tests/testthat/test-triangle.R

In PlaneGeometry: Plane Geometry

context("Triangle")

test_that("Triangle$contains", {
  t <- Triangle$new(c(0,0), c(1,5), c(3,3))
  set.seed(666)
  pts <- t$randomPoints(3, "in")
  expect_true(all(apply(pts, 1L, t$contains)))
})

test_that("Malfatti circles are tangent", {
  t <- Triangle$new(c(0,0), c(1,5), c(3,3))
  Mcircles <- t$MalfattiCircles(tangencyPoints = TRUE)
  C1 <- Mcircles[[1L]]; C2 <- Mcircles[[2L]]; C3 <- Mcircles[[3L]]
  I1 <- intersectionCircleCircle(C1, C2)
  expect_true(is.numeric(I1) && length(I1) == 2L)
  I2 <- intersectionCircleCircle(C1, C3)
  expect_true(is.numeric(I2) && length(I2) == 2L)
  I3 <- intersectionCircleCircle(C2, C3)
  expect_true(is.numeric(I3) && length(I3) == 2L)
  tpoints <- attr(Mcircles, "tangencyPoints")
  expect_equal(tpoints$TA, I3)
  expect_equal(tpoints$TB, I2)
  expect_equal(tpoints$TC, I1)
})

test_that("Gergonne point is the symmedian point of the Gergonne triangle", {
  t <- Triangle$new(c(0,0), c(1,5), c(4,3))
  gpoint <- t$GergonnePoint()
  intouchTriangle <- t$GergonneTriangle()
  sympoint <- intouchTriangle$symmedianPoint()
  expect_equal(gpoint, sympoint)
})

test_that("Symmedian point of a right triangle", {
  t <- Triangle$new(c(0,0), c(1,5), c(3,3))
  sympoint <- t$symmedianPoint()
  orthic <- t$orthicTriangle()
  H <- orthic$C
  expect_equal(sympoint, (t$C+H)/2)
})

test_that("Gergonne triangle of tangential triangle is reference triangle", {
  tref <- Triangle$new(c(0,0), c(1,5), c(4,3))
  ttref <- tref$tangentialTriangle()
  gergonnettref <- ttref$GergonneTriangle()
  expect_equal(
    cbind(tref$A, tref$B, tref$C),
    cbind(gergonnettref$A, gergonnettref$B, gergonnettref$C)
  )
})

test_that("Orthogonality Parry circle", {
  t <- Triangle$new(c(0,0), c(1,5), c(4,3))
  parry <- t$ParryCircle()
  brocard <- t$BrocardCircle()
  circum <- t$circumcircle()
  expect_true(parry$isOrthogonal(brocard))
  expect_true(parry$isOrthogonal(circum))
})

test_that("Brocard points - concurrency", {
  t <- Triangle$new(c(0,0), c(1,5), c(5,2))
  bpoints <- t$BrocardPoints()
  bline1 <- Line$new(t$A, bpoints$Z1)
  bline2 <- Line$new(t$A, bpoints$Z2)
  median <- Line$new(t$B, t$centroid())
  symmedian <- Line$new(t$C, t$symmedianPoint())
  P <- intersectionLineLine(bline1, median)
  expect_true(symmedian$includes(P))
  # Q <- intersectionLineLine(bline2, median)
  # expect_true(symmedian$includes(Q)) ???
})

test_that("Brocard points - distance from circumcenter", {
  t <- Triangle$new(c(0,0), c(1,5), c(5,2))
  bpoints <- t$BrocardPoints()
  O <- t$circumcenter()
  R <- t$circumradius()
  edges <- as.list(t$edges())
  d <- R * with(edges, sqrt((a^4+b^4+c^4)/(a^2*b^2+a^2*c^2+b^2*c^2)-1))
  expect_equal(d, .distance(bpoints$Z1, O))
  expect_equal(d, .distance(bpoints$Z2, O))
})

test_that("Pedal triangles", {
  t <- Triangle$new(c(1,1), c(0,3), c(2,-3))
  #
  I <- t$incircle()$center
  ptI <- t$pedalTriangle(I)
  gerg <- t$GergonneTriangle()
  expect_equal(cbind(gerg$A,gerg$B,gerg$C), cbind(ptI$A,ptI$B,ptI$C))
  #
  H <- t$orthocenter()
  ptH <- t$pedalTriangle(H)
  orthic <- t$orthicTriangle()
  expect_equal(cbind(orthic$A,orthic$B,orthic$C), cbind(ptH$A,ptH$B,ptH$C))
  #
  O <- t$circumcenter()
  ptO <- t$pedalTriangle(O)
  medial <- t$medialTriangle()
  expect_equal(cbind(medial$A,medial$B,medial$C), cbind(ptO$A,ptO$B,ptO$C))
  #
  B <- t$BevanPoint()
  ptB <- t$pedalTriangle(B)
  nagel <- t$NagelTriangle()
  expect_equal(cbind(nagel$A,nagel$B,nagel$C), cbind(ptB$A,ptB$B,ptB$C))
})

test_that("Cevian triangles", {
  t <- Triangle$new(c(1,1), c(0,3), c(2,-3))
  #
  I <- t$incircle()$center
  ctI <- t$CevianTriangle(I)
  incentral <- t$incentralTriangle()
  expect_equal(cbind(incentral$A,incentral$B,incentral$C),
               cbind(ctI$A,ctI$B,ctI$C))
  #
  G <- t$centroid()
  ctG <- t$CevianTriangle(G)
  medial <- t$medialTriangle()
  expect_equal(cbind(medial$A,medial$B,medial$C), cbind(ctG$A,ctG$B,ctG$C))
  #
  H <- t$orthocenter()
  ctH <- t$CevianTriangle(H)
  orthic <- t$orthicTriangle()
  expect_equal(cbind(orthic$A,orthic$B,orthic$C), cbind(ctH$A,ctH$B,ctH$C))
  #
  K <- t$symmedianPoint()
  ctK <- t$CevianTriangle(K)
  symm <- t$symmedialTriangle()
  expect_equal(cbind(symm$A,symm$B,symm$C), cbind(ctK$A,ctK$B,ctK$C))
  #
  Ge <- t$GergonnePoint()
  ctGe <- t$CevianTriangle(Ge)
  gerg <- t$GergonneTriangle()
  expect_equal(cbind(gerg$A,gerg$B,gerg$C), cbind(ctGe$A,ctGe$B,ctGe$C))
  #
  N <- t$NagelPoint()
  ctN <- t$CevianTriangle(N)
  extouch <- t$NagelTriangle()
  expect_equal(cbind(extouch$A,extouch$B,extouch$C), cbind(ctN$A,ctN$B,ctN$C))
})

test_that("Steiner ellipse/inellipse", {
  t <- Triangle$new(c(0,0), c(2,0.5), c(1.5,2))
  inell <- t$SteinerInellipse()
  ell <- t$medialTriangle()$SteinerEllipse()
  expect_true(ell$isEqual(inell))
})

test_that("Hexyl triangle", {
  t <- Triangle$new(c(0,0), c(1,5), c(3,3))
  ht <- t$hexylTriangle()
  et <- t$excentralTriangle()
  HA <- ht$A; HB <- ht$B; HC <- ht$C
  JA <- et$A; JB <- et$B; JC <- et$C
  HAJC <- Line$new(HA, JC)
  HCJA <- Line$new(HC, JA)
  expect_true(HAJC$isParallel(HCJA))
})