zoi_functions: Zone of Influence (ZOI) functions
In NINAnor/oneimpact: Tools for the assessment of the cumulative impacts of anthropogenic features in ecological studies
zoi_functions R Documentation
Zone of Influence (ZOI) functions
Description
Computes the decay functions that represent the Zone of
Influence (ZOI). The functions' radius (parameter radius)
controls how far the zone of influence of an infrastructure or disturbance reaches,
and the functions' shape (parameter type) represent represent how the ZOI
decays in space. Given a function shape (type) is chosen, the rate
of decay of the different ZOI functions is parameterized based on
the ZOI radius – e.g the slope of linear_decay() is defined
so that the function decreases to zero at the ZOI radius.
These functions can be used to transform arrays of (Euclidean)
distance values (in one dimension) or rasters of (Euclidean) distance
(in two dimensions) into ZOI values. The distances might represent
the distance to human infrastructure, sources of disturbance, or
more broadly any type of land use class or spatial variable.
Usage
dist_decay(
x,
radius = NULL,
type = c("exp_decay", "gaussian_decay", "linear_decay", "threshold_decay")[1],
zoi_limit = 0.05,
origin = 0,
oneside = TRUE,
...
)
threshold_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
## S3 method for class 'numeric'
threshold_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
## S3 method for class 'SpatRaster'
threshold_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
step_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
bartlett_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
## S3 method for class 'numeric'
bartlett_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
## S3 method for class 'SpatRaster'
bartlett_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
tent_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
linear_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
gaussian_decay(
x,
radius = NULL,
zoi_limit = 0.05,
intercept = 1,
lambda = NULL,
sigma = NULL,
origin = 0,
...
)
half_norm_decay(
x,
radius = NULL,
zoi_limit = 0.05,
intercept = 1,
lambda = NULL,
sigma = NULL,
origin = 0,
...
)
exp_decay(
x,
radius = NULL,
zoi_limit = 0.05,
intercept = 1,
lambda = NULL,
origin = 0,
oneside = TRUE,
half_life = NULL,
zoi_hl_ratio = NULL
)
Arguments
x
[numeric,SpatRaster,RasterLayer]
Euclidean distance from an infrastructure, source
of disturbance, or feature/class of interest. It can be a single value, an array
of values, or a raster object. It must not necessarily be an Euclidean distance,
but preferably it should be a distance measured in meters, to ease interpretation
(e.g. geodesic distance).
radius
[numeric(1)]
Radius of the zone of influence (ZOI),
the distance at which the ZOI vanishes or goes below a given minimum limit value
zoi_limit. See details.
type
[character(1)="Gauss"]{"Gauss", "exp_decay", "bartlett", "linear", "tent", "threshold", "step"}
Type or shape of the decay distance.
If "Gauss" or "half_norm", the ZOI follows a half-normal shape:
intercept * exp(-lambda * (euclidean_distance^2)). intercept and lambda are
parameters to be defined – see details.
If "exp_decay", the ZOI follows an exponential decay shape:
intercept * exp(-lambda * euclidean_distance). intercept and lambda are
parameters to be defined – see details.
If "bartlett", "linear_decay", or "tent_decay", the ZOI follows a
linear decay shape within the ZOI radius (parameter radius).
If "threshold" or "step", a constant influence is consider within the
zone of influence radius (parameter radius). All pixels closer than
radius to infrastructure are considered as "under the influence" of
the nearest feature, with a constant influence value defined by the
intercept parameter, and all values/pixels beyond radius are
assumed to have zero influence.
zoi_limit
[numeric(1)=0.05]
For non-vanishing functions
(e.g. exp_decay, gaussian_decay), this value is used to set the relationship
between the ZOI radius and the decay functions:
radius is defined as the minimum distance x at which the ZOI assumes values
below zoi_limit. The default is 0.05. This parameter is used only
if radius is not NULL.
origin
[numeric(1)=0]
In which position (in 1 dimension) is located
the infrastructure or source of disturbance? Default is zero. For raster objects,
this parameter should be ignored.
oneside
[logical(1)=TRUE]
If FALSE, negative distance values
are considered symmetrically and their transformation is always positive.
This parameter is only meaningful if x is a vector of values, not a
raster object.
intercept
[numeric(1)=1]
Maximum value of the ZOI function at
when the distance from disturbance sources is zero (x = 0).
For the threshold_decay and step_decay functions, intercept is
the constant value of the Zone of Influence within the ZOI radius.
For the other ZOI functions, intercept
is the value of the functions at the origin (where the sources of disturbance
are located, i.e. x = 0).
Default is intercept = 1.
lambda
[numeric(2)=NULL]
For the gaussian_decay and exp_decay
functions, lambda is the decay parameter of the Gaussian or exponential decay
function. Notice that the interpretation of lambda is different depending on the
the function – see details for definitions.
For the Gaussian decay function, the value for lambda is only considered if both
radius = NULL and sigma = NULL. For the exponential decay function,
the value for lambda is only considered if both radius = NULL and half_life = NULL.
sigma
[numeric(1)=NULL]
Standard deviation of the Gaussian decay
function. It is related to the Gaussian decay rate \lambda as
lambda = 1/(2*sigma^2). Only considered to compute the ZOI
for the gaussian_decay function when the ZOI radius parameter is null
(radius = NULL).
half_life
[numeric(1)=NULL]
Half life of the exponential decay
function, in meters (or map units, for rasters). By definition, the half life is
the distance where the exponential decay function reaches 0.5 of its
maximum value. For the exp_decay function,
if the ZOI radius parameter is null (radius = NULL), the value of the
exponential half life (half_life = log(2)/lambda) can be used to parameterize the
exponential decay function.
zoi_hl_ratio
[numeric(1)=NULL]
For the exp_decay function,
if both the ZOI radius radius and zoi_hl_ratio are given and
half_life is NULL, this value is used
to set the ZOI radius (and zoi_limit is ignored).
zoi_hl_ratio is the ratio between the
ZOI radius value and the half life of the exponential function.
For instance, if radius = 1200 and zoi_hl_ratio = 6, this means
half_life is 200. As a consequence, the exponential decay ZOI function
decreases to 0.5 at distance 200, and the ZOI radius = 1200
is defined as the distance
at which the ZOI decreases to 0.5**6 = 0.015625.
Details
A generic function dist_decay() can be used to compute
ZOI values according to functions with different shapes (parameter type)
and radii (parameter radius). Alternatively, there are specific functions
implemented for each ZOI shape.
For the threshold function (threshold_decay()) and the linear decay
function (linear_decay()), the ZOI radius (parameter radius) is the
distance x where the ZOI function value decreases to zero.
For the linear decay, this is done by setting
the slope of the linear function as -intercept/radius, where intercept
is the intercept of the linear function (here, the maximum value at x = 0).
For non-vanishing functions that approach zero asymptotically
(exp_decay(), gaussian_decay()), a certain limit value must be given to define
the ZOI radius – so that the ZOI radius is defined as the distance x where the
ZOI function goes below this limit value. For these functions,
different parameters are available
for setting the relationship between the ZOI function value and the ZOI radius.
Some functions have multiple possible names, for the sake of flexibility:
-
linear_decay(), bartlett_decay(), and
tent_decay() are the same function;
-
threshold_decay() and step_decay() are the same function;
-
gaussian_decay() and half_norm_decay() are the same function.
Alternatively, dist_decay() can call all of them, given a
ZOI shape is specified through the parameter type.
Other functions might be implemented in the future.
Value
The ZOI values for a given array of distance values if x is numeric,
or a raster object delimiting the ZOI if x corresponds to the distance from
infrastructure or disturbance sources in 2 dimensions space.
Definitions
Here are some formal definitions for the ZOI functions \phi(d_i, r),
where d_i is the distance to the feature i of an infrastructure or
source of disturbance and r is the radius of the zone of influence:
-
threshold_decay(): the threshold or step decay function \phi_{threshold} is
positive and constant within the ZOI radius r, and null for x \ge r:
\phi_{threshold}(d_i, r_k) = c \text{ if } d_i < r, 0 \text{ otherwise}
where c is a constant value (by default c = 1).
-
linear_decay(): the linear (or tent/Bartlett) decay function \phi_{linear}
decreases
linearly from a maximum value c (the intercept, by default c = 1) to
zero when x \ge r:
\phi_{linear}(d_i, r) = c - c/r \text{ if } x < r, \text{ 0 otherwise}
-
exp_decay(): the exponential decay function \phi_{exp} decreases
exponentially from a maximum value c (by default c = 1) with a rate
\lambda, which is defined by r and a ZOI limit value
\phi_{lim}, a small ZOI value below which the influence is considered negligible:
\phi_{exp}(d_i, r, \phi_{lim}) = c exp(-\lambda d_i)
with
\lambda = ln(1/\phi_{lim}) / r
In this context, the ZOI radius r is the distance beyond which
\phi_{exp} < \phi_{lim}.
-
gaussian_decay(): the Gaussian decay function \phi_{Gauss}
follows a Gaussian (half-normal) decay with maximum c (by default c = 1)
and a decay rate \lambda
defined by r and a ZOI limit value
\phi_{lim}, a small ZOI value below which the influence is considered negligible:
\phi_{Gauss}(d_i, r, \phi_{lim}) = c exp(-\lambda d_i^2)
with
\lambda = ln(1/\phi_{lim}) / (r^2)
In this context, the ZOI radius r is the distance beyond which
\phi_{exp} < \phi_{lim}. Note that \lambda is defined differently
for the gaussian_decay and the exp_decay functions.
Parameterization
Some of the shapes of the ZOI (parameter type in dist_decay()) might be
parameterized in multiple ways. Here is a brief description of each possibility:
For the "Gauss" or "half_norm" shapes, the ZOI follows a half-normal shape:
intercept * exp(-lambda * (euclidean_distance^2)). intercept and lambda are
parameters to be defined. There are three ways of specifying lambda:
If the radius = NULL (default), lambda is a parameter by itself to
be specified by the user. In all other cases (below)
the value of this parameter is ignored, even if provided.
If the parameter radius is provided, the rate of decay is given by
lambda = log(1/zoi_limit) / (radius**2). In other words, lambda is defined
so that the function decreases to zoi_limit when x = radius.
If the radius = NULL and sigma is provided, lambda is defined as
lambda = 1/(2*sigma**2).
For the "exp_decay" shape, the ZOI follows an exponential decay shape:
intercept * exp(-lambda * euclidean_distance). intercept and lambda are
parameters to be defined. There are four ways of specifying lambda:
If the radius = NULL (default), lambda is a parameter by itself to
be specified by the user. In all other cases (below)
the value of this parameter is ignored, even if provided.
If the parameter radius is provided, the rate of decay is given by
lambda = log(1/zoi_limit) / radius. In other words, lambda is defined
so that the function decreases to zoi_limit when x = radius.
If the radius = NULL and half_life is given, lambda is defined
based on the half life of the exponential function – the distance at which
the function decreases to 1/2. If zoi_hl_ratio = NULL, lambda is defined
as lambda = log(2)/half_life.
The last possibility is to specify zoi_hl_ratio, the ratio between
the ZOI radius and the half life of the exponential function. For instance,
if zoi_hl_ratio = 4, this means the ZOI radius is defined as 4*half_life.
If zoi_hl_ratio is provided, the exponential half_life is defined based on
this parameter and lambda is defined accordingly, based on the relationship
above. In this case, radius is ignored, even if specified.
For the "bartlett", "linear_decay", or "tent_decay" shapes, the ZOI follows a
linear decay shape (y = a*x + b) within the ZOI radius (parameter radius).
The intercept of the linear function (b) is given by the parameter intercept
and the slope (a) is given by -intercept/radius.
For the "threshold" or "step" shapes, a constant influence is consider
within the
zone of influence radius (parameter radius). All pixels closer than
radius to infrastructure are considered as "under the influence" of
the nearest feature, with a constant influence value defined by the
intercept parameter, and all values/pixels beyond radius are assumed to have
zero influence.
Examples
# generic dist_decay function
oneimpact::dist_decay(500, radius = 1000, type = "exp_decay")
oneimpact::dist_decay(500, radius = 1000, type = "gaussian_decay")
oneimpact::dist_decay(500, radius = 1000, type = "linear_decay")
oneimpact::dist_decay(500, radius = 1000, type = "step_decay")
# test the zone of influence functions
# here we use ggplot() to illustrate the functions, to make the figures more
# widely reproducible
# to ease the plots, use the function plot_zoi1d()
library(ggplot2)
# exponential decay
exp_decay(10, radius = 30)
f1 <- ggplot(data.frame(x = c(0, 30)), aes(x = x)) +
stat_function(fun = exp_decay, args = list(radius = 20)) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f1
# exponential decay - two sides
f1_2 <- ggplot(data.frame(x = c(-30, 30)), aes(x = x)) +
stat_function(fun = exp_decay,
args = list(radius = 20, oneside = FALSE)) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f1_2
# threshold
threshold_decay(5, radius = 10)
threshold_decay(10, radius = 10)
f2 <- ggplot(data.frame(x = c(0, 30)), aes(x = x)) +
stat_function(fun = threshold_decay,
args = list(radius = 20), linetype = 2) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f2
# threshold - two sides
f2_2 <- ggplot(data.frame(x = c(-30, 50)), aes(x = x)) +
stat_function(fun = threshold_decay,
args = list(radius = 20, oneside = FALSE), linetype = 2) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f2_2
# linear, tent, or bartlett decay
bartlett_decay(5, radius = 10)
bartlett_decay(8, radius = 10)
f3 <- ggplot(data.frame(x = c(0, 30)), aes(x = x)) +
stat_function(fun = bartlett_decay, args = list(radius = 20), linetype = 3) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f3
# linear, two sides
f3_3 <- ggplot(data.frame(x = c(-30, 40)), aes(x = x)) +
stat_function(fun = bartlett_decay,
args = list(radius = 20, origin = 10, oneside = FALSE), linetype = 3) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f3_3
# guassian or half normal
gaussian_decay(5, sigma = 6)
f4 <- ggplot(data.frame(x = c(0, 30)), aes(x = x)) +
stat_function(fun = gaussian_decay,
args = list(radius = 20, zoi_limit = 0.05), linetype = 4) +
labs(x = "Distance", y = "Zone of Influence") +
geom_vline(xintercept = 20, linetype = 2, color = "darkgrey") +
geom_hline(yintercept = 0.05, linetype = 2, color = "darkgrey") +
theme_bw()
f4
# half normal - two sides
gaussian_decay(5, sigma = 6)
f4_2 <- ggplot(data.frame(x = c(-30, 30)), aes(x = x)) +
stat_function(fun = gaussian_decay,
args = list(radius = 20, zoi_limit = 0.05), linetype = 4) +
labs(x = "Distance", y = "Zone of Influence") +
geom_vline(xintercept = c(-20, 20), linetype = 2, color = "darkgrey") +
geom_hline(yintercept = 0.05, linetype = 2, color = "darkgrey") +
theme_bw()
f4_2
# plot several ZoI with the same radius
f1 +
stat_function(fun = threshold_decay, args = list(radius = 20), linetype = 2) +
stat_function(fun = bartlett_decay, args = list(radius = 20), linetype = 3) +
stat_function(fun = gaussian_decay, args = list(radius = 20, zoi_limit = 0.05), linetype = 4) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
#---
# applying dist_decay functions for rasters
library(terra)
# calculate Euclidean distance
f <- system.file("raster/sample_area_cabins.tif", package = "oneimpact")
cabins <- terra::rast(f)
cabins_dist <- calc_zoi_nearest(cabins, type = "euclidean")
# transform Euclidean in distance decay
# exponential decay
plot(oneimpact::dist_decay(cabins_dist, radius = 1000, type = "exp_decay"))
# linear decay
plot(oneimpact::dist_decay(cabins_dist, radius = 1000, type = "tent_decay"))
NINAnor/oneimpact documentation built on June 14, 2025, 12:27 a.m.
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| zoi_functions | R Documentation |
Zone of Influence (ZOI) functions
Description
Computes the decay functions that represent the Zone of
Influence (ZOI). The functions' radius (parameter radius)
controls how far the zone of influence of an infrastructure or disturbance reaches,
and the functions' shape (parameter type) represent represent how the ZOI
decays in space. Given a function shape (type) is chosen, the rate
of decay of the different ZOI functions is parameterized based on
the ZOI radius – e.g the slope of linear_decay() is defined
so that the function decreases to zero at the ZOI radius.
These functions can be used to transform arrays of (Euclidean)
distance values (in one dimension) or rasters of (Euclidean) distance
(in two dimensions) into ZOI values. The distances might represent
the distance to human infrastructure, sources of disturbance, or
more broadly any type of land use class or spatial variable.
Usage
dist_decay(
x,
radius = NULL,
type = c("exp_decay", "gaussian_decay", "linear_decay", "threshold_decay")[1],
zoi_limit = 0.05,
origin = 0,
oneside = TRUE,
...
)
threshold_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
## S3 method for class 'numeric'
threshold_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
## S3 method for class 'SpatRaster'
threshold_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
step_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
bartlett_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
## S3 method for class 'numeric'
bartlett_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
## S3 method for class 'SpatRaster'
bartlett_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
tent_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
linear_decay(x, radius, intercept = 1, origin = 0, oneside = TRUE)
gaussian_decay(
x,
radius = NULL,
zoi_limit = 0.05,
intercept = 1,
lambda = NULL,
sigma = NULL,
origin = 0,
...
)
half_norm_decay(
x,
radius = NULL,
zoi_limit = 0.05,
intercept = 1,
lambda = NULL,
sigma = NULL,
origin = 0,
...
)
exp_decay(
x,
radius = NULL,
zoi_limit = 0.05,
intercept = 1,
lambda = NULL,
origin = 0,
oneside = TRUE,
half_life = NULL,
zoi_hl_ratio = NULL
)
Arguments
x |
|
radius |
|
type |
|
zoi_limit |
|
origin |
|
oneside |
|
intercept |
|
lambda |
|
sigma |
|
half_life |
|
zoi_hl_ratio |
|
Details
A generic function dist_decay() can be used to compute
ZOI values according to functions with different shapes (parameter type)
and radii (parameter radius). Alternatively, there are specific functions
implemented for each ZOI shape.
For the threshold function (threshold_decay()) and the linear decay
function (linear_decay()), the ZOI radius (parameter radius) is the
distance x where the ZOI function value decreases to zero.
For the linear decay, this is done by setting
the slope of the linear function as -intercept/radius, where intercept
is the intercept of the linear function (here, the maximum value at x = 0).
For non-vanishing functions that approach zero asymptotically
(exp_decay(), gaussian_decay()), a certain limit value must be given to define
the ZOI radius – so that the ZOI radius is defined as the distance x where the
ZOI function goes below this limit value. For these functions,
different parameters are available
for setting the relationship between the ZOI function value and the ZOI radius.
Some functions have multiple possible names, for the sake of flexibility:
-
linear_decay(),bartlett_decay(), andtent_decay()are the same function; -
threshold_decay()andstep_decay()are the same function; -
gaussian_decay()andhalf_norm_decay()are the same function.
Alternatively, dist_decay() can call all of them, given a
ZOI shape is specified through the parameter type.
Other functions might be implemented in the future.
Value
The ZOI values for a given array of distance values if x is numeric,
or a raster object delimiting the ZOI if x corresponds to the distance from
infrastructure or disturbance sources in 2 dimensions space.
Definitions
Here are some formal definitions for the ZOI functions \phi(d_i, r),
where d_i is the distance to the feature i of an infrastructure or
source of disturbance and r is the radius of the zone of influence:
-
threshold_decay(): the threshold or step decay function\phi_{threshold}is positive and constant within the ZOI radiusr, and null forx \ge r:\phi_{threshold}(d_i, r_k) = c \text{ if } d_i < r, 0 \text{ otherwise}where
cis a constant value (by defaultc = 1). -
linear_decay(): the linear (or tent/Bartlett) decay function\phi_{linear}decreases linearly from a maximum valuec(the intercept, by defaultc = 1) to zero whenx \ge r:\phi_{linear}(d_i, r) = c - c/r \text{ if } x < r, \text{ 0 otherwise} -
exp_decay(): the exponential decay function\phi_{exp}decreases exponentially from a maximum valuec(by defaultc = 1) with a rate\lambda, which is defined byrand a ZOI limit value\phi_{lim}, a small ZOI value below which the influence is considered negligible:\phi_{exp}(d_i, r, \phi_{lim}) = c exp(-\lambda d_i)with
\lambda = ln(1/\phi_{lim}) / rIn this context, the ZOI radius
ris the distance beyond which\phi_{exp} < \phi_{lim}. -
gaussian_decay(): the Gaussian decay function\phi_{Gauss}follows a Gaussian (half-normal) decay with maximumc(by defaultc = 1) and a decay rate\lambdadefined byrand a ZOI limit value\phi_{lim}, a small ZOI value below which the influence is considered negligible:\phi_{Gauss}(d_i, r, \phi_{lim}) = c exp(-\lambda d_i^2)with
\lambda = ln(1/\phi_{lim}) / (r^2)In this context, the ZOI radius
ris the distance beyond which\phi_{exp} < \phi_{lim}. Note that\lambdais defined differently for thegaussian_decayand theexp_decayfunctions.
Parameterization
Some of the shapes of the ZOI (parameter type in dist_decay()) might be
parameterized in multiple ways. Here is a brief description of each possibility:
For the
"Gauss"or"half_norm"shapes, the ZOI follows a half-normal shape:
intercept * exp(-lambda * (euclidean_distance^2)).interceptandlambdaare parameters to be defined. There are three ways of specifyinglambda:If the
radius = NULL(default),lambdais a parameter by itself to be specified by the user. In all other cases (below) the value of this parameter is ignored, even if provided.If the parameter
radiusis provided, the rate of decay is given bylambda = log(1/zoi_limit) / (radius**2). In other words,lambdais defined so that the function decreases tozoi_limitwhenx = radius.If the
radius = NULLandsigmais provided,lambdais defined aslambda = 1/(2*sigma**2).
For the
"exp_decay"shape, the ZOI follows an exponential decay shape:
intercept * exp(-lambda * euclidean_distance).interceptandlambdaare parameters to be defined. There are four ways of specifyinglambda:If the
radius = NULL(default),lambdais a parameter by itself to be specified by the user. In all other cases (below) the value of this parameter is ignored, even if provided.If the parameter
radiusis provided, the rate of decay is given bylambda = log(1/zoi_limit) / radius. In other words,lambdais defined so that the function decreases tozoi_limitwhenx = radius.If the
radius = NULLandhalf_lifeis given,lambdais defined based on the half life of the exponential function – the distance at which the function decreases to 1/2. Ifzoi_hl_ratio = NULL,lambdais defined aslambda = log(2)/half_life.The last possibility is to specify
zoi_hl_ratio, the ratio between the ZOI radius and the half life of the exponential function. For instance, ifzoi_hl_ratio = 4, this means the ZOI radius is defined as4*half_life. Ifzoi_hl_ratiois provided, the exponentialhalf_lifeis defined based on this parameter andlambdais defined accordingly, based on the relationship above. In this case,radiusis ignored, even if specified.
For the
"bartlett","linear_decay", or"tent_decay"shapes, the ZOI follows a linear decay shape (y = a*x + b) within the ZOI radius (parameterradius). The intercept of the linear function (b) is given by the parameterinterceptand the slope (a) is given by-intercept/radius.For the
"threshold"or"step"shapes, a constant influence is consider within the zone of influence radius (parameterradius). All pixels closer thanradiusto infrastructure are considered as "under the influence" of the nearest feature, with a constant influence value defined by theinterceptparameter, and all values/pixels beyondradiusare assumed to have zero influence.
Examples
# generic dist_decay function
oneimpact::dist_decay(500, radius = 1000, type = "exp_decay")
oneimpact::dist_decay(500, radius = 1000, type = "gaussian_decay")
oneimpact::dist_decay(500, radius = 1000, type = "linear_decay")
oneimpact::dist_decay(500, radius = 1000, type = "step_decay")
# test the zone of influence functions
# here we use ggplot() to illustrate the functions, to make the figures more
# widely reproducible
# to ease the plots, use the function plot_zoi1d()
library(ggplot2)
# exponential decay
exp_decay(10, radius = 30)
f1 <- ggplot(data.frame(x = c(0, 30)), aes(x = x)) +
stat_function(fun = exp_decay, args = list(radius = 20)) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f1
# exponential decay - two sides
f1_2 <- ggplot(data.frame(x = c(-30, 30)), aes(x = x)) +
stat_function(fun = exp_decay,
args = list(radius = 20, oneside = FALSE)) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f1_2
# threshold
threshold_decay(5, radius = 10)
threshold_decay(10, radius = 10)
f2 <- ggplot(data.frame(x = c(0, 30)), aes(x = x)) +
stat_function(fun = threshold_decay,
args = list(radius = 20), linetype = 2) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f2
# threshold - two sides
f2_2 <- ggplot(data.frame(x = c(-30, 50)), aes(x = x)) +
stat_function(fun = threshold_decay,
args = list(radius = 20, oneside = FALSE), linetype = 2) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f2_2
# linear, tent, or bartlett decay
bartlett_decay(5, radius = 10)
bartlett_decay(8, radius = 10)
f3 <- ggplot(data.frame(x = c(0, 30)), aes(x = x)) +
stat_function(fun = bartlett_decay, args = list(radius = 20), linetype = 3) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f3
# linear, two sides
f3_3 <- ggplot(data.frame(x = c(-30, 40)), aes(x = x)) +
stat_function(fun = bartlett_decay,
args = list(radius = 20, origin = 10, oneside = FALSE), linetype = 3) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
f3_3
# guassian or half normal
gaussian_decay(5, sigma = 6)
f4 <- ggplot(data.frame(x = c(0, 30)), aes(x = x)) +
stat_function(fun = gaussian_decay,
args = list(radius = 20, zoi_limit = 0.05), linetype = 4) +
labs(x = "Distance", y = "Zone of Influence") +
geom_vline(xintercept = 20, linetype = 2, color = "darkgrey") +
geom_hline(yintercept = 0.05, linetype = 2, color = "darkgrey") +
theme_bw()
f4
# half normal - two sides
gaussian_decay(5, sigma = 6)
f4_2 <- ggplot(data.frame(x = c(-30, 30)), aes(x = x)) +
stat_function(fun = gaussian_decay,
args = list(radius = 20, zoi_limit = 0.05), linetype = 4) +
labs(x = "Distance", y = "Zone of Influence") +
geom_vline(xintercept = c(-20, 20), linetype = 2, color = "darkgrey") +
geom_hline(yintercept = 0.05, linetype = 2, color = "darkgrey") +
theme_bw()
f4_2
# plot several ZoI with the same radius
f1 +
stat_function(fun = threshold_decay, args = list(radius = 20), linetype = 2) +
stat_function(fun = bartlett_decay, args = list(radius = 20), linetype = 3) +
stat_function(fun = gaussian_decay, args = list(radius = 20, zoi_limit = 0.05), linetype = 4) +
labs(x = "Distance", y = "Zone of Influence") +
theme_bw()
#---
# applying dist_decay functions for rasters
library(terra)
# calculate Euclidean distance
f <- system.file("raster/sample_area_cabins.tif", package = "oneimpact")
cabins <- terra::rast(f)
cabins_dist <- calc_zoi_nearest(cabins, type = "euclidean")
# transform Euclidean in distance decay
# exponential decay
plot(oneimpact::dist_decay(cabins_dist, radius = 1000, type = "exp_decay"))
# linear decay
plot(oneimpact::dist_decay(cabins_dist, radius = 1000, type = "tent_decay"))
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