55m/s, which seems reasonable; and 4 gives us 11.4m/s which feels higher than I imagine billiard balls are moving. So how do we accomplish this?
Discrete Collisions with Frame Subdivisions using Linear Interpolation
Using subdivisions is expensive so it's worth putting time into candidate detection to use it only where needed. This is another problem with a bunch of fun solutions, and unfortunately out of scope of the question.
So you have two candidate circles which will very probably collide between the current frame and the next frame. So in pseudo code the algorithm looks like:
dt = 0.01
subdivisions = 4
circle1.next_position = circle1.position + (circle1.velocity * dt)
circle2.next_position = circle2.position + (circle2.velocity * dt)
for i from 0 to subdivisions:
temp_c1.position = interpolate(circle1.position, circle1.next_position, (i + 1) / subdivisions)
temp_c2.position = interpolate(circle2.position, circle2.next_position, (i + 1) / subdivisions)
if intersecting(temp_c1, temp_c2):
intersection confirmed
no intersection
Where the interpolate signature is interpolate(start, end, alpha)
So here you have interpolation being used to "move" the circles along the path they would take between the current and the next frame. On a confirmed intersection you can get the penetration depth and pass the delta time (dt / subdivisions), the two circles, the penetration depth and the collision points along to a resolution step that determines how they should respond to the collision.
I want to make a non-real time simulation of overlapping repulsive balls, initially in 2D and later in 3D.
First of all, consider a simple closed domain for simplicity. In practice, domains will be complex and irregular but always closed.
The balls on the boundaries are fixed and could be overlapping. A fixed ball duplicates itself to produce a free ball of the same size whenever no other ball overlaps it. Both fixed and free balls repel each other but fixed balls cannot move. Note that, duplicant ball should be sufficiently tilted to start repulsion. In elastic colliding balls case, after two balls collide they change direction with some velocity but in this case the balls can stop quickly once they stop overlapping. Free balls move until there is no motion or let's say we solve motion problem until convergence. Then each fixed ball produce a free ball again and this process goes on until no fixed ball can duplicate due to being overlapped by any other ball(s).
I think GPU (CUDA) would be faster to solve this problem but initially I am thinking to write on CPU. However, before proceeding to coding I would like to know "feasibility" of this work. That is, considering a million of balls, approximately how long it would take to simulate this or similar kind of problems in non-real time. For a million of balls, if solution time is in order of minutes, I will dive into the problem.
You might look into using Box2D for a prototype. Setting up your collision constraints to be 'soft' would give you about the kind of behavior you're showing in your diagrams.
As for simulating a million objects in real time, you're going to be working on a GPU.
I am at the start of developing a software using OpenCV in Microsoft Visual 2010 Express. Now what I need to know before i get into coding is the procedures i have to follow.
Overview:
I want to develop software that detects simple boxing moves such as (Left punch, right punch) and outputs the results.
Now where am struggling is what approach should i take how should i tackle this development i.e.
Capture Video Footage and be able to extract lets say every 5th frame for processing.
Do i have to extract and store this frame perhaps have a REFERENCE image to subtract the capture frame from it.
Once i capture a frame what would be the best way to process it:
* Threshold it, then
* Detect the edges, then
* Smooth the edges using some filter, then
* Draw some BOUNDING boxes....?
What is your view on this guys or am i missing something or are there better simpler ways...? Any suggestions...?
Any answer will be much appreciated
Ps...its not my homework :)
I'm not sure if analyzing only every 5th frame will be enough, because usually punches are so fast that they could be overlooked.
I assume what you actually want to find is fast forward (towards camera) movements of fists.
In case of OpenCV I would first start off with such movements of faces, since some examples are already provided on how to do that in software package.
To detect and track faces you can use CvHaarClassifierCascade, but since this won't be fast enough for runtime detection, continue tracking such found face with Lukas-Kanade. Just pick some good-to-track points inside previously found face, remember their distance from arbitrary face middle, and at each frame update it. See this guy http://www.youtube.com/watch?v=zNqCNMefyV8 - example of just some random points tracked with Lukas-Kanade. Note that unlike faces, fists may not be so easy to track since their surface is rather uniform, better check Lukas-Kanade demo in OpenCV.
Of course with each frame actual face will drift away, once in a while re-run CvHaarClassifierCascade and interpolate to it your currently held face position.
You should be able to do above for fists also, but that will require training classifier with pictures of fists (classifier trained with faces is already provided in OpenCV).
Now having fists/face tracked you may try observing what happens to the points - when someone punches they move rapidly in some direction, while on the fist that remains still they don't move to much. And so, when you calculate average movement of single points in recent frames, the higher the value, the bigger chance that there was a punch. Alternatively, if somehow you've managed to track them accurately, if distance between each of them increases, that means object is closer to camera - and so a likely punch.
Note that without at least knowing change of a size of the fist in picture, it might be hard to distinguish if a movement of hand was forward or backward, or if the user was faking it by moving fists left or right. You may have to come up with some specialized algorithm (maybe with trial and error) to detect that, like say, increase a number of screen color pixels in location that previously fist was found.
What you are looking for is the research field of action recognition e.g. www.nada.kth.se/cvap/actions/ or an possible solution is e.g the STIP ( Space-time interest points) method www.di.ens.fr/~laptev/actions/ . But finally this is a tough job if you have to deal with occlusion or different point of views.
I'm trying to develop a game where cars move along roads and stop according to the signal of the traffic lights. They've got different velocities. Sometimes cars need to decelerate in order to not hit the leading car. They need to stop at the red lights. They have to make turns and etc. This is all relatively easy when working with straight intersecting roads. But how can I move a car/cars along a curved path? So far it was easy because I was just using either x or y of a car's position. But this time it's not the case, both coordinates seem to be necessary for moving it ahead. With straight roads I can just give a car an arbitrary speed and it will move along x or y axis with that speed. But how can I determine the velocity, if both coordinates have to be taken into account? Acceleration and decelerations are also mistery to me in this case. Thanks ahead.
Although this is about moving a train over a freeform track, the same issues and principles apply to cars moving across freeform roads. Actually, cars may be easier because they don't need to stick to their track 100% accurately.
In short: it's not easy, but doable. How hard it is going to be depends on how realistic you want your cars to look and finding corners to cut.
In your case the cars should simply follow a path (series of points). Since CCActions are bad for frequent direction/velocity changes, you should use your own system of detecting path points and heading to the next. Movement along a bezier curve is not going to have your cards move at constant speed, that rules out the CCBezier* actions.
For Operating Systems class I'm going to write a scheduling simulator entitled "Jurrasic Park".
The ultimate goal is for me to have a series of cars following a set path and passengers waiting in line at a set location for those cars to return to so they can be picked up and be taken on the tour. This will be a simple 2d, top-down view of the track and the cars moving along it.
While I can code this easily without having to visually display anything I'm not quite sure what the best way would be to implement a car moving along a fixed track.
To start out, I'm going to simply use OpenGL to draw my cars as rectangles but I'm still a little confused about how to approach updating the car's position and ensuring it is moving along the set path for the simulated theme park.
Should I store vertices of the track in a list and have each call to update() move the cars a step closer to the next vertex?
If you want curved track, you can use splines, which are mathematically defined curves specified by two vector endpoints. You plop down the endpoints, and then solve for a nice curve between them. A search should reveal source code or math that you can derive into source code. The nice thing about this is that you can solve for the heading of your vehicle exactly, as well as get the next location on your path by doing a percentage calculation. The difficult thing is that you have to do a curve length calculation if you don't want the same number of steps between each set of endpoints.
An alternate approach is to use a hidden bitmap with the path drawn on it as a single pixel wide curve. You can find the next location in the path by matching the pixels surrounding your current location to a direction-of-travel vector, and then updating the vector with a delta function at each step. We used this approach for a path traveling prototype where a "vehicle" was being "driven" along various paths using a joystick, and it works okay until you have some intersections that confuse your vector calculations. But if it's a unidirectional closed loop, this would work just fine, and it's dead simple to implement. You can smooth out the heading angle of your vehicle by averaging the last few deltas. Also, each pixel becomes one "step", so your velocity control is easy.
In the former case, you can have specially tagged endpoints for start/stop locations or points of interest. In the latter, just use a different color pixel on the path for special nodes. In either case, what you display will probably not be the underlying path data, but some prettied up representation of your "park".
Just pick whatever is easiest, and write a tick() function that steps to the next path location and updates your vehicle heading whenever the car is in motion. If you're really clever, you can do some radius based collision handling so that cars will automatically stop when a car in front of them on the track has halted.
I would keep it simple:
Run a timer (every 100msec), and on each timer draw each ones of the cars in the new location. The location is read from a file, which contains the 2D coordinates of the car (each car?).
If you design the road to be very long (lets say, 30 seconds) writing 30*10 points would be... hard. So how about storing at the file the location at every full second? Then between those 2 intervals you will have 9 blind spots, just move the car in constant speed (x += dx/9, y+= dy/9).
I would like to hear a better approach :)
Well you could use some path as you describe, ether a fixed point path or spline. Then move as a fixed 'velocity' on this path. This may look stiff, if the car moves at the same spend on the straight as cornering.
So you could then have speeds for each path section, but you would need many speed set points, or blend the speeds, otherwise you'll get jerky speed changes.
Or you could go for full car simulation, and use an A* to build the optimal path. That's over kill but very cool.
If there is only going forward and backward, and you know that you want to go forward, you could just look at the cells around you, find the ones that are the color of the road and move so you stay in the center of the road.
If you assume that you won't have abrupt curves then you can assume that the road is directly in front of you and just scan to the left and right to see if the road curves a bit, to stay in the center, to cut down on processing.
There are other approaches that could work, but this one is simple, IMO, and allows you to have gentle curves in your road.
Another approach is just to have it be tile-based, so you just look at the tile before you, and have different tiles for changes in road direction an so you know how to turn the car to stay on the tile.
This wouldn't be as smooth but is also easy to do.