import Blender
from Blender import NMesh
from math import pow


def Bezier3(p1,p2,p3,mu):
   #_________________________________________
   #Three control point Bezier interpolation
   #Parameters: p1 to p3- 3 point tuple [x,y,z]
   #mu ranges from 0 to 1 (start to end of curve)
   #_________________________________________
   p = [0,0,0]

   mu2 = mu * mu
   mum1 = 1 - mu
   mum12 = mum1 * mum1
   for z in range(3): 
      p[z] = p1[z] * mum12 + 2 * p2[z] * mum1 * mu + p3[z] * mu2

   return(p);


def Bezier4(p1,p2,p3,p4,mu):
   #_________________________________________
   #Four control point Bezier interpolation
   #Parameters: p1 to p4- 3 point tuple [x,y,z]
   #mu ranges from 0 to 1 (start to end of curve)
   #_________________________________________
   p = [0,0,0]
   mum1 = 1 - mu
   mum13 = mum1 * mum1 * mum1
   mu3 = mu * mu * mu

   for z in range(3):
      p[z] = mum13*p1[z] + 3*mu*mum1*mum1*p2[z] + 3*mu*mu*mum1*p3[z] + mu3*p4[z]
   return(p)
   
def Bezier(p,mu):
   #_________________________________________
   #General Bezier curve
   #Parameters: p array of points ( etc [[x1,y1,z1],[x2,y2,z2],...] )
   #mu ranges from 0 to 1 (start to end of curve)
   #IMPORTANT, the last point is not computed
   #_________________________________________
   b = [0,0,0]
   n = len(p)
   muk = 1
   munk = pow(1-mu,n)

   
   for k in range(n): 
      nn = n
      kn = k
      nkn = n - k
      blend = muk * munk
      muk *= mu
      munk /= (1-mu)
      while nn >= 1:
         blend *= nn
         nn -=1
         if kn > 1:
            blend /= float(kn)
            kn-=1
         if nkn > 1:
            blend /= float(nkn)
            nkn-=1
        for z in range(3):   
         b[z] += p[k][z] * blend
   return(b)

me = NMesh.GetRaw()

verts = [[8,-1,-20],[-9,2,8],[10,36,-3],[8,8,8],[10,4,-10],[0,0,0],[10,10,2]]

points = 300

for y in range(points):
   #vertex = Bezier3(verts[1],verts[2],verts[3], float(y)/s)
   #vertex = Bezier4(verts[1],verts[2],verts[3],verts[4], float(y)/s)
   vertex = Bezier(verts,float(y)/s)
   vert = NMesh.Vert(vertex[0],vertex[1],vertex[2])
   me.verts.append(vert)

NMesh.PutRaw(me)