I generate Poisson point processes with this method First the area being studied (part of space which can be in 1D, 2D, 3D, ..., in our example is a 2D shape i.e., square) is divided into cells (gridding). Second, for each cell a random number n is drawn from a Poisson distribution with density of d. Then within each cell n points are uniformly distributed. The resulting point pattern is a homogeneous point process. question: how do i obtain the points coordinate in the 3D space for example in the box with Dimensional (30m,30m,30m) Thanks for attention
obtain the points coordinate with poisson distributuin in the space
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probability
coordinate-systems
1 Answers
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Draw $3n$ i.i.d. uniform random variables on $(0,1)$, say $(u_k)_{1\leqslant k\leqslant3n}$ and decide that the $n$ points are located at the base point of a box plus $(u_{3k-2},u_{3k-1},u_{3k})$ times the dimensions of the box, for each $1\leqslant k\leqslant n$.