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Points

Base.rand — Method
rand([rng], process::PointProcess, geometry, [nreals])
rand([rng], process::PointProcess, domain, [nreals])

Generate one or nreals realizations of the point process inside geometry or domain. Optionally specify the random number generator rng.

# geometry of interest
sphere = Sphere((0, 0, 0), 1)

# homogeneous Poisson process
proc = PoissonProcess(5.0)

# sample two point patterns
pset = rand(proc, sphere, 2)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], sphere)
viz!(fig[1,1], pset[1], color = :black)
viz(fig[1,2], sphere)
viz!(fig[1,2], pset[2], color = :black)
fig

Processes

# geometry of interest
box = Box((0, 0), (100, 100))

# Binomial process
proc = BinomialProcess(1000)

# sample point patterns
pset = rand(proc, box, 2)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset[1], color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset[2], color = :black)
fig
GeoStatsProcesses.PoissonProcess — Type
PoissonProcess(λ)

A Poisson process with intensity λ. For a homogeneous process, define λ as a constant real value, while for an inhomogeneous process, define λ as a function or vector of values. If λ is a vector, it is assumed that the process is associated with a Domain with the same number of elements as λ.

# geometry of interest
box = Box((0, 0), (100, 100))

# intensity function
λ(p) = sum(coordinates(p))^2 / 10000

# homogeneous process
proc₁ = PoissonProcess(0.5)

# inhomogeneous process
proc₂ = PoissonProcess(λ)

# sample point patterns
pset₁ = rand(proc₁, box)
pset₂ = rand(proc₂, box)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset₁, color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset₂, color = :black)
fig
# geometry of interest
box = Box((0, 0), (100, 100))

# inhibition process
proc = InhibitionProcess(2.0)

# sample point pattern
pset = rand(proc, box, 2)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset[1], color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset[2], color = :black)
fig
GeoStatsProcesses.ClusterProcess — Type
ClusterProcess(proc, ofun)

A cluster process with parent process proc and offsprings generated with ofun. It is a function that takes a parent point and returns a point pattern from another point process.

ClusterProcess(proc, offs, gfun)

Alternatively, specify the parent process proc, the offspring process offs and the geometry function gfun. It is a function that takes a parent point and returns a geometry or domain for the offspring process.

# geometry of interest
box = Box((0, 0), (5, 5))

# Matérn process
proc₁ = ClusterProcess(
  PoissonProcess(1),
  PoissonProcess(1000),
  p -> Ball(p, 0.2)
)

# inhomogeneous parent and offspring processes
proc₂ = ClusterProcess(
  PoissonProcess(p -> 0.1 * sum(coordinates(p) .^ 2)),
  p -> rand(PoissonProcess(x -> 5000 * sum((x - p).^2)), Ball(p, 0.5))
)

# sample point patterns
pset₁ = rand(proc₁, box)
pset₂ = rand(proc₂, box)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset₁, color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset₂, color = :black)
fig

Operations

Base.union — Method
p₁ ∪ p₂

Return the union of point processes p₁ and p₂.

# geometry of interest
box = Box((0, 0), (100, 100))

# superposition of two Binomial processes
proc₁ = BinomialProcess(500)
proc₂ = BinomialProcess(500)
proc  = proc₁ ∪ proc₂ # 1000 points

pset = rand(proc, box, 2)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset[1], color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset[2], color = :black)
fig
GeoStatsProcesses.RandomThinning — Type
RandomThinning(p)

Random thinning with retention probability p, which can be a constant probability value in [0,1] or a function mapping a point to a probability.

Examples

RandomThinning(0.5)
RandomThinning(p -> sum(coordinates(p)))
# geometry of interest
box = Box((0, 0), (100, 100))

# reduce intensity of Poisson process by half
proc₁ = PoissonProcess(0.5)
proc₂ = thin(proc₁, RandomThinning(0.5))

# sample point patterns
pset₁ = rand(proc₁, box)
pset₂ = rand(proc₂, box)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset₁, color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset₂, color = :black)
fig
# geometry of interest
box = Box((0, 0), (100, 100))

# Binomial process
proc = BinomialProcess(2000)

# sample point pattern
pset₁ = rand(proc, box)

# thin point pattern with probability 0.5
pset₂ = thin(pset₁, RandomThinning(0.5))

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset₁, color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset₂, color = :black)
fig