How to check if a polygon is regular or convex

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How to check if a polygon is regular or convex

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#1 by (4 votes)

4

Is there a function in the R that checks whether a polygon is regular or not and some that checks whether it is convex or not?

If either answer is no, any ideas? As I thought:

#Por exemplo um quadrilátero, a primeira coluna é x e a segunda coluna é y.
quadrilatero = matrix(c(0,2,-7,1,4,3, 4,5), ncol = 2)

#o input (poligono) tem duas colunas obrigatoriamente 
verifica_regular = function(poligono){
  distancias = apply(poligono, 1, dist)
  if(distancias == distancias[1]) return(T)
  else return(F)
}
verifica_regular(quadrilatero)

But the dist function within apply computes the difference between one value and the next column value.

To check the convexity I have no idea.

r geometria

asked by anonymous 27.04.2016 / 17:53

1 answer

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score 4 · Accepted Answer

To verify that the polygon is regular, you need the distance from all points, including the "last" point of your polygon to the "first" - in the code examples below, if you do not "close" the polygon, you will get an incorrect result in the first case.

And in this case you do not need the apply function. dist already gives you the distance between all the points, so what you need is to get the diagonal from the bottom (or top) of the matrix that returns you.

And as @Joao noted, the condition of equal sides is necessary, but not sufficient for the polygon to be regular. All your angles need to be identical too. One way to verify this, since the sides are the same, is to verify that the center of the polygon is equidistant from all points. The updated code is below.

verifica_lados_iguais <- function(poligono) {
    no_vertices <- nrow(poligono)
    poligono_fechado <- rbind(poligono, poligono[1])
    distancias <- diag(as.matrix(dist(poligono_fechado))[1:no_vertices, 2:(no_vertices + 1)])
    lados_iguais <- all(distancias == distancias[1])
}

verifica_equidistancia_centro <- function(poligono) {
    c <- apply(poligono, 2, sum) / nrow(poligono)
    dist_centro <- apply(poligono, 1, function(p) sqrt((c[1] - p[1])^2 + (c[2] - p[2])^2))
    equidistanteCentro <- all((abs(dist_centro - dist_centro[1]) < 0.00001))
}

verifica_regular <- function(poligono) {
    regular <- verifica_lados_iguais(poligono) &&
        verifica_equidistancia_centro(poligono)
}

print(quadrilatero <- matrix(c(0, 0, 0, 5, 5, 5, 2, 1), ncol = 2, byrow = TRUE))
print(verifica_regular(quadrilatero))
print(quadrado <- matrix(c(0, 0, 0, 5, 5, 5, 5, 0), ncol = 2, byrow = TRUE))
print(verifica_regular(quadrado))
print(losango <- matrix(c(0, 0, 2, 1, 4, 0, 2, -1), ncol = 2, byrow = TRUE))
print(verifica_regular(losango))