Class: Delaunator::Triangulator

Inherits:
Object
  • Object
show all
Defined in:
lib/delaunator/triangulator.rb

Constant Summary collapse

EPSILON = 
2 ** -52
EDGE_STACK = 
Array.new(512, 0)

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(coords) ⇒ Triangulator

Returns a new instance of Triangulator.



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# File 'lib/delaunator/triangulator.rb', line 9

def initialize(coords)
  @coords = coords
  @n = @coords.length >> 1
  @max_triangles = [2 * @n - 5, 0].max
  @triangles_len = 0
  @_triangles = Array.new(@max_triangles * 3, 0)
  @_halfedges = Array.new(@max_triangles * 3, 0)

  @hash_size = Math.sqrt(@n).ceil
  @hull_prev = Array.new(@n, 0)
  @hull_next = Array.new(@n, 0)
  @hull_tri = Array.new(@n, 0)
  @hull_hash = Array.new(@hash_size, -1)
end

Instance Attribute Details

#coords ⇒ Object (readonly)

Returns the value of attribute coords.



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# File 'lib/delaunator/triangulator.rb', line 3

def coords
  @coords
end

#halfedges ⇒ Object (readonly)

Returns the value of attribute halfedges.



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# File 'lib/delaunator/triangulator.rb', line 3

def halfedges
  @halfedges
end

#hull ⇒ Object (readonly)

Returns the value of attribute hull.



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# File 'lib/delaunator/triangulator.rb', line 3

def hull
  @hull
end

#triangles ⇒ Object (readonly)

Returns the value of attribute triangles.



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# File 'lib/delaunator/triangulator.rb', line 3

def triangles
  @triangles
end

Instance Method Details

#add_triangle(i0, i1, i2, a, b, c) ⇒ Object 



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# File 'lib/delaunator/triangulator.rb', line 321

def add_triangle(i0, i1, i2, a, b, c)
  i = @triangles_len
  @_triangles[i] = i0
  @_triangles[i + 1] = i1
  @_triangles[i + 2] = i2
  link(i, a)
  link(i + 1, b)
  link(i + 2, c)
  @triangles_len += 3
  i
end

#circumcenter(ax, ay, bx, by, cx, cy) ⇒ Object 



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# File 'lib/delaunator/triangulator.rb', line 262

def circumcenter(ax, ay, bx, by, cx, cy)
  dx = bx - ax
  dy = by - ay
  ex = cx - ax
  ey = cy - ay

  bl = dx * dx + dy * dy
  cl = ex * ex + ey * ey
  d = 0.5 / ( dx * ey - dy * ex).to_f

  x = ax + (ey * bl - dy * cl) * d
  y = ay + (dx * cl - ex * bl) * d
  [x, y]
end

#circumradius(ax, ay, bx, by, cx, cy) ⇒ Object 



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# File 'lib/delaunator/triangulator.rb', line 277

def circumradius(ax, ay, bx, by, cx, cy)
  dx = bx - ax
  dy = by - ay
  ex = cx - ax
  ey = cy - ay

  bl = dx * dx + dy * dy
  cl = ex * ex + ey * ey
  d = 0.5 / (dx * ey - dy * ex).to_f

  x = (ey * bl - dy * cl) * d
  y = (dx * cl - ex * bl) * d

  r = x * x + y * y

  return 0 if [bl, cl, d, r].include? 0

  r
end

#dist(ax, ay, bx, by) ⇒ Object 



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# File 'lib/delaunator/triangulator.rb', line 244

def dist(ax, ay, bx, by)
  dx = ax - bx
  dy = ay - by
  dx * dx + dy * dy
end

#hash_key(x, y) ⇒ Object 



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# File 'lib/delaunator/triangulator.rb', line 333

def hash_key(x, y)
  angle = (pseudo_angle(x - @cx, y - @cy) * @hash_size).floor()
  angle % @hash_size
end

#in_circle(ax, ay, bx, by, cx, cy, px, py) ⇒ Object 



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# File 'lib/delaunator/triangulator.rb', line 297

def in_circle(ax, ay, bx, by, cx, cy, px, py)
  dx = ax - px
  dy = ay - py
  ex = bx - px
  ey = by - py
  fx = cx - px
  fy = cy - py

  ap = dx * dx + dy * dy
  bp = ex * ex + ey * ey
  cp = fx * fx + fy * fy

  (
    dx * (ey * cp - bp * fy) -
    dy * (ex * cp - bp * fx) +
    ap * (ex * fy - ey * fx)
  ) < 0
end

#legalize(a) ⇒ Object 



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# File 'lib/delaunator/triangulator.rb', line 343

def legalize(a)
  # if the pair of triangles doesn't satisfy the Delaunay condition
  # (p1 is inside the circumcircle of [p0, pl, pr]), flip them,
  # then do the same check/flip recursively for the new pair of triangles
  #
  #           pl                    pl
  #          /||\                  /  \
  #       al/ || \bl            al/    \a
  #        /  ||  \              /      \
  #       /  a||b  \    flip    /___ar___\
  #     p0\   ||   /p1   =>   p0\---bl---/p1
  #        \  ||  /              \      /
  #       ar\ || /br             b\    /br
  #          \||/                  \  /
  #           pr                    pr
  i = 0
  ar = 0
  loop do
    b = @_halfedges[a]
    a0 = a - a % 3

    ar = a0 + (a + 2) % 3
    # convex hull edge
    if b == -1
      break if i.zero?
      i -= 1
      a = EDGE_STACK[i]
      next
    end

    b0 = b - b % 3
    al = a0 + (a + 1) % 3
    bl = b0 + (b + 2) % 3

    p0 = @_triangles[ar]
    pr = @_triangles[a]
    pl = @_triangles[al]
    p1 = @_triangles[bl]

    illegal = in_circle(@coords[2 * p0], @coords[2 * p0 + 1],
                        @coords[2 * pr], @coords[2 * pr + 1],
                        @coords[2 * pl], @coords[2 * pl + 1],
                        @coords[2 * p1], @coords[2 * p1 + 1])

    if illegal
      @_triangles[a] = p1
      @_triangles[b] = p0
      hbl = @_halfedges[bl]
      # edge swapped on the other side of the hull (rare)
      # fix the halfedge reference
      if hbl == -1
        e = @hull_start
        loop do
          if @hull_tri[e] == bl
            @hull_tri[e] = a
            break
          end
          e = @hull_prev[e]
          break if e != @hull_start
        end
      end
      link(a, hbl)
      link(b, @_halfedges[ar])
      link(ar, bl)

      br = b0 + (b + 1) % 3

      if i < EDGE_STACK.length
        EDGE_STACK[i] = br
        i += 1
      end
    else
      break if i.zero?

      i -= 1
      a = EDGE_STACK[i]
    end
  end
  ar
end

#link(a, b) ⇒ Object 



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# File 'lib/delaunator/triangulator.rb', line 338

def link(a, b)
  @_halfedges[a] = b
  @_halfedges[b] = a if b != -1
end

#orient(rx, ry, qx, qy, px, py) ⇒ Object

a more robust orientation test that’s stable in a given triangle (to fix robustness issues)



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# File 'lib/delaunator/triangulator.rb', line 258

def orient(rx, ry, qx, qy, px, py)
  (orient_if_sure(px, py, rx, ry, qx, qy) || orient_if_sure(rx, ry, qx, qy, px, py) || orient_if_sure(qx, qy, px, py, rx, ry)) < 0
end

#orient_if_sure(px, py, rx, ry, qx, qy) ⇒ Object

return 2d orientation sign if we’re confident in it through J. Shewchuk’s error bound check



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# File 'lib/delaunator/triangulator.rb', line 251

def orient_if_sure(px, py, rx, ry, qx, qy)
  l = (ry - py) * (qx - px)
  r = (rx - px) * (qy - py)
  ((l - r).abs >= (3.3306690738754716e-16 * (l + r).abs)) ? l - r : 0
end

#pseudo_angle(dx, dy) ⇒ Object 



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# File 'lib/delaunator/triangulator.rb', line 316

def pseudo_angle(dx, dy)
  p = dx / (dx.abs + dy.abs).to_f
  (dy > 0 ? 3 - p : 1 + p) / 4.to_f
end

#triangulate ⇒ Object 



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# File 'lib/delaunator/triangulator.rb', line 24

def triangulate
  dists = Array.new(@n, 0.0)
  ids = Array.new(@n, 0)
  min_x = Float::INFINITY
  min_y = Float::INFINITY
  max_x = -Float::INFINITY
  max_y = -Float::INFINITY
  # compute bounds
  (0..@n - 1).each do |i|
    x = @coords[2 * i]
    y = @coords[2 * i + 1]
    min_x = x if x < min_x
    min_y = y if y < min_y
    max_x = x if x > max_x
    max_y = y if y > max_y
  end

  cx = (min_x + max_x).to_f / 2
  cy = (min_y + max_y).to_f / 2
  min_dist = Float::INFINITY
  i0 = 0
  i1 = 0
  i2 = 0

  # pick a seed point close to midpoint i0
  (0..@n - 1).each do |i|
    d = dist(cx, cy, @coords[2 * i], @coords[2 * i + 1])
    if d < min_dist
      i0 = i
      min_dist = d
    end
  end
  i0x = @coords[2 * i0]
  i0y = @coords[2 * i0 + 1]

  min_dist = Float::INFINITY

  (0..@n - 1).each do |i|
    next if i == i0

    d = dist(i0x, i0y, @coords[2 * i], @coords[2 * i + 1])
    if (d < min_dist) && (d > 0)
      i1 = i
      min_dist = d
    end
  end
  i1x = @coords[2 * i1]
  i1y = @coords[2 * i1 + 1]

  min_radius = Float::INFINITY

  # find the third point which forms the smallest circumcircle with the first two

  (0..@n - 1).each do |i|
    next if (i == i0) || (i == i1)

    r = circumradius(i0x, i0y, i1x, i1y, @coords[2 * i], @coords[2 * i + 1])
    if r < min_radius
      i2 = i
      min_radius = r
    end
  end

  i2x = @coords[2 * i2]
  i2y = @coords[2 * i2 + 1]
  if min_radius == Float::INFINITY
    # order collinear points by dx (or dy if all x are identical)
    # and return the list as a hull
    (0..n - 1).each do |i|
      dists[i] = (@coords[2 * i] - @coords[0]) || (@coords[2 * i + 1] - @coords[1])
    end
    ids = dists.map.with_index.sort.map(&:last)
    @hull = Array.new(@n, 0)
    j = 0
    d0 = -Float::INFINITY
    (0..@n - 1).each do |i|
      id = ids[i]
      next unless dists[id] > d0

      @hull[j] = id
      j += 1
      d0 = dists[id]
    end
    @hull = hull.slice(0, j)
    @triangles = []
    @halfedges = []
    return
  end

  # swap the order of the seed points for counter-clockwise orientation
  if orient(i0x, i0y, i1x, i1y, i2x, i2y)
    i = i1
    x = i1x
    y = i1y
    i1 = i2
    i1x = i2x
    i1y = i2y
    i2 = i
    i2x = x
    i2y = y
  end
  center = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y)
  @cx, @cy = center

  (0..@n - 1).each do |k|
    dists[k] = dist(@coords[2 * k], @coords[2 * k + 1], center[0], center[1])
  end
  # sort the points by distance from the seed triangle circumcenter
  ids = dists.map.with_index.sort.map(&:last)

  @hull_start = i0
  @hull_size = 3

  @hull_next[i0] = @hull_prev[i2] = i1
  @hull_next[i1] = @hull_prev[i0] = i2
  @hull_next[i2] = @hull_prev[i1] = i0

  @hull_tri[i0] = 0
  @hull_tri[i1] = 1
  @hull_tri[i2] = 2

  @hull_hash.fill(-1)
  @hull_hash[hash_key(i0x, i0y)] = i0
  @hull_hash[hash_key(i1x, i1y)] = i1
  @hull_hash[hash_key(i2x, i2y)] = i2

  @triangles_len = 0
  add_triangle(i0, i1, i2, -1, -1, -1)
  xp = 0
  yp = 0
  (0..ids.length - 1).each do |k|
    i = ids[k]
    x = @coords[2 * i]
    y = @coords[2 * i + 1]
    if (k > 0 && (x - xp).abs <= EPSILON && (y - yp).abs <= EPSILON)
      next
    end
    xp = x
    yp = y
    #skip seed triangle points
    if i == i0 || i == i1 || i == i2
      next
    end
    # find a visible edge on the convex hull using edge hash

    start = 0

    key = hash_key(x, y)
    (0..@hash_size - 1).each do |m|
      start = @hull_hash[(key + m) % @hash_size]
      break if (start != -1) && (start != @hull_next[start])
    end
    start = @hull_prev[start]
    e = start
    q = nil
    loop do
      q = @hull_next[e]
      break if orient(x, y, @coords[2 * e], @coords[2 * e + 1], @coords[2 * q], @coords[2 * q + 1])
      e = q
      if e == start
        e = -1
        break
      end
    end

    if e == -1
      next
    end
    t = add_triangle(e, i, @hull_next[e], -1, -1, @hull_tri[e])
    @hull_tri[i] = legalize(t + 2)
    @hull_tri[e] = t
    @hull_size += 1
    n = @hull_next[e]
    loop do
      q = @hull_next[n]
      break if !orient(x, y, @coords[2 * n], @coords[2 * n + 1], @coords[2 * q], @coords[2 * q + 1])
      t = add_triangle(n, i, q, @hull_tri[i], -1, @hull_tri[n])
      @hull_tri[i] = legalize(t + 2)
      @hull_next[n] = n
      @hull_size -= 1
      n = q
    end

    if e == start
      loop do
        q = @hull_prev[e]
        break if !orient(x, y, @coords[2 * q], @coords[2 * q + 1], @coords[2 * e], @coords[2 * e + 1])

        t = add_triangle(q, i, e, -1, @hull_tri[e], @hull_tri[q])

        legalize(t + 2)
        @hull_tri[q] = t
        @hull_next[e] = e
        @hull_size -= 1
        e = q
      end
    end
    @hull_start = e
    @hull_prev[i] = e
    @hull_next[e] = i
    @hull_prev[n] = i
    @hull_next[i] = n

    # save the two new edges in the hash table
    @hull_hash[hash_key(x, y)] = i
    @hull_hash[hash_key(@coords[2 * e], @coords[2 * e + 1])] = e
  end
  @hull = Array.new(@hull_size, 0)
  e = @hull_start
  (0..@hull_size - 1).each do |k|
    @hull[k] = e
    e = @hull_next[e]
  end

  # trim typed triangle mesh arrays
  @halfedges = @_halfedges.slice(0, @triangles_len)
  @triangles = @_triangles.slice(0, @triangles_len)
  @triangles
end