Evaluate the membership degree of a point in a pgeometry object

spa_eval() evaluates the membership degree of a given point in a spatial plateau object of any type. It returns a value in [0, 1] that indicates to which extent the point belongs to the pgeometry object.

Usage

spa_eval(pgo, point)

Arguments

pgo

A pgeometry object of any type.

point

An sfg object of the type POINT.

Value

A numeric value between 0 and 1 that indicates the membership degree of a point (i.e., sfg object) in a spatial plateau object (i.e., pgeometry object).

Details

The spa_eval() returns the membership degree of a simple point object (i.e., sfg object) in a given spatial plateau object (i.e., pgeometry object). This evaluation depends on the following basic cases:

• if the simple point object belongs to the interior or boundary of one component of the spatial plateau object, it returns the membership degree of that component.

• if the simple point object intersects more components (e.g., boundaries of region components, or different line components), it returns the maximum membership degree of all intersected components.

• if the simple point object is disjoint to the support of the spatial plateau object, it returns 0.

References

Formal definitions of this function are described in:

• Carniel, A. C.; Galdino, F.; Schneider, M. Evaluating Region Inference Methods by Using Fuzzy Spatial Inference Models. In Proceedings of the 2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2022), pp. 1-8, 2022.

• Carniel, A. C.; Schneider, M. Spatial Plateau Algebra: An Executable Type System for Fuzzy Spatial Data Types. In Proceedings of the 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2018), pp. 1-8, 2018.

Examples

library(sf)

# Point components
pcp1 <- create_component("POINT(0 0)", 0.3)
pcp2 <- create_component("MULTIPOINT((2 2), (2 4), (2 0))", 0.5)
pcp3 <- create_component("MULTIPOINT((1 1), (3 1), (1 3), (3 3))", 0.9)
pcp4 <- create_component("MULTIPOINT((1 2), (2 1), (3 2))", 1)
pcp5 <- create_component("MULTIPOINT((0 0.5), (2 3))", 0.7)
pcp6 <- create_component("MULTIPOINT((0 1), (3 3.5))", 0.85)
pcp7 <- create_component("MULTIPOINT((1 0), (4 2))", 0.4)
# Line components
lcp1 <- create_component("LINESTRING(0 0, 1 1.5)", 0.2)
lcp2 <- create_component("LINESTRING(1 3, 1 2, 2 0.5)", 0.5)
lcp3 <- create_component("LINESTRING(2 1.2, 3 1.6, 4 4)", 0.7)
lcp4 <- create_component("LINESTRING(1 1.5, 2 1.2)", 1.0)
lcp5 <- create_component("LINESTRING(-1 1, 2 2)", 0.9)
# Polygon components
rcp1 <- create_component("POLYGON((0 0, 1 4, 2 2, 0 0))", 0.4)
rcp2 <- create_component("POLYGON((2 0.5, 4 1, 4 0, 2 0.5))", 0.8)

# Creating spatial plateau objects
ppoint <- create_pgeometry(list(pcp1, pcp2, pcp3, pcp4, pcp5), "PLATEAUPOINT")
pline <- create_pgeometry(list(lcp1, lcp2, lcp3), "PLATEAULINE")
pregion <- create_pgeometry(list(rcp1, rcp2), "PLATEAUREGION")
pcomp <- create_pgeometry(list(pcp6, pcp7, lcp4, lcp5), "PLATEAUCOMPOSITION")
pcol <- create_pgeometry(list(ppoint, pline, pregion, pcomp), "PLATEAUCOLLECTION")

point <- st_point(c(0, 0))

spa_eval(ppoint, point)
#> [1] 0.3
spa_eval(pline, point)
#> [1] 0.2
spa_eval(pregion, point)
#> [1] 0.4
spa_eval(pcomp, point)
#> [1] 0
spa_eval(pcol, point)
#> [1] 0.4