verticies = [
  Vector( 0.2000,  0.0000, 2.70000), Vector( 0.2000, -0.1120, 2.70000),
  Vector( 0.1120, -0.2000, 2.70000), Vector( 0.0000, -0.2000, 2.70000),
  Vector( 1.3375,  0.0000, 2.53125), Vector( 1.3375, -0.7490, 2.53125),
  Vector( 0.7490, -1.3375, 2.53125), Vector( 0.0000, -1.3375, 2.53125),
  Vector( 1.4375,  0.0000, 2.53125), Vector( 1.4375, -0.8050, 2.53125),
  Vector( 0.8050, -1.4375, 2.53125), Vector( 0.0000, -1.4375, 2.53125),
  Vector( 1.5000,  0.0000, 2.40000), Vector( 1.5000, -0.8400, 2.40000),
  Vector( 0.8400, -1.5000, 2.40000), Vector( 0.0000, -1.5000, 2.40000),
  Vector( 1.7500,  0.0000, 1.87500), Vector( 1.7500, -0.9800, 1.87500),
  Vector( 0.9800, -1.7500, 1.87500), Vector( 0.0000, -1.7500, 1.87500),
  Vector( 2.0000,  0.0000, 1.35000), Vector( 2.0000, -1.1200, 1.35000),
  Vector( 1.1200, -2.0000, 1.35000), Vector( 0.0000, -2.0000, 1.35000),
  Vector( 2.0000,  0.0000, 0.90000), Vector( 2.0000, -1.1200, 0.90000),
  Vector( 1.1200, -2.0000, 0.90000), Vector( 0.0000, -2.0000, 0.90000),
  Vector(-2.0000,  0.0000, 0.90000), Vector( 2.0000,  0.0000, 0.45000),
  Vector( 2.0000, -1.1200, 0.45000), Vector( 1.1200, -2.0000, 0.45000),
  Vector( 0.0000, -2.0000, 0.45000), Vector( 1.5000,  0.0000, 0.22500),
  Vector( 1.5000, -0.8400, 0.22500), Vector( 0.8400, -1.5000, 0.22500),
  Vector( 0.0000, -1.5000, 0.22500), Vector( 1.5000,  0.0000, 0.15000),
  Vector( 1.5000, -0.8400, 0.15000), Vector( 0.8400, -1.5000, 0.15000),
  Vector( 0.0000, -1.5000, 0.15000), Vector(-1.6000,  0.0000, 2.02500),
  Vector(-1.6000, -0.3000, 2.02500), Vector(-1.5000, -0.3000, 2.25000),
  Vector(-1.5000,  0.0000, 2.25000), Vector(-2.3000,  0.0000, 2.02500),
  Vector(-2.3000, -0.3000, 2.02500), Vector(-2.5000, -0.3000, 2.25000),
  Vector(-2.5000,  0.0000, 2.25000), Vector(-2.7000,  0.0000, 2.02500),
  Vector(-2.7000, -0.3000, 2.02500), Vector(-3.0000, -0.3000, 2.25000),
  Vector(-3.0000,  0.0000, 2.25000), Vector(-2.7000,  0.0000, 1.80000),
  Vector(-2.7000, -0.3000, 1.80000), Vector(-3.0000, -0.3000, 1.80000),
  Vector(-3.0000,  0.0000, 1.80000), Vector(-2.7000,  0.0000, 1.57500),
  Vector(-2.7000, -0.3000, 1.57500), Vector(-3.0000, -0.3000, 1.35000),
  Vector(-3.0000,  0.0000, 1.35000), Vector(-2.5000,  0.0000, 1.12500),
  Vector(-2.5000, -0.3000, 1.12500), Vector(-2.6500, -0.3000, 0.93750),
  Vector(-2.6500,  0.0000, 0.93750), Vector(-2.0000, -0.3000, 0.90000),
  Vector(-1.9000, -0.3000, 0.60000), Vector(-1.9000,  0.0000, 0.60000),
  Vector( 1.7000,  0.0000, 1.42500), Vector( 1.7000, -0.6600, 1.42500),
  Vector( 1.7000, -0.6600, 0.60000), Vector( 1.7000,  0.0000, 0.60000),
  Vector( 2.6000,  0.0000, 1.42500), Vector( 2.6000, -0.6600, 1.42500),
  Vector( 3.1000, -0.6600, 0.82500), Vector( 3.1000,  0.0000, 0.82500),
  Vector( 2.3000,  0.0000, 2.10000), Vector( 2.3000, -0.2500, 2.10000),
  Vector( 2.4000, -0.2500, 2.02500), Vector( 2.4000,  0.0000, 2.02500),
  Vector( 2.7000,  0.0000, 2.40000), Vector( 2.7000, -0.2500, 2.40000),
  Vector( 3.3000, -0.2500, 2.40000), Vector( 3.3000,  0.0000, 2.40000),
  Vector( 2.8000,  0.0000, 2.47500), Vector( 2.8000, -0.2500, 2.47500),
  Vector( 3.5250, -0.2500, 2.49375), Vector( 3.5250,  0.0000, 2.49375),
  Vector( 2.9000,  0.0000, 2.47500), Vector( 2.9000, -0.1500, 2.47500),
  Vector( 3.4500, -0.1500, 2.51250), Vector( 3.4500,  0.0000, 2.51250),
  Vector( 2.8000,  0.0000, 2.40000), Vector( 2.8000, -0.1500, 2.40000),
  Vector( 3.2000, -0.1500, 2.40000), Vector( 3.2000,  0.0000, 2.40000),
  Vector( 0.0000,  0.0000, 3.15000), Vector( 0.8000,  0.0000, 3.15000),
  Vector( 0.8000, -0.4500, 3.15000), Vector( 0.4500, -0.8000, 3.15000),
  Vector( 0.0000, -0.8000, 3.15000), Vector( 0.0000,  0.0000, 2.85000),
  Vector( 1.4000,  0.0000, 2.40000), Vector( 1.4000, -0.7840, 2.40000),
  Vector( 0.7840, -1.4000, 2.40000), Vector( 0.0000, -1.4000, 2.40000),
  Vector( 0.4000,  0.0000, 2.55000), Vector( 0.4000, -0.2240, 2.55000),
  Vector( 0.2240, -0.4000, 2.55000), Vector( 0.0000, -0.4000, 2.55000),
  Vector( 1.3000,  0.0000, 2.55000), Vector( 1.3000, -0.7280, 2.55000),
  Vector( 0.7280, -1.3000, 2.55000), Vector( 0.0000, -1.3000, 2.55000),
  Vector( 1.3000,  0.0000, 2.40000), Vector( 1.3000, -0.7280, 2.40000),
  Vector( 0.7280, -1.3000, 2.40000), Vector( 0.0000, -1.3000, 2.40000),
  Vector( 0.0000,  0.0000, 0.00000), Vector( 1.4250, -0.7980, 0.00000),
  Vector( 1.5000,  0.0000, 0.07500), Vector( 1.4250,  0.0000, 0.00000),
  Vector( 0.7980, -1.4250, 0.00000), Vector( 0.0000, -1.5000, 0.07500),
  Vector( 0.0000, -1.4250, 0.00000), Vector( 1.5000, -0.8400, 0.07500),
  Vector( 0.8400, -1.5000, 0.07500)
]

#print("static const dmnsn_vector dmnsn_teapot_verticies[%d] = {" % \
#      len(verticies))
#for i in range(len(verticies)):
#  v = verticies[i]
#  v = Vector(v.x, v.z - 1.575, v.y)
#  print("  { .x = %+.5f, .y = %+.5f, .z = %+.5f }," % (v.x, v.y, v.z))
#print("};")

ntriangles = 0

B = [
  lambda x: (1 - x)*(1 -x)*(1 - x),
  lambda x: 3*x*(1 - x)*(1 - x),
  lambda x: 3*x*x*(1 - x),
  lambda x: x*x*x,
]
Bprime = [
  lambda x: -3*(1-x)*(1-x),
  lambda x: 3*(1-x)*(1-x) - 6*x*(1-x),
  lambda x: 6*x*(1-x) - 3*x*x,
  lambda x: 3*x*x,
]

class _BicubicPatch(Union):
  def __init__(self, indicies):
    if len(indicies) != 16:
      raise ValueError("expected 16 control points")

    self.control_points = []
    for i in indicies:
      self.control_points.append(verticies[i])

    resolution = 8
    triangles = []
    global ntriangles
    for i in range(resolution):
      for j in range(resolution):
        a = self._eval(i/resolution, j/resolution)
        an = self._eval_normal(i/resolution, j/resolution)
        b = self._eval((i + 1)/resolution, j/resolution)
        bn = self._eval_normal((i + 1)/resolution, j/resolution)
        c = self._eval((i + 1)/resolution, (j + 1)/resolution)
        cn = self._eval_normal((i + 1)/resolution, (j + 1)/resolution)
        d = self._eval(i/resolution, (j + 1)/resolution)
        dn = self._eval_normal(i/resolution, (j + 1)/resolution)
        triangles.append(Triangle(a, b, c, an, bn, cn))
        triangles.append(Triangle(c, d, a, cn, dn, an))
        ntriangles += 2
        if ntriangles%1000000 == 0:
          print(ntriangles)

    Union.__init__(self, triangles)

  def _eval(self, u, v):
    r = Vector(0)
    for i in range(4):
      for j in range(4):
        r += self.control_points[4*j + i]*B[i](u)*B[j](v)
    return r

  def _eval_normal(self, u, v):
    ru = Vector(0)
    for i in range(4):
      for j in range(4):
        ru += self.control_points[4*j + i]*Bprime[i](u)*B[j](v)

    rv = Vector(0)
    for i in range(4):
      for j in range(4):
        rv += self.control_points[4*j + i]*B[i](u)*Bprime[j](v)

    return cross(ru, rv)

class _Teapot(Union):
  def __init__(self, *args, **kwargs):
    patches = [
      self.reflectY(),
      self.reflectY().scale(1, -1, 1),
    ]
    Union.__init__(self, patches, *args, **kwargs)
    self.rotate(-90*X).translate(-1.575*Y)

  @classmethod
  def rim(cls):
    return _BicubicPatch([
      102, 103, 104, 105, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
    ])

  @classmethod
  def body(cls):
    body1 = _BicubicPatch([
      12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27
    ])
    body2 = _BicubicPatch([
      24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40
    ])
    return Union([body1, body2])

  @classmethod
  def lid(cls):
    lid1 = _BicubicPatch([
      96, 96, 96, 96, 97, 98, 99, 100, 101, 101, 101, 101, 0, 1, 2, 3
    ])
    lid2 = _BicubicPatch([
      0, 1, 2, 3, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117
    ])
    return Union([lid1, lid2])

  @classmethod
  def bottom(cls):
    return _BicubicPatch([
      118, 118, 118, 118, 124, 122, 119, 121, 123, 126, 125, 120, 40, 39, 38, 37
    ])

  @classmethod
  def reflectXY(cls):
    return Union([
      cls.rim(),
      cls.body(),
      cls.lid(),
      cls.bottom(),
    ])

  @classmethod
  def handle(cls):
    handle1 = _BicubicPatch([
      41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56
    ])
    handle2 = _BicubicPatch([
      53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 28, 65, 66, 67
    ])
    return Union([handle1, handle2])

  @classmethod
  def spout(cls):
    spout1 = _BicubicPatch([
      68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83
    ])
    spout2 = _BicubicPatch([
      80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95
    ])
    return Union([spout1, spout2])

  @classmethod
  def reflectY(cls):
    return Union([
      cls.reflectXY(),
      cls.reflectXY().scale(-1, 1, 1),
      cls.handle(),
      cls.spout(),
    ])

camera = PerspectiveCamera(
  location = -5*Z,
  look_at  = 0,
)

lights.append(PointLight(location = (-15, 20, -10), color = White))

objects.append(Teapot(pigment = White).rotate(-80*X))

if ntriangles > 0:
  print(ntriangles)