   Recogonising a Circular Guesture
  Hi Everyone,I'm trying to detect a circular hand guesture, I would also like to differientiate between anti-clockwise and clockwise motions. With every method (e.g.) ive looked into so far the maths goes a little over my head and im wondering if anyone could help break down a simple way for me? Scenario:Im creating a little game test bed and i want a clockwise circular hand motion on the Z plane to cycle to the next weapon and an anti clockwise circular hand motion to go to the previous weapon.Data available:Im analysing I.R points in 3D space using wiimotes, the difference in the position between the ir points is added to my "guesture object". The guesture object records its position every half a second in by pushing it in the front of a deque which stores up to 25 points and then starts popping the back.Thanks for taking the time to read this post! - Chris   
  Seems like you would need to record the change in velocity angle every time you sample.  Accumulate the angle change.  When the angle has gone a full circle either positive or negative, you know it has gone all the way around.  If the change in angle velocity is too low for long enough, you can discard the results because they aren't in a gesture.   ;  Well the first problem is figuring out what part of the image the hand is.  That's not easy. Consider the case where you're walking behind me or lighting conditions change or part of me is in the sun and part in shadow so my hand changes color.  This stuff isn't easy.Are you already at a point where you can recognize where the hand is as a single point?  If not, you're way ahead of yourself [smile].  That seems like the hardest problem to me.If you can already identify the hand as a single point then frob's suggestion seems like a pretty good place to start.  I would say you also need ways to mark begin and end of gestures.  you'd need checks for things like x frames of no or low velocity = gesture over, or x frames where the angle changes from one direction to the other = gesture over.  As soon as one gesture aborts or completes you start a new gesture.-me   ;  @frob Thank you for the quick reply, this seems like a good idea! i shall have a go at implementing this and let you know!&Palidine well im already up to the point of tracking points using the wiimotes, when i say "circular hand motion" i'm really saying circular motion of an IR source which is atatched to the hand. hmm i suppose would be usefull to mark the begin and end of a guesture, this is true and i could signify this but prefrably i would like the system to be able to simply detect the guesture without being told the gesture is starting and then when its finished. Im going to try frobs suggestion and let everyone know what i got up to!Thank you both for your quick replies   ;  Was the algorithm that Frob gave good enough?I was thinking you could project your points on a plane and then do least squares circle fitting on the planar points to find the circle closest to all the points, then you could decide if the user made a circular gesture or not based on the error. Although circle fitting is probably too slow to do in real time... Three points determine a circle. Maybe you could randomly sample a few sets of three points from your 25 points, find the average circle from the circles the samples define, and calculate the error between all the points and the average circle?   ;  As an extra detail to what I suggested above, you'll want to make sure that there is maximum angle magnitude and a minimum sample size to prevent small wiggles from setting it off.   ;  ooo thanks guys, unforntunatley ive not had a chancce to try it out, shortly after putting togeether an implementation and fiddling with some other bits, i managed to break a few other things and have been wrestling with that! ill probably run another little test today and hopefully start testing the guesture stuff! I promise i will post back when i have some results! thank you guys so much for your help!   ;  I've implemented a simple gesture recognition system after reading an interesting article somewhere on the net. Unluckily I don't remember where I saw it, so I can't give the inventor proper credit.The algorithm was really easy:1. record the deltas between sample points2. "normalize" this collection of 2D vectors into a set of known size, for example 100 vectors2. a) this can be regarded as a 100-dimensional vector3. do a dot product between this 100-dimensional vector and each of your well-known gesture vectors (i.e. multiply-add)4. this gives you a measure of how closely the gesture points into the same general direction as each recorded gesture (averaged over the whole curve)5. define some (more or less arbitrary) threshold, for example 0.7 or 0.8 and discard everything below as "not recognised"6. choose the gesture that gives the biggest dot product, this is the one that matches bestThis surprisingly simple scheme is able to detect all kinds of movements, clockwise or counter-clockwise circles, all kinds of sweeps, and even complicated zig-zag movements.   ;  What samoth posted is basically like what I worked with once, 10 years ago. It is very generic, able to be taught a huge range of gestures! However you might be able to do something simpler if circles are all you're interested in...To detect a circle, you want to find a series of points whose sum-of-angles sums to either very close to 360 or very close to -360 degrees, and whose sum-of-angles-squared is minimised, and the number of points needs to be between a certain minimum and maximum. Any sharper turns inflate the sum-of-angle-squared, and by rejecting series with a sum-of-angle-squared values above a certain value, you will reject say the drawing of a rough triangle, square, pentagon, or hexagon whilst being relaxed enough to accept an octagon etc. Or perhaps rejecting a highly eliptical oval, whilst accepting a less-eliptical one.I believe that minmising the sum-of-angles-squared is the key to detecting near circular motion, though you will need to vary your tolerance value according to the number of points. Perhaps rating each sum-of-angle-squared values against the corresponding value for an optimal circle approximation with the same number of points, e.g. perfect octagon for 8 points. You could use a precalculated table for that, or just approximate it with a function.To find the most recent sequence of points whose angles sum to about 360 without brute forcing it, you should be able to have a cursor walk some number of points behind the realtime data, staying between some minimum and some maximum number of points behind, and moving forward somewhat sporadically over time so to try and line up with a sum of 360 or -360 degrees between itself and the most recent data point.   ;  Hi Everyone, thank you for all your replies, ive been aiming towards the summing of angles methods posted by iMalc and frob but...my vector math clearly sucks as im getting no were with the summing bit.First i thought that a dot product would do the trick:vecAngle = acos(vec1Normalised.dotProduct(vec2Normalised)); //angle to increase by[\source]but that cant give me minus angles due to the fact the vectors are normalised. I also tried something mad trig with working out the velocity and then using acoswhich went something like this:vecAngle = acos( pos1.squaredlength() / velocity.squaredlength())[\source]and now im trying this:vecAngle = atan2(vec1.x-vec2.x,vec1.y-vec2.y); //this one does give me minus angles, but only because the velocity is now technically the other way[\source]and all are not working....and now im just stabbing at ideas can anyone point me in the right direction for this? When i say they are not working i mean they are often giving high angles even when im slowly going round, the acculation will quickly add up to 360. here is the full code:cicular guesture functionCircularGestureResult GuestureObject::CircularGuesture(){float acuumulatatedAngle = 0;CircularGestureResult result = CircularGestureResult::NONE;;if( mLastposistions.empty())return result;std::deque<Ogre::Vector3>::iterator it = mLastposistions.begin();std::deque<Ogre::Vector3>::iterator it2 = mLastposistions.begin();++it2;int sharpTurns = 0;float vecAngle = 0.0f;for(; it2 != mLastposistions.end();  ++it2,++it){Ogre::Vector3 vec13D = (*it);Ogre::Vector3 vec23D = (*it2);Ogre::Vector2 vec1 = Ogre::Vector2(vec13D.x,vec13D.z);Ogre::Vector2 vec2 = Ogre::Vector2(vec23D.x,vec23D.z);Ogre::Vector2 vec1Normalised = vec1.normalisedCopy();Ogre::Vector2 vec2Normalised = vec2.normalisedCopy();vecAngle = 0.0f;vecAngle = atan2(vec1.x-vec2.x,vec1.y-vec2.y);vecAngle*=DEG; //convert to degrees;if((vecAngle) > mTurnThreshold || (vecAngle) < -mTurnThreshold){//to sharp returnsharpTurns++;if(sharpTurns > 3){SSELOG << "points cleared";this->mLastposistions.clear();return CircularGestureResult::NONE;}}else{acuumulatatedAngle+=vecAngle;}if(acuumulatatedAngle > 360){result = CircularGestureResult::CLOCKWISE;}else if(acuumulatatedAngle < -360){result = CircularGestureResult::ANTICLOCKWISE;}if(acuumulatatedAngle > 360+mCicularThreshold){result = CircularGestureResult::NONE;this->mLastposistions.clear();return result;}if(acuumulatatedAngle < -360-mCicularThreshold){result = CircularGestureResult::NONE;this->mLastposistions.clear();return result;}}SSELOG << "last angle added:" << vecAngle;SSELOG << acuumulatatedAngle;return result;}[\source]update function:GestureObjectResult GuestureObject::Update( Ogre::Vector3 trackingPos,float dT ){newGivenPosition = trackingPos;Ogre::Vector3 differnce = newGivenPosition - oldGivenPosition;if(differnce.length() > MaxChangeThreshold){newGivenPosition = oldGivenPosition;return GestureObjectResult::ThresholdExceeded; //we assume that the points have become confused}mPosition+=differnce;oldGivenPosition = newGivenPosition;mTimePassed+=(dT);if(mTimePassed > ){RecordPos(mPosition );mTimePassed = 0.0f;}if(mDebugDraw){Draw();}return GestureObjectResult::SUCCESS;}[\source]recording positions:void GuestureObject::RecordPos( Ogre::Vector3 pos ){this->mLastposistions.push_front(pos);if(mLastposistions.size() > MAX_GUESTURE_STORAGE){this->mLastposistions.pop_back();}}[\source]mTimeThreshold is set to 0.2 (1/5th of a second). and MAX_GUESTURE_STORAGE is 36 points.and im running with mCicularThreshold = 1000000.0f;mTurnThreshold = 1000000.0f;just so i can actually print some values of vecangle and see what im getting.Any help will be greatly appreciated!