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Community Bot
Community Bot
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If the objects are circular, then the probability of them colliding is the probability that their distance is below a threshold. The difference between two independent normally distributed vectors is itself a normally distributed vector. The length of such a vector has a non-central chi-square distribution. So the problem boils down to computing the cumulative distribution of a non-central chi-squared variate. See the page on Probability of collision (two bivariate normal distributions)Probability of collision (two bivariate normal distributions) for more details.

If the objects are circular, then the probability of them colliding is the probability that their distance is below a threshold. The difference between two independent normally distributed vectors is itself a normally distributed vector. The length of such a vector has a non-central chi-square distribution. So the problem boils down to computing the cumulative distribution of a non-central chi-squared variate. See the page on Probability of collision (two bivariate normal distributions) for more details.

If the objects are circular, then the probability of them colliding is the probability that their distance is below a threshold. The difference between two independent normally distributed vectors is itself a normally distributed vector. The length of such a vector has a non-central chi-square distribution. So the problem boils down to computing the cumulative distribution of a non-central chi-squared variate. See the page on Probability of collision (two bivariate normal distributions) for more details.

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Tom Minka
Tom Minka
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If the objects are circular, then the probability of them colliding is the probability that their distance is below a threshold. The difference between two independent normally distributed vectors is itself a normally distributed vector. The length of such a vector has a non-central chi-square distribution. So the problem boils down to computing the cumulative distribution of a non-central chi-squared variate. See the page on Probability of collision (two bivariate normal distributions) for more details.