What's a better way to model a distribution of hits on a target: normally distributed around center on x and y scales, or normally distributed on distance from the center and uniformly on the angle?
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Any mathematicians here?
Moderators: rexifelis, pilkguns
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Spencer C
depends on how familiar you are with working with polar coor
: What's a better way to model a distribution of hits on a target: normally distributed around center on x and y scales, or normally distributed on distance from the center and uniformly on the angle?
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Spencer C
depends on how you handle polar coordinates
x/y coordinates are normally easier to do the measurements for data collection.
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Chris L in NC
Polar coordinates for humans, cartesian for computers (?)
Funny, this issue is going to become important to me, since I'm doing an extra credit project in statistics class based on the data sets I generated at the Fall Selection.
Score of course depends only on the displacement from center, that is, the r in (r, theta). When somebody is spotting for you on the rifle range, they can call both the value and "angle" or clock reference, say, "tight nine at six". This is polar in action, only you have just 12 sectors to choose the angle from, not 360 degrees or 2pi radians. It would be kind of strange to call "13 inches over, 11 up" on the range since we don't think of shots being located relative to the bottom left corner of the frame.
But computers don't care which you use. They're smart enough to figure it out. Throw in the conversion formula somewhere (x=r*cos(theta), y=r*sin(theta), or if appropriate, r=sqrt(x^2+y^2), remember to convert to/from radians/degrees if necessary) and your software is happy.
I haven't tried it myself, so that's why the question mark at the end of the subject line.
chrisatty-at-hotmail.com.45175.45155
Score of course depends only on the displacement from center, that is, the r in (r, theta). When somebody is spotting for you on the rifle range, they can call both the value and "angle" or clock reference, say, "tight nine at six". This is polar in action, only you have just 12 sectors to choose the angle from, not 360 degrees or 2pi radians. It would be kind of strange to call "13 inches over, 11 up" on the range since we don't think of shots being located relative to the bottom left corner of the frame.
But computers don't care which you use. They're smart enough to figure it out. Throw in the conversion formula somewhere (x=r*cos(theta), y=r*sin(theta), or if appropriate, r=sqrt(x^2+y^2), remember to convert to/from radians/degrees if necessary) and your software is happy.
I haven't tried it myself, so that's why the question mark at the end of the subject line.
chrisatty-at-hotmail.com.45175.45155
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Val
Re: Polar coordinates for humans, cartesian for computers (?
I know how to convert between cartesian and polar coordinates, but my question was a bit different:
I need to design a "shot generator" for some stat. analysis, that will use random number generator to generate hits, given specified "skill" of the virtual shooter.
One way to go to make a shot is to generate two random numbers that follow Gaussian distribution, and say that one number is the displacement on X, and the other one is displacement on Y.
Another way to go is to generate one random number that follows normal distribution, and say "this is my displacement from the center", and generate another one that follows unifrom distribution, and say "this is my angular displacement". These polar coordinates can then be converted to cartesian X and Y.
These two approaches will yield two different kinds of probability density distribution profiles, and I was wondering which approach is more "real".
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I need to design a "shot generator" for some stat. analysis, that will use random number generator to generate hits, given specified "skill" of the virtual shooter.
One way to go to make a shot is to generate two random numbers that follow Gaussian distribution, and say that one number is the displacement on X, and the other one is displacement on Y.
Another way to go is to generate one random number that follows normal distribution, and say "this is my displacement from the center", and generate another one that follows unifrom distribution, and say "this is my angular displacement". These polar coordinates can then be converted to cartesian X and Y.
These two approaches will yield two different kinds of probability density distribution profiles, and I was wondering which approach is more "real".
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Val
Re: Polar coordinates for humans, cartesian for computers (?
The two graphs on the bottom illustrate the two different shot generation strategies.
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David M
Does not matter!
It does not matter how you call it, a lousy triggered low left 7, is still a 7.
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Steve Maly
Re: Any mathematicians here?
I think the best way to actually model one a shot distribution pattern is to get several people to shoot 100 shots each, then analyze their distribution patterns, then try to create a model.
You haven't said what kind of shooting you want to model; machine (like a tank) or human.
Prone rifle in a sling (for example) should give you a dumb-bell shape due to the heart pumping and sling tension, (depending on how much the sling is tightened, and how much skill the shooter has). Air pistol (I suspect) would give you a Gaussian distribution, of angularly uniform.
Asking which one works the best presupposes that there is only one accurate model. That eliminates the need for observation and formulation (like ancient Greek physics did) and might overlook the realistic ones.
: What's a better way to model a distribution of hits on a target: normally distributed around center on x and y scales, or normally distributed on distance from the center and uniformly on the angle?
smaly-at-kes.ns.ca.45183.45155
You haven't said what kind of shooting you want to model; machine (like a tank) or human.
Prone rifle in a sling (for example) should give you a dumb-bell shape due to the heart pumping and sling tension, (depending on how much the sling is tightened, and how much skill the shooter has). Air pistol (I suspect) would give you a Gaussian distribution, of angularly uniform.
Asking which one works the best presupposes that there is only one accurate model. That eliminates the need for observation and formulation (like ancient Greek physics did) and might overlook the realistic ones.
: What's a better way to model a distribution of hits on a target: normally distributed around center on x and y scales, or normally distributed on distance from the center and uniformly on the angle?
smaly-at-kes.ns.ca.45183.45155
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Steve
Re: Any mathematicians here?
Val,
The probability distribution I believe you are looking for is the bivariate normal distribution. This is basically two independent normal distributions for x and y. It does have radial symmetry, and if you prefer to work in polar coordinates you can get the same probability distribution by using a rayleigh distribution in radius, and a uniform distribution in angle. I don't think using a normal distribution for radius will give you what you want.
I do this kind of stuff all the time for bullseye targets and shotgun patterns, and I just generate two sets of normal distributions, one for x, and one for y. If you use Matlab (or Octave, a free s/w alternative) you can use the randn function to generate random samples with normal distributions.
Good luck with your modeling,
Steve.
: What's a better way to model a distribution of hits on a target: normally distributed around center on x and y scales, or normally distributed on distance from the center and uniformly on the angle?
tenex-at-sbcglobal.net.45193.45155
The probability distribution I believe you are looking for is the bivariate normal distribution. This is basically two independent normal distributions for x and y. It does have radial symmetry, and if you prefer to work in polar coordinates you can get the same probability distribution by using a rayleigh distribution in radius, and a uniform distribution in angle. I don't think using a normal distribution for radius will give you what you want.
I do this kind of stuff all the time for bullseye targets and shotgun patterns, and I just generate two sets of normal distributions, one for x, and one for y. If you use Matlab (or Octave, a free s/w alternative) you can use the randn function to generate random samples with normal distributions.
Good luck with your modeling,
Steve.
: What's a better way to model a distribution of hits on a target: normally distributed around center on x and y scales, or normally distributed on distance from the center and uniformly on the angle?
tenex-at-sbcglobal.net.45193.45155
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Val
Re: Any mathematicians here?
Thanks everybody for the replies. Got more info than I was originally looking for :)
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Paul
Re: Any mathematicians here?
Doing an analysis is actually very useful.
I was fortunate enough to shoot at Wolf Creek using the SUIS-Ascor system there, and after 100 shots, it told me that my centre of mass was off by about one click high. I made the adjustment, and my scores went up by a few points.
Doing the statistical analysis can help identify bad habits, bad sighting, inconsistent velocities, etc.
paul.ruppert-at-utoronto.ca.45221.45197
I was fortunate enough to shoot at Wolf Creek using the SUIS-Ascor system there, and after 100 shots, it told me that my centre of mass was off by about one click high. I made the adjustment, and my scores went up by a few points.
Doing the statistical analysis can help identify bad habits, bad sighting, inconsistent velocities, etc.
paul.ruppert-at-utoronto.ca.45221.45197