How exactly do you work out a 3D pos from 2 cameras
Author
Hi everyone!
Ive been playing around with wimmotes after being inspired by Johnny lee and i want to have a stab at the 3D tracking just for fun, but my maths is useless and i have no idea where to really start.
I have 2D data coming from both wiimote cameras and i dont know how to put this into 3D. Poking around has lead me so far to parralax, but from my understanding you work out the X and Y from the distance and not the other way round. Im getting X and y data from both remotes, how do i turn this into usefull 3D data.
Although it would be nice, im not too fussed on it be accurate world space, i just want to wave a lightsabre around in 3D so it doesnt need to be to scale or 100% accurate.
At the moment im moving a point by the difference in the data of the wiimote from the last frame and this. This is pretty much what im doing at the minute.
rawPosX = (wiimote[0].ir.dot.x + wiimote[1].ir.dot.x)/2;
rawPosY = (wiimote[0].ir.dot.y + wiimote[1].ir.dot.y)/2;
rawPosZ = wiimote[0].ir.dot.x - wiimote[1].ir.dot.x;
Vector3 difference = Vector3(oldRawPosX ,oldRawPosY , oldRawPosZ ) - Vector3(rawPosX ,rawPosY , rawPosZ );
pointPosition += difference;
This doesnt really seem to work, and i think one of the main logical reasons for this is the fact i have no scaling for how far apart the wiimotes are.
I understand that some methods use a calibration step but prefrably i would like to skip this and say make sure the cameras are always next to each other or at some other predetermined arrangement.
As far as my current maths skills go we have just gone over trigonometry again in school and i can just about get my head around that. it feels like trigonometry is the solution here but as good as much as i understand the concept of trig i cant figure out how to apply it to this problem....
please help ill be very gratefull!
Im using C++, Ogre and wiiyourself.
The further apart the x positions from wiimote to wiimote the closer the point is. Try something like
rawPosZ = constant/(wiimote[0].ir.dot.x - wiimote[1].ir.dot.x).
Also, your 3D x and y will be a little more complicated since they will get bigger with z. I pulled this code from one of my projects:
px = scalexy*(x-width/2)*pz*2/width ;
py = scalexy*(y-height/2)*pz*2/width ;
That should give a believable 3D position.
rawPosZ = constant/(wiimote[0].ir.dot.x - wiimote[1].ir.dot.x).
Also, your 3D x and y will be a little more complicated since they will get bigger with z. I pulled this code from one of my projects:
px = scalexy*(x-width/2)*pz*2/width ;
py = scalexy*(y-height/2)*pz*2/width ;
That should give a believable 3D position.
Author
@Alrecenk
Thank you so much for your reply, but ive found that if i use this:
rawPosZ = constant/(wiimote[0].ir.dot.x - wiimote[1].ir.dot.x)
that rawPosZ will change as i move left and right aswell :S
and
px = scalexy*(x-width/2)*pz*2/width ;
py = scalexy*(y-height/2)*pz*2/width ;
(is this meant to be py = scalexy*(y-height/2)*pz*2/height?
what do would you recomend as scalexy & constant?
and is width and height the screen width and height?
and is x and y the average x and y?
thank you fro your patience
Thank you so much for your reply, but ive found that if i use this:
rawPosZ = constant/(wiimote[0].ir.dot.x - wiimote[1].ir.dot.x)
that rawPosZ will change as i move left and right aswell :S
and
px = scalexy*(x-width/2)*pz*2/width ;
py = scalexy*(y-height/2)*pz*2/width ;
(is this meant to be py = scalexy*(y-height/2)*pz*2/height?
what do would you recomend as scalexy & constant?
and is width and height the screen width and height?
and is x and y the average x and y?
thank you fro your patience
That z calculation is assuming that you have two wiimotes right next to each other facing the same direction and lined up on the x-axis, and even then it's just an approximation. Still, moving left and right shouldn't cause the depth to change too much. Here are my notes on scalexy:
It's basically a parameter representing the view angle of the camera. In my code I've assumed that the ratio of the horizontal to vertical view angle is the same as the image width to the image height(hence dividing by width for both x and y). Width and height are the width and height of the camera or in this case the wiimote. I believe wiimotes are 1024x768. The average x and y from the two wiimotes should work fine. It's mostly a matter of where the origin is in your 3D space. In some cases it works better to pick one camera, but for simple 3D positioning it's not going to make much difference. It all sounds like a hack, but I've managed to get fairly decent results this way:
http://www.alrecenk.com/resume/images/FacialRecognition/mymodels.png
//the internal camera parameter//when something is 1 away from the camera along z//the camera image will range from -scalexy to scalexy and -scalexy*width/height to scalexy*width/heightdouble scalexy=.6;It's basically a parameter representing the view angle of the camera. In my code I've assumed that the ratio of the horizontal to vertical view angle is the same as the image width to the image height(hence dividing by width for both x and y). Width and height are the width and height of the camera or in this case the wiimote. I believe wiimotes are 1024x768. The average x and y from the two wiimotes should work fine. It's mostly a matter of where the origin is in your 3D space. In some cases it works better to pick one camera, but for simple 3D positioning it's not going to make much difference. It all sounds like a hack, but I've managed to get fairly decent results this way:
http://www.alrecenk.com/resume/images/FacialRecognition/mymodels.png
http://en.wikipedia.org/wiki/Eight-point_algorithm
It's also much easier to do with quaternions, there is a good example in a free paper on the web titled "Object modeling and motion anaylsis using clifford algebra". It's written in the context of geometric algebra, which if you don't know, just replace the word rotor with quaternion and the wedge product a^b with the cross product a x b.
It's also much easier to do with quaternions, there is a good example in a free paper on the web titled "Object modeling and motion anaylsis using clifford algebra". It's written in the context of geometric algebra, which if you don't know, just replace the word rotor with quaternion and the wedge product a^b with the cross product a x b.
Author
@ Alrecenk thanks for all your help so far, im afraid its still not really working, I dont suppose you could have a look at my function and results and see anything obvious?
here is the slightly butchered function that im currently using:
Ive put my current results below, and in an easier to read excell file I set it up so that i could hit a,s,d,cntrl so that i could say when i what i was doing at that point, in the results below and in the excell file you will notice it has *right* samples and "forward samples etc, the main point of iterest is the right sample, this is when i moved the IR right and yet get a sudden change in z, looking at the data myself it appears that in actuall fact the x stays the same as the z grows untill a bit later, which is strange. You wll also notice im outputing the 3D point i get when i use the average and the 3D point i get when i use the x and y from just one camera.
@robert_porter thank you for the links, im looking through them now!
here is the slightly butchered function that im currently using:
Vector3 FPSGameScreen::WorkOutGoodEnough3DPosition2(Vector2D PointFromCamera1, Vector2D PointFromCamera2){ PointFromCamera1 = Vector2(mWiiMotes[0]->IR.Dot[0].RawX , mWiiMotes[0]->IR.Dot[0].RawY); PointFromCamera2 = Vector2(mWiiMotes[1]->IR.Dot[0].RawX , mWiiMotes[1]->IR.Dot[0].RawY); float constant = 0.5;//8.5f * 25.4f; float scaleXY = 0.6f; float width = 1024; float height = 768; float avgX = (PointFromCamera1.x + PointFromCamera2.x) / 2.0f; float avgY = (PointFromCamera1.y + PointFromCamera2.y) / 2.0f; float x = avgX; float y = avgY; float pz = constant/(PointFromCamera1.x - PointFromCamera2.x); float px = scaleXY*(x-width/2)*pz*2/width ; float py = scaleXY*(y-height/2)*pz*2/width ; Vector3 Point3D = Vector3(px,py,pz); x = PointFromCamera1.x; y = PointFromCamera1.y; pz = constant/(PointFromCamera1.x - PointFromCamera2.x); px = scaleXY*(x-width/2)*pz*2/width ; py = scaleXY*(y-height/2)*pz*2/width ; Vector3 Point3D2 = Vector3(px,py,pz); DebugMessage(toFile) << sep << sep << "3D point with average x/y " << sep << SEP(Point3D) << sep << "3D point with average x from one camera" << sep << SEP(Point3D2); return Point3D;}Ive put my current results below, and in an easier to read excell file I set it up so that i could hit a,s,d,cntrl so that i could say when i what i was doing at that point, in the results below and in the excell file you will notice it has *right* samples and "forward samples etc, the main point of iterest is the right sample, this is when i moved the IR right and yet get a sudden change in z, looking at the data myself it appears that in actuall fact the x stays the same as the z grows untill a bit later, which is strange. You wll also notice im outputing the 3D point i get when i use the average and the 3D point i get when i use the x and y from just one camera.
3D point with average x/y -3.26E-05 -0.000331182 -0.00241546 3D point with average x from one camera 0.000260417 -0.000350996 -0.00241546 3D point with average x/y -3.26E-05 -0.000331182 -0.00241546 3D point with average x from one camera 0.000260417 -0.000350996 -0.00241546 3D point with average x/y -3.94E-05 -0.000298603 -0.00240385 3D point with average x from one camera 0.000253531 -0.000318322 -0.00240385 3D point with average x/y -3.94E-05 -0.000298603 -0.00240385 3D point with average x from one camera 0.000253531 -0.000318322 -0.00240385 *********************************** STILL SAMPLE *********************************** 3D point with average x/y -8.15E-05 -0.000271532 -0.00243902 3D point with average x from one camera 0.000211509 -0.000294398 -0.00243902 3D point with average x/y -8.15E-05 -0.000271532 -0.00243902 3D point with average x from one camera 0.000211509 -0.000294398 -0.00243902 3D point with average x/y -9.38E-05 -0.000259775 -0.00246305 3D point with average x 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-0.000194346 -0.00247525 3D point with average x/y -0.000136332 -0.00017114 -0.00247525 3D point with average x from one camera 0.000156637 -0.000194346 -0.00247525 3D point with average x/y -0.000126379 -0.000159409 -0.00245098 3D point with average x from one camera 0.00016659 -0.000180951 -0.00245098 3D point with average x/y -0.000126379 -0.000159409 -0.00245098 3D point with average x from one camera 0.00016659 -0.000180951 -0.00245098 3D point with average x/y -0.000131331 -0.000163081 -0.00246305 3D point with average x from one camera 0.000161638 -0.000184729 -0.00246305 3D point with average x/y -0.000131331 -0.000163081 -0.00246305 3D point with average x from one camera 0.000161638 -0.000184729 -0.00246305 3D point with average x/y -0.000135553 -0.000169076 -0.00248756 3D point with average x from one camera 0.000157416 -0.000192397 -0.00248756 3D point with average x/y -0.000135553 -0.000169076 -0.00248756 3D point with average x from one camera 0.000157416 -0.000192397 -0.00248756 3D point with average x/y -0.000132638 -0.000167619 -0.00248756 3D point with average x from one camera 0.000160331 -0.000189482 -0.00248756 3D point with average x/y -0.000132638 -0.000167619 -0.00248756 3D point with average x from one camera 0.000160331 -0.000189482 -0.00248756 3D point with average x/y -0.000136332 -0.000165339 -0.00247525 3D point with average x from one camera 0.000156637 -0.000188544 -0.00247525 3D point with average x/y -0.000136332 -0.000165339 -0.00247525 3D point with average x from one camera 0.000156637 -0.000188544 -0.00247525 3D point with average x/y -0.000143612 -0.000163718 -0.00245098 3D point with average x from one camera 0.000149357 -0.000186696 -0.00245098 3D point with average x/y -0.000143612 -0.000163718 -0.00245098 3D point with average x from one camera 0.000149357 -0.000186696 -0.00245098 3D point with average x/y -0.000177513 -0.000178956 -0.00246305 3D point with average x from one camera 0.000115456 -0.000202047 -0.00246305 3D point with average x/y -0.000177513 -0.000178956 -0.00246305 3D point with average x from one camera 0.000115456 -0.000202047 -0.00246305 3D point with average x/y -0.000180399 -0.000181843 -0.00246305 3D point with average x from one camera 0.000112569 -0.000204934 -0.00246305 3D point with average x/y -0.000180399 -0.000181843 -0.00246305 3D point with average x from one camera 0.000112569 -0.000204934 -0.00246305 3D point with average x/y -0.000179842 -0.000189995 -0.00247525 3D point with average x from one camera 0.000113127 -0.00021175 -0.00247525 3D point with average x/y -0.000179842 -0.000189995 -0.00247525 3D point with average x from one camera 0.000113127 -0.00021175 -0.00247525 3D point with average x/y -0.000179842 -0.000198697 -0.00247525 3D point with average x from one camera 0.000113127 -0.000223352 -0.00247525 3D point with average x/y -0.000179842 -0.000198697 -0.00247525 3D point with average x from one camera 0.000113127 -0.000223352 -0.00247525 3D point with 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point with average x from one camera 0.000167411 -0.00020782 -0.00246305 3D point with average x/y -0.000125558 -0.000184729 -0.00246305 3D point with average x from one camera 0.000167411 -0.00020782 -0.00246305 3D point with average x/y -0.000128444 -0.000178956 -0.00246305 3D point with average x from one camera 0.000164524 -0.000202047 -0.00246305 3D point with average x/y -0.000128444 -0.000178956 -0.00246305 3D point with average x from one camera 0.000164524 -0.000202047 -0.00246305 *********************************** END SAMPLE *********************************** 3D point with average x/y -0.000132638 -0.000179279 -0.00248756 3D point with average x from one camera 0.000160331 -0.000204058 -0.00248756 3D point with average x/y -0.000132638 -0.000179279 -0.00248756 3D point with average x from one camera 0.000160331 -0.000204058 -0.00248756 3D point with average x/y -0.000145034 -0.000176942 -0.00247525 3D point with average x from one camera 0.000147935 -0.000200147 -0.00247525 3D point with average x/y -0.000145034 -0.000176942 -0.00247525 3D point with average x from one camera 0.000147935 -0.000200147 -0.00247525 3D point with average x/y -0.000158874 -0.000179279 -0.00248756 3D point with average x from one camera 0.000134095 -0.000201143 -0.00248756 3D point with average x/y -0.000158874 -0.000179279 -0.00248756 3D point with average x from one camera 0.000134095 -0.000201143 -0.00248756 3D point with average x/y -0.000143612 -0.000195313 -0.00245098 3D point with average x from one camera 0.000149357 -0.00021829 -0.00245098 3D point with average x/y -0.000143612 -0.000195313 -0.00245098 3D point with average x from one camera 0.000149357 -0.00021829 -0.00245098 3D point with average x/y -0.000137695 -0.000196289 -0.0025 3D point with average x from one camera 0.000155273 -0.000219727 -0.0025 3D point with average x/y -0.000137695 -0.000196289 -0.0025 3D point with average x from one camera 0.000155273 -0.000219727 -0.0025 3D point with average x/y 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-0.000116669 -0.00221239 *********************************** FORWARD SAMPLE *********************************** 3D point with average x/y -0.000138637 -9.81E-05 -0.00223214 3D point with average x from one camera 0.000154332 -0.000120326 -0.00223214 3D point with average x/y -0.000138637 -9.81E-05 -0.00223214 3D point with average x from one camera 0.000154332 -0.000120326 -0.00223214 3D point with average x/y -0.000105574 -0.000118771 -0.00225225 3D point with average x from one camera 0.000187394 -0.000139886 -0.00225225 3D point with average x/y -0.000105574 -0.000118771 -0.00225225 3D point with average x from one camera 0.000187394 -0.000139886 -0.00225225 3D point with average x/y -2.35E-05 -0.000125558 -0.00223214 3D point with average x from one camera 0.000269427 -0.000143869 -0.00223214 3D point with average x/y -2.35E-05 -0.000125558 -0.00223214 3D point with average x from one camera 0.000269427 -0.000143869 -0.00223214 3D point with average x/y 7.59E-05 -0.000121634 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0.00103666 -0.000125357 -0.00240385 3D point with average x from one camera 0.00132963 -0.000118314 -0.00240385 3D point with average x/y 0.00103666 -0.000125357 -0.00240385 3D point with average x from one camera 0.00132963 -0.000118314 -0.00240385 3D point with average x/y 0.000887398 -0.000155684 -0.00241546 3D point with average x from one camera 0.00118037 -0.000152853 -0.00241546 3D point with average x/y 0.000887398 -0.000155684 -0.00241546 3D point with average x from one camera 0.00118037 -0.000152853 -0.00241546 3D point with average x/y 0.000746132 -0.000178956 -0.00246305 3D point with average x from one camera 0.0010391 -0.000181843 -0.00246305 3D point with average x/y 0.000746132 -0.000178956 -0.00246305 3D point with average x from one camera 0.0010391 -0.000181843 -0.00246305 3D point with average x/y 0.000526794 -0.0001568 -0.00234742 3D point with average x from one camera 0.000819762 -0.000165053 -0.00234742 3D point with average x/y 0.000526794 -0.0001568 -0.00234742 3D point with average x from one camera 0.000819762 -0.000165053 -0.00234742 3D point with average x/y 0.000397198 -0.000161978 -0.00240385 3D point with average x from one camera 0.000690167 -0.000171837 -0.00240385 3D point with average x/y 0.000397198 -0.000161978 -0.00240385 3D point with average x from one camera 0.000690167 -0.000171837 -0.00240385 3D point with average x/y 0.000267616 -0.000183105 -0.00240385 3D point with average x from one camera 0.000560584 -0.000197191 -0.00240385 3D point with average x/y 0.000267616 -0.000183105 -0.00240385 3D point with average x from one camera 0.000560584 -0.000197191 -0.00240385 3D point with average x/y 0.000198552 -0.000205495 -0.00236967 3D point with average x from one camera 0.000491521 -0.000219379 -0.00236967 3D point with average x/y 0.000198552 -0.000205495 -0.00236967 3D point with average x from one camera 0.000491521 -0.000219379 -0.00236967 3D point with average x/y 0.000134163 -0.000214935 -0.00233645 3D point with average x from one camera 0.000427132 -0.000229994 -0.00233645 3D point with average x/y 0.000134163 -0.000214935 -0.00233645 3D point with average x from one camera 0.000427132 -0.000229994 -0.00233645 3D point with average x/y 1.12E-05 -0.000216239 -0.00238095 3D point with average x from one camera 0.000304129 -0.000234375 -0.00238095 3D point with average x/y 1.12E-05 -0.000216239 -0.00238095 3D point with average x from one camera 0.000304129 -0.000234375 -0.00238095 3D point with average x/y -6.25E-05 -0.00020966 -0.00236967 3D point with average x from one camera 0.000230487 -0.000230487 -0.00236967 3D point with average x/y -6.25E-05 -0.00020966 -0.00236967 3D point with average x from one camera 0.000230487 -0.000230487 -0.00236967 3D point with average x/y -8.73E-05 -0.000201416 -0.00240385 3D point with average x from one camera 0.000205642 -0.000222544 -0.00240385 3D point with average x/y -8.73E-05 -0.000201416 -0.00240385 3D point with average x from one camera 0.000205642 -0.000222544 -0.00240385 3D point with average x/y -0.000106027 -0.000209263 -0.00238095 3D point with average x from one camera 0.000186942 -0.000231585 -0.00238095 3D point with average x/y -0.000106027 -0.000209263 -0.00238095 3D point with average x from one camera 0.000186942 -0.000231585 -0.00238095 *********************************** END SAMPLE *********************************** 3D point with average x/y -0.000116346 -0.000220077 -0.00239234 3D point with average x from one camera 0.000176622 -0.000241103 -0.00239234 3D point with average x/y -0.000116346 -0.000220077 -0.00239234 3D point with average x from one camera 0.000176622 -0.000241103 -0.00239234 3D point with average x/y -0.000109863 -0.000239446 -0.00240385 3D point with average x from one camera 0.000183105 -0.000261982 -0.00240385 3D point with average x/y -0.000109863 -0.000239446 -0.00240385 3D point with average x from one camera 0.000183105 -0.000261982 -0.00240385 3D point with average x/y -0.000115497 -0.000254939 -0.00240385 3D point with average x from one camera 0.000177471 -0.000276067 -0.00240385 3D point with average x/y -0.000115497 -0.000254939 -0.00240385 3D point with average x from one camera 0.000177471 -0.000276067 -0.00240385 3D point with average x/y -9.39E-05 -0.000263532 -0.00239234 3D point with average x from one camera 0.000199051 -0.000283156 -0.00239234 3D point with average x/y -9.39E-05 -0.000263532 -0.00239234 3D point with average x from one camera 0.000199051 -0.000283156 -0.00239234 3D point with average x/y -7.71E-05 -0.000234095 -0.00239234 3D point with average x from one camera 0.000215872 -0.000255121 -0.00239234 3D point with average x/y -7.71E-05 -0.000234095 -0.00239234 3D point with average x from one camera 0.000215872 -0.000255121 -0.00239234 3D point with average x/y -7.89E-05 -0.000215501 -0.00240385 3D point with average x from one camera 0.000214093 -0.000236629 -0.00240385 3D point with average x/y -7.89E-05 -0.000215501 -0.00240385 3D point with average x from one camera 0.000214093 -0.000236629 -0.00240385@robert_porter thank you for the links, im looking through them now!
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