StackGenVis/frontend/node_modules/incremental-convex-hull/ich.js

"use strict"

//High level idea:
// 1. Use Clarkson's incremental construction to find convex hull
// 2. Point location in triangulation by jump and walk

module.exports = incrementalConvexHull

var orient = require("robust-orientation")
var compareCell = require("simplicial-complex").compareCells

function compareInt(a, b) {
  return a - b
}

function Simplex(vertices, adjacent, boundary) {
  this.vertices = vertices
  this.adjacent = adjacent
  this.boundary = boundary
  this.lastVisited = -1
}

Simplex.prototype.flip = function() {
  var t = this.vertices[0]
  this.vertices[0] = this.vertices[1]
  this.vertices[1] = t
  var u = this.adjacent[0]
  this.adjacent[0] = this.adjacent[1]
  this.adjacent[1] = u
}

function GlueFacet(vertices, cell, index) {
  this.vertices = vertices
  this.cell = cell
  this.index = index
}

function compareGlue(a, b) {
  return compareCell(a.vertices, b.vertices)
}

function bakeOrient(d) {
  var code = ["function orient(){var tuple=this.tuple;return test("]
  for(var i=0; i<=d; ++i) {
    if(i > 0) {
      code.push(",")
    }
    code.push("tuple[", i, "]")
  }
  code.push(")}return orient")
  var proc = new Function("test", code.join(""))
  var test = orient[d+1]
  if(!test) {
    test = orient
  }
  return proc(test)
}

var BAKED = []

function Triangulation(dimension, vertices, simplices) {
  this.dimension = dimension
  this.vertices = vertices
  this.simplices = simplices
  this.interior = simplices.filter(function(c) {
    return !c.boundary
  })

  this.tuple = new Array(dimension+1)
  for(var i=0; i<=dimension; ++i) {
    this.tuple[i] = this.vertices[i]
  }

  var o = BAKED[dimension]
  if(!o) {
    o = BAKED[dimension] = bakeOrient(dimension)
  }
  this.orient = o
}

var proto = Triangulation.prototype

//Degenerate situation where we are on boundary, but coplanar to face
proto.handleBoundaryDegeneracy = function(cell, point) {
  var d = this.dimension
  var n = this.vertices.length - 1
  var tuple = this.tuple
  var verts = this.vertices

  //Dumb solution: Just do dfs from boundary cell until we find any peak, or terminate
  var toVisit = [ cell ]
  cell.lastVisited = -n
  while(toVisit.length > 0) {
    cell = toVisit.pop()
    var cellVerts = cell.vertices
    var cellAdj = cell.adjacent
    for(var i=0; i<=d; ++i) {
      var neighbor = cellAdj[i]
      if(!neighbor.boundary || neighbor.lastVisited <= -n) {
        continue
      }
      var nv = neighbor.vertices
      for(var j=0; j<=d; ++j) {
        var vv = nv[j]
        if(vv < 0) {
          tuple[j] = point
        } else {
          tuple[j] = verts[vv]
        }
      }
      var o = this.orient()
      if(o > 0) {
        return neighbor
      }
      neighbor.lastVisited = -n
      if(o === 0) {
        toVisit.push(neighbor)
      }
    }
  }
  return null
}

proto.walk = function(point, random) {
  //Alias local properties
  var n = this.vertices.length - 1
  var d = this.dimension
  var verts = this.vertices
  var tuple = this.tuple

  //Compute initial jump cell
  var initIndex = random ? (this.interior.length * Math.random())|0 : (this.interior.length-1)
  var cell = this.interior[ initIndex ]

  //Start walking
outerLoop:
  while(!cell.boundary) {
    var cellVerts = cell.vertices
    var cellAdj = cell.adjacent

    for(var i=0; i<=d; ++i) {
      tuple[i] = verts[cellVerts[i]]
    }
    cell.lastVisited = n

    //Find farthest adjacent cell
    for(var i=0; i<=d; ++i) {
      var neighbor = cellAdj[i]
      if(neighbor.lastVisited >= n) {
        continue
      }
      var prev = tuple[i]
      tuple[i] = point
      var o = this.orient()
      tuple[i] = prev
      if(o < 0) {
        cell = neighbor
        continue outerLoop
      } else {
        if(!neighbor.boundary) {
          neighbor.lastVisited = n
        } else {
          neighbor.lastVisited = -n
        }
      }
    }
    return
  }

  return cell
}

proto.addPeaks = function(point, cell) {
  var n = this.vertices.length - 1
  var d = this.dimension
  var verts = this.vertices
  var tuple = this.tuple
  var interior = this.interior
  var simplices = this.simplices

  //Walking finished at boundary, time to add peaks
  var tovisit = [ cell ]

  //Stretch initial boundary cell into a peak
  cell.lastVisited = n
  cell.vertices[cell.vertices.indexOf(-1)] = n
  cell.boundary = false
  interior.push(cell)

  //Record a list of all new boundaries created by added peaks so we can glue them together when we are all done
  var glueFacets = []

  //Do a traversal of the boundary walking outward from starting peak
  while(tovisit.length > 0) {
    //Pop off peak and walk over adjacent cells
    var cell = tovisit.pop()
    var cellVerts = cell.vertices
    var cellAdj = cell.adjacent
    var indexOfN = cellVerts.indexOf(n)
    if(indexOfN < 0) {
      continue
    }

    for(var i=0; i<=d; ++i) {
      if(i === indexOfN) {
        continue
      }

      //For each boundary neighbor of the cell
      var neighbor = cellAdj[i]
      if(!neighbor.boundary || neighbor.lastVisited >= n) {
        continue
      }

      var nv = neighbor.vertices

      //Test if neighbor is a peak
      if(neighbor.lastVisited !== -n) {      
        //Compute orientation of p relative to each boundary peak
        var indexOfNeg1 = 0
        for(var j=0; j<=d; ++j) {
          if(nv[j] < 0) {
            indexOfNeg1 = j
            tuple[j] = point
          } else {
            tuple[j] = verts[nv[j]]
          }
        }
        var o = this.orient()

        //Test if neighbor cell is also a peak
        if(o > 0) {
          nv[indexOfNeg1] = n
          neighbor.boundary = false
          interior.push(neighbor)
          tovisit.push(neighbor)
          neighbor.lastVisited = n
          continue
        } else {
          neighbor.lastVisited = -n
        }
      }

      var na = neighbor.adjacent

      //Otherwise, replace neighbor with new face
      var vverts = cellVerts.slice()
      var vadj = cellAdj.slice()
      var ncell = new Simplex(vverts, vadj, true)
      simplices.push(ncell)

      //Connect to neighbor
      var opposite = na.indexOf(cell)
      if(opposite < 0) {
        continue
      }
      na[opposite] = ncell
      vadj[indexOfN] = neighbor

      //Connect to cell
      vverts[i] = -1
      vadj[i] = cell
      cellAdj[i] = ncell

      //Flip facet
      ncell.flip()

      //Add to glue list
      for(var j=0; j<=d; ++j) {
        var uu = vverts[j]
        if(uu < 0 || uu === n) {
          continue
        }
        var nface = new Array(d-1)
        var nptr = 0
        for(var k=0; k<=d; ++k) {
          var vv = vverts[k]
          if(vv < 0 || k === j) {
            continue
          }
          nface[nptr++] = vv
        }
        glueFacets.push(new GlueFacet(nface, ncell, j))
      }
    }
  }

  //Glue boundary facets together
  glueFacets.sort(compareGlue)

  for(var i=0; i+1<glueFacets.length; i+=2) {
    var a = glueFacets[i]
    var b = glueFacets[i+1]
    var ai = a.index
    var bi = b.index
    if(ai < 0 || bi < 0) {
      continue
    }
    a.cell.adjacent[a.index] = b.cell
    b.cell.adjacent[b.index] = a.cell
  }
}

proto.insert = function(point, random) {
  //Add point
  var verts = this.vertices
  verts.push(point)

  var cell = this.walk(point, random)
  if(!cell) {
    return
  }

  //Alias local properties
  var d = this.dimension
  var tuple = this.tuple

  //Degenerate case: If point is coplanar to cell, then walk until we find a non-degenerate boundary
  for(var i=0; i<=d; ++i) {
    var vv = cell.vertices[i]
    if(vv < 0) {
      tuple[i] = point
    } else {
      tuple[i] = verts[vv]
    }
  }
  var o = this.orient(tuple)
  if(o < 0) {
    return
  } else if(o === 0) {
    cell = this.handleBoundaryDegeneracy(cell, point)
    if(!cell) {
      return
    }
  }

  //Add peaks
  this.addPeaks(point, cell)
}

//Extract all boundary cells
proto.boundary = function() {
  var d = this.dimension
  var boundary = []
  var cells = this.simplices
  var nc = cells.length
  for(var i=0; i<nc; ++i) {
    var c = cells[i]
    if(c.boundary) {
      var bcell = new Array(d)
      var cv = c.vertices
      var ptr = 0
      var parity = 0
      for(var j=0; j<=d; ++j) {
        if(cv[j] >= 0) {
          bcell[ptr++] = cv[j]
        } else {
          parity = j&1
        }
      }
      if(parity === (d&1)) {
        var t = bcell[0]
        bcell[0] = bcell[1]
        bcell[1] = t
      }
      boundary.push(bcell)
    }
  }
  return boundary
}

function incrementalConvexHull(points, randomSearch) {
  var n = points.length
  if(n === 0) {
    throw new Error("Must have at least d+1 points")
  }
  var d = points[0].length
  if(n <= d) {
    throw new Error("Must input at least d+1 points")
  }

  //FIXME: This could be degenerate, but need to select d+1 non-coplanar points to bootstrap process
  var initialSimplex = points.slice(0, d+1)

  //Make sure initial simplex is positively oriented
  var o = orient.apply(void 0, initialSimplex)
  if(o === 0) {
    throw new Error("Input not in general position")
  }
  var initialCoords = new Array(d+1)
  for(var i=0; i<=d; ++i) {
    initialCoords[i] = i
  }
  if(o < 0) {
    initialCoords[0] = 1
    initialCoords[1] = 0
  }

  //Create initial topological index, glue pointers together (kind of messy)
  var initialCell = new Simplex(initialCoords, new Array(d+1), false)
  var boundary = initialCell.adjacent
  var list = new Array(d+2)
  for(var i=0; i<=d; ++i) {
    var verts = initialCoords.slice()
    for(var j=0; j<=d; ++j) {
      if(j === i) {
        verts[j] = -1
      }
    }
    var t = verts[0]
    verts[0] = verts[1]
    verts[1] = t
    var cell = new Simplex(verts, new Array(d+1), true)
    boundary[i] = cell
    list[i] = cell
  }
  list[d+1] = initialCell
  for(var i=0; i<=d; ++i) {
    var verts = boundary[i].vertices
    var adj = boundary[i].adjacent
    for(var j=0; j<=d; ++j) {
      var v = verts[j]
      if(v < 0) {
        adj[j] = initialCell
        continue
      }
      for(var k=0; k<=d; ++k) {
        if(boundary[k].vertices.indexOf(v) < 0) {
          adj[j] = boundary[k]
        }
      }
    }
  }

  //Initialize triangles
  var triangles = new Triangulation(d, initialSimplex, list)

  //Insert remaining points
  var useRandom = !!randomSearch
  for(var i=d+1; i<n; ++i) {
    triangles.insert(points[i], useRandom)
  }
  
  //Extract boundary cells
  return triangles.boundary()
}