Closest 3D point on triangle. Expanded from SharpDX implementation.

closest.js

function closest (result, p, a, b, c) {
  var px = p[0]
  var py = p[1]
  var pz = p[2]
  var ax = a[0]
  var ay = a[1]
  var az = a[2]
  var bx = b[0]
  var by = b[1]
  var bz = b[2]
  var cx = c[0]
  var cy = c[1]
  var cz = c[2]
  var abx = bx - ax
  var aby = by - ay
  var abz = bz - az
  var acx = cx - ax
  var acy = cy - ay
  var acz = cz - az
  var apx = px - ax
  var apy = py - ay
  var apz = pz - az
  var d1 = abx * apx + aby * apy + abz * apz
  var d2 = acx * apx + acy * apy + acz * apz
  if (d1 <= 0 && d2 <= 0) {
    result[0] = ax
    result[1] = ay
    result[2] = az
    return
  }
  var bpx = px - bx
  var bpy = py - by
  var bpz = pz - bz
  var d3 = abx * bpx + aby * bpy + abz * bpz
  var d4 = acx * bpx + acy * bpy + acz * bpz
  if (d3 >= 0 && d4 <= d3) {
    result[0] = bx
    result[1] = by
    result[2] = bz
    return
  }
  var vc = d1 * d4 - d3 * d2
  if (vc <= 0 && d1 >= 0 && d3 <= 0) {
    var v = d1 / (d1 - d3)
    result[0] = ax + abx * v
    result[1] = ay + aby * v
    result[2] = az + abz * v
    return
  }
  var cpx = px - cx
  var cpy = py - cy
  var cpz = pz - cz
  var d5 = abx * cpx + aby * cpy + abz * cpz
  var d6 = acx * cpx + acy * cpy + acz * cpz
  if (d6 >= 0 && d5 <= d6) {
    result[0] = cx
    result[1] = cy
    result[2] = cz
    return
  }
  var vb = d5 * d2 - d1 * d6
  if (vb <= 0 && d2 >= 0 && d6 <= 0) {
    var w = d2 / (d2 - d6)
    result[0] = ax + acx * w
    result[1] = ay + acy * w
    result[2] = az + acz * w
    return
  }
  var va = d3 * d6 - d5 * d4
  if (va <= 0 && (d4 - d3) >= 0 && (d5 - d6) >= 0) {
    var w = (d4 - d3) / ((d4 - d3) + (d5 - d6))
    result[0] = bx + (cx - bx) * w
    result[1] = by + (cy - by) * w
    result[2] = bz + (cz - bz) * w
    return
  }
  var denom = 1 / (va + vb + vc)
  var v2 = vb * denom
  var w2 = vc * denom
  result[0] = ax + abx * v2 + acx * w2
  result[1] = ay + aby * v2 + acy * w2
  result[2] = az + abz * v2 + acz * w2
}