// Last edited on 2011-09-12 03:31:05 by stolfilocal
// _*_ latin-1 _*_ 
// C1-smooth Tubes built with Bézier patches.

// The tube consists of rings. Each ring consists of two 
// Bezier patches, /top/ and /bottom/, controlled
// by 2x2 arrays {T,B} of points. These are the middle
// Bézier points of each patch (excluding the 4 corner points
// and the 8 edge points).

// Points {T[0][0]} and {T[1][0]} are closer to one edge of the ring;
// Points {T[0][1]} and {T[1][1]} are closer to the other edge.
// Point {B[i][j]} is topologically the mirror image of {T[i][j]}.

#macro bztube_ring2(T0,B0,T1,B1,T2,B2, txT, txB, rad, txg)
  // A 2-patch ring of the tube, given the 2x2 control arrays
  // {T0,B0} of the previous ring (or posfork, or reversed cap)
  // {T1,B1} of this ring
  // {T2,B2} of the next ring (or reversed posfork, or cap).
  
  // Control points for top patch, minus the lateral seams:
  #local PT = array[4][4];
  #local PT[1][0] = (T0[0][1] + T1[0][0])/2;
  #local PT[2][0] = (T0[1][1] + T1[1][0])/2;
  #local PT[1][1] = T1[0][0];
  #local PT[2][1] = T1[1][0];
  #local PT[1][2] = T1[0][1];
  #local PT[2][2] = T1[1][1];
  #local PT[1][3] = (T1[0][1] + T2[0][0])/2;
  #local PT[2][3] = (T1[1][1] + T2[1][0])/2;
  
  // Control points for bottom patch, minus the lateral seams:
  #local PB = array[4][4];
  #local PB[1][0] = (B0[0][1] + B1[0][0])/2;
  #local PB[2][0] = (B0[1][1] + B1[1][0])/2;
  #local PB[1][1] = B1[0][0];
  #local PB[2][1] = B1[1][0];
  #local PB[1][2] = B1[0][1];
  #local PB[2][2] = B1[1][1];
  #local PB[1][3] = (B1[0][1] + B2[0][0])/2;
  #local PB[2][3] = (B1[1][1] + B2[1][0])/2;
 
  // Control points along the lateral seams:
  #local PT[0][0] = (PT[1][0] + PB[1][0])/2; #local PB[0][0] = PT[0][0];
  #local PT[0][1] = (PT[1][1] + PB[1][1])/2; #local PB[0][1] = PT[0][1];
  #local PT[0][2] = (PT[1][2] + PB[1][2])/2; #local PB[0][2] = PT[0][2];
  #local PT[0][3] = (PT[1][3] + PB[1][3])/2; #local PB[0][3] = PT[0][3];
  
  #local PT[3][0] = (PT[2][0] + PB[2][0])/2; #local PB[3][0] = PT[3][0];
  #local PT[3][1] = (PT[2][1] + PB[2][1])/2; #local PB[3][1] = PT[3][1];
  #local PT[3][2] = (PT[2][2] + PB[2][2])/2; #local PB[3][2] = PT[3][2];
  #local PT[3][3] = (PT[2][3] + PB[2][3])/2; #local PB[3][3] = PT[3][3];
  
  union{
    object{ bzpatch(PT, txT, rad, txg) }
    object{ bzpatch(PB, txB, rad, txg) }
  }
#end

#macro bztube_cap2(T0,B0,T1,B1, txT, txB, rad, txg)
  // A cap for the 2-patch tube, given the 2x2 control arrays {T0,B0} of the
  // previous ring, and {T1,B1} of the cap.  Only the points 
  // {T1[i][0]} and {B1[i][0]} are used in the latter.
  
  // Control points for top patch, minus the lateral and extremal seams:
  #local PT = array[4][4];
  #local PT[1][0] = (T0[0][1] + T1[0][0])/2;
  #local PT[2][0] = (T0[1][1] + T1[1][0])/2;
  #local PT[1][1] = T1[0][0];
  #local PT[2][1] = T1[1][0];
  #local PT[1][2] = (T1[0][0] + T1[1][0])/2;
  #local PT[2][2] = (T1[0][0] + T1[1][0])/2;
  
  // Control points for bottom patch, minus the lateral and extremal seams:
  #local PB = array[4][4];
  #local PB[1][0] = (B0[0][1] + B1[0][0])/2;
  #local PB[2][0] = (B0[1][1] + B1[1][0])/2;
  #local PB[1][1] = B1[0][0];
  #local PB[2][1] = B1[1][0];
  #local PB[1][2] = (B1[0][0] + B1[1][0])/2;
  #local PB[2][2] = (B1[0][0] + B1[1][0])/2;
 
  // Control points along the lateral seams:
  #local PT[0][0] = (PT[1][0] + PB[1][0])/2; #local PB[0][0] = PT[0][0];
  #local PT[0][1] = (PT[1][1] + PB[1][1])/2; #local PB[0][1] = PT[0][1];
  #local PT[0][2] = (PT[1][2] + PB[1][2])/2; #local PB[0][2] = PT[0][2];
  
  #local PT[3][0] = (PT[2][0] + PB[2][0])/2; #local PB[3][0] = PT[3][0];
  #local PT[3][1] = (PT[2][1] + PB[2][1])/2; #local PB[3][1] = PT[3][1];
  #local PT[3][2] = (PT[2][2] + PB[2][2])/2; #local PB[3][2] = PT[3][2];
  
  // Control points along the extremal seam:
  #local PT[1][3] = PT[0][2]; #local PB[1][3] = PT[1][3];
  #local PT[2][3] = PT[3][2]; #local PB[2][3] = PT[2][3];

  // Control points at extremal corner:
  #local PT[0][3] = PT[0][2]; #local PB[0][3] = PT[0][3];
  #local PT[3][3] = PT[3][2]; #local PB[3][3] = PT[3][3];

  union{
    object{ bzpatch(PT, txT, rad, txg) }
    object{ bzpatch(PB, txB, rad, txg) }
  }

#end

#macro bztube_ring4(Ta0,Ba0,Tb0,Bb0, Ta1,Ba1,Tb1,Bb1, Ta2,Ba2,Tb2,Bb2, txT, txB, rad, txg)
  // A 4-patch ring of the tube, given the 2x2 control arrays
  //  {Ta0,Ba0} {Tb0,Bb0} of the previous 4-patch ring (or reversed prefork),
  //  {Ta1,Ba1} {Tb1,Bb1} of this 4-patch ring,
  //  {Ta2,Ba2} {Tb2,Bb2} of the following 4-patch ring (or prefork).
  
  // Control points for top patches, minus the lateral seams:
  #local PTa = array[4][4];
  #local PTa[1][0] = (Ta0[0][1] + Ta1[0][0])/2;
  #local PTa[2][0] = (Ta0[1][1] + Ta1[1][0])/2;
  #local PTa[1][1] = Ta1[0][0];
  #local PTa[2][1] = Ta1[1][0];
  #local PTa[1][2] = Ta1[0][1];
  #local PTa[2][2] = Ta1[1][1];
  #local PTa[1][3] = (Ta1[0][1] + Ta2[0][0])/2;
  #local PTa[2][3] = (Ta1[1][1] + Ta2[1][0])/2;
  
  #local PTb = array[4][4];
  #local PTb[1][0] = (Tb0[0][1] + Tb1[0][0])/2;
  #local PTb[2][0] = (Tb0[1][1] + Tb1[1][0])/2;
  #local PTb[1][1] = Tb1[0][0];
  #local PTb[2][1] = Tb1[1][0];
  #local PTb[1][2] = Tb1[0][1];
  #local PTb[2][2] = Tb1[1][1];
  #local PTb[1][3] = (Tb1[0][1] + Tb2[0][0])/2;
  #local PTb[2][3] = (Tb1[1][1] + Tb2[1][0])/2;
  
  // Control points for bottom patches, minus the lateral seams:
  #local PBa = array[4][4];
  #local PBa[1][0] = (Ba0[0][1] + Ba1[0][0])/2;
  #local PBa[2][0] = (Ba0[1][1] + Ba1[1][0])/2;
  #local PBa[1][1] = Ba1[0][0];
  #local PBa[2][1] = Ba1[1][0];
  #local PBa[1][2] = Ba1[0][1];
  #local PBa[2][2] = Ba1[1][1];
  #local PBa[1][3] = (Ba1[0][1] + Ba2[0][0])/2;
  #local PBa[2][3] = (Ba1[1][1] + Ba2[1][0])/2;
  
  #local PBb = array[4][4];
  #local PBb[1][0] = (Bb0[0][1] + Bb1[0][0])/2;
  #local PBb[2][0] = (Bb0[1][1] + Bb1[1][0])/2;
  #local PBb[1][1] = Bb1[0][0];
  #local PBb[2][1] = Bb1[1][0];
  #local PBb[1][2] = Bb1[0][1];
  #local PBb[2][2] = Bb1[1][1];
  #local PBb[1][3] = (Bb1[0][1] + Bb2[0][0])/2;
  #local PBb[2][3] = (Bb1[1][1] + Bb2[1][0])/2;
 
  // Control points along the lateral seams, minus singular corners:
  #local PTa[0][0] = (PTa[1][0] + PBa[1][0])/2; #local PBa[0][0] = PTa[0][0];
  #local PTa[0][1] = (PTa[1][1] + PBa[1][1])/2; #local PBa[0][1] = PTa[0][1];
  #local PTa[0][2] = (PTa[1][2] + PBa[1][2])/2; #local PBa[0][2] = PTa[0][2];
  #local PTa[0][3] = (PTa[1][3] + PBa[1][3])/2; #local PBa[0][3] = PTa[0][3];
  
  #local PTa[3][0] = (PTa[2][0] + PTb[1][0])/2; #local PTb[0][0] = PTa[3][0];
  #local PTa[3][1] = (PTa[2][1] + PTb[1][1])/2; #local PTb[0][1] = PTa[3][1];
  #local PTa[3][2] = (PTa[2][2] + PTb[1][2])/2; #local PTb[0][2] = PTa[3][2];
  #local PTa[3][3] = (PTa[2][3] + PTb[1][3])/2; #local PTb[0][3] = PTa[3][3];
  
  #local PBa[3][0] = (PBa[2][0] + PBb[1][0])/2; #local PBb[0][0] = PBa[3][0];
  #local PBa[3][1] = (PBa[2][1] + PBb[1][1])/2; #local PBb[0][1] = PBa[3][1];
  #local PBa[3][2] = (PBa[2][2] + PBb[1][2])/2; #local PBb[0][2] = PBa[3][2];
  #local PBa[3][3] = (PBa[2][3] + PBb[1][3])/2; #local PBb[0][3] = PBa[3][3];

  #local PTb[3][0] = (PTb[2][0] + PBb[2][0])/2; #local PBb[3][0] = PTb[3][0];
  #local PTb[3][1] = (PTb[2][1] + PBb[2][1])/2; #local PBb[3][1] = PTb[3][1];
  #local PTb[3][2] = (PTb[2][2] + PBb[2][2])/2; #local PBb[3][2] = PTb[3][2];
  #local PTb[3][3] = (PTb[2][3] + PBb[2][3])/2; #local PBb[3][3] = PTb[3][3];
  
  union{
    #debug "\nring4 Ta\n"
    object{ bzpatch(PTa, txT, rad, txg) }
    #debug "\nring4 Tb\n"
    object{ bzpatch(PTb, txT, rad, txg) }
    #debug "\nring4 Ba\n"
    object{ bzpatch(PBa, txB, rad, txg) }
    #debug "\nring4 Bb\n"
    object{ bzpatch(PBb, txB, rad, txg) }
  }
#end

#macro bztube_prefork42(Ta0,Ba0,Tb0,Bb0, Ta1,Ba1,Tb1,Bb1, Ta2,Ba2,Tb2,Bb2, txT, txB, rad, txg)
  // The first part of a fork in the tube, connecting a 4-patch ring to two 2-patch rings.
  // Given the 2x2 control arrays
  //  {Ta0,Ba0} {Tb0,Bb0} of the previous 4-patch ring,
  //  {Ta1,Ba1} {Tb1,Bb1} of the prefork's 4-patch ring,
  //  {Ta2,Ba2} {Tb2,Bb2} of the posfork's 2-patch rings.
  
  // Control points for top patches, minus the lateral seams:
  #local PTa = array[4][4];
  #local PTa[1][0] = (Ta0[0][1] + Ta1[0][0])/2;
  #local PTa[2][0] = (Ta0[1][1] + Ta1[1][0])/2;
  #local PTa[1][1] = Ta1[0][0];
  #local PTa[2][1] = Ta1[1][0];
  #local PTa[1][2] = Ta1[0][1];
  #local PTa[2][2] = Ta1[1][1];
  #local PTa[1][3] = (Ta1[0][1] + Ta2[0][0])/2;
  #local PTa[2][3] = (Ta1[1][1] + Ta2[1][0])/2;
  
  #local PTb = array[4][4];
  #local PTb[1][0] = (Tb0[0][1] + Tb1[0][0])/2;
  #local PTb[2][0] = (Tb0[1][1] + Tb1[1][0])/2;
  #local PTb[1][1] = Tb1[0][0];
  #local PTb[2][1] = Tb1[1][0];
  #local PTb[1][2] = Tb1[0][1];
  #local PTb[2][2] = Tb1[1][1];
  #local PTb[1][3] = (Tb1[0][1] + Tb2[0][0])/2;
  #local PTb[2][3] = (Tb1[1][1] + Tb2[1][0])/2;
  
  // Control points for bottom patches, minus the lateral seams:
  #local PBa = array[4][4];
  #local PBa[1][0] = (Ba0[0][1] + Ba1[0][0])/2;
  #local PBa[2][0] = (Ba0[1][1] + Ba1[1][0])/2;
  #local PBa[1][1] = Ba1[0][0];
  #local PBa[2][1] = Ba1[1][0];
  #local PBa[1][2] = Ba1[0][1];
  #local PBa[2][2] = Ba1[1][1];
  #local PBa[1][3] = (Ba1[0][1] + Ba2[0][0])/2;
  #local PBa[2][3] = (Ba1[1][1] + Ba2[1][0])/2;
  
  #local PBb = array[4][4];
  #local PBb[1][0] = (Bb0[0][1] + Bb1[0][0])/2;
  #local PBb[2][0] = (Bb0[1][1] + Bb1[1][0])/2;
  #local PBb[1][1] = Bb1[0][0];
  #local PBb[2][1] = Bb1[1][0];
  #local PBb[1][2] = Bb1[0][1];
  #local PBb[2][2] = Bb1[1][1];
  #local PBb[1][3] = (Bb1[0][1] + Bb2[0][0])/2;
  #local PBb[2][3] = (Bb1[1][1] + Bb2[1][0])/2;
 
  // Control points along the lateral seams, minus singular corners:
  #local PTa[0][0] = (PTa[1][0] + PBa[1][0])/2; #local PBa[0][0] = PTa[0][0];
  #local PTa[0][1] = (PTa[1][1] + PBa[1][1])/2; #local PBa[0][1] = PTa[0][1];
  #local PTa[0][2] = (PTa[1][2] + PBa[1][2])/2; #local PBa[0][2] = PTa[0][2];
  #local PTa[0][3] = (PTa[1][3] + PBa[1][3])/2; #local PBa[0][3] = PTa[0][3];
  
  #local PTa[3][0] = (PTa[2][0] + PTb[1][0])/2; #local PTb[0][0] = PTa[3][0];
  #local PTa[3][1] = (PTa[2][1] + PTb[1][1])/2; #local PTb[0][1] = PTa[3][1];
  #local PTa[3][2] = (PTa[2][2] + PTb[1][2])/2; #local PTb[0][2] = PTa[3][2];
  
  #local PBa[3][0] = (PBa[2][0] + PBb[1][0])/2; #local PBb[0][0] = PBa[3][0];
  #local PBa[3][1] = (PBa[2][1] + PBb[1][1])/2; #local PBb[0][1] = PBa[3][1];
  #local PBa[3][2] = (PBa[2][2] + PBb[1][2])/2; #local PBb[0][2] = PBa[3][2];

  #local PTb[3][0] = (PTb[2][0] + PBb[2][0])/2; #local PBb[3][0] = PTb[3][0];
  #local PTb[3][1] = (PTb[2][1] + PBb[2][1])/2; #local PBb[3][1] = PTb[3][1];
  #local PTb[3][2] = (PTb[2][2] + PBb[2][2])/2; #local PBb[3][2] = PTb[3][2];
  #local PTb[3][3] = (PTb[2][3] + PBb[2][3])/2; #local PBb[3][3] = PTb[3][3];
  
  // Control points at singular corners:
  #local Psing = (PTa[2][3] + PTb[1][3] + PBa[2][3] + PBb[1][3])/4;
  #local PTa[3][3] = Psing;
  #local PTb[0][3] = Psing;
  #local PBa[3][3] = Psing;
  #local PBb[0][3] = Psing;

  union{
    #debug "\nprefork Ta\n"
    object{ bzpatch(PTa, txT, rad, txg) }
    #debug "\nprefork Tb\n"
    object{ bzpatch(PTb, txT, rad, txg) }
    #debug "\nprefork Ba\n"
    object{ bzpatch(PBa, txB, rad, txg) }
    #debug "\nprefork Bb\n"
    object{ bzpatch(PBb, txB, rad, txg) }
  }

#end

#macro bztube_posfork42(Ta0,Ba0,Tb0,Bb0, Ta1,Ba1,Tb1,Bb1, Ta2,Ba2,Tb2,Bb2, txT, txB, rad, txg)
  // The second part of a fork in the tube, connecting a 4-patch ring to two 2-patch rings.
  // Given the 2x2 control arrays
  //  {Ta0,Ba0} {Tb0,Bb0} of the prefork's 4-patch ring,
  //  {Ta1,Ba1} {Tb1,Bb1} of the posfork's 4-patch ring,
  //  {Ta2,Ba2} {Tb2,Bb2} of the following 2-patch rings.
  
  // Control points for top patches, minus the lateral seams:
  #local PTa = array[4][4];
  #local PTa[1][0] = (Ta0[0][1] + Ta1[0][0])/2;
  #local PTa[2][0] = (Ta0[1][1] + Ta1[1][0])/2;
  #local PTa[1][1] = Ta1[0][0];
  #local PTa[2][1] = Ta1[1][0];
  #local PTa[1][2] = Ta1[0][1];
  #local PTa[2][2] = Ta1[1][1];
  #local PTa[1][3] = (Ta1[0][1] + Ta2[0][0])/2;
  #local PTa[2][3] = (Ta1[1][1] + Ta2[1][0])/2;
  
  #local PTb = array[4][4];
  #local PTb[1][0] = (Tb0[0][1] + Tb1[0][0])/2;
  #local PTb[2][0] = (Tb0[1][1] + Tb1[1][0])/2;
  #local PTb[1][1] = Tb1[0][0];
  #local PTb[2][1] = Tb1[1][0];
  #local PTb[1][2] = Tb1[0][1];
  #local PTb[2][2] = Tb1[1][1];
  #local PTb[1][3] = (Tb1[0][1] + Tb2[0][0])/2;
  #local PTb[2][3] = (Tb1[1][1] + Tb2[1][0])/2;
  
  // Control points for bottom patches, minus the lateral seams:
  #local PBa = array[4][4];
  #local PBa[1][0] = (Ba0[0][1] + Ba1[0][0])/2;
  #local PBa[2][0] = (Ba0[1][1] + Ba1[1][0])/2;
  #local PBa[1][1] = Ba1[0][0];
  #local PBa[2][1] = Ba1[1][0];
  #local PBa[1][2] = Ba1[0][1];
  #local PBa[2][2] = Ba1[1][1];
  #local PBa[1][3] = (Ba1[0][1] + Ba2[0][0])/2;
  #local PBa[2][3] = (Ba1[1][1] + Ba2[1][0])/2;
  
  #local PBb = array[4][4];
  #local PBb[1][0] = (Bb0[0][1] + Bb1[0][0])/2;
  #local PBb[2][0] = (Bb0[1][1] + Bb1[1][0])/2;
  #local PBb[1][1] = Bb1[0][0];
  #local PBb[2][1] = Bb1[1][0];
  #local PBb[1][2] = Bb1[0][1];
  #local PBb[2][2] = Bb1[1][1];
  #local PBb[1][3] = (Bb1[0][1] + Bb2[0][0])/2;
  #local PBb[2][3] = (Bb1[1][1] + Bb2[1][0])/2;
 
  // Control points along the lateral seams, minus singular corners:
  #local PTa[0][0] = (PTa[1][0] + PBa[1][0])/2; #local PBa[0][0] = PTa[0][0];
  #local PTa[0][1] = (PTa[1][1] + PBa[1][1])/2; #local PBa[0][1] = PTa[0][1];
  #local PTa[0][2] = (PTa[1][2] + PBa[1][2])/2; #local PBa[0][2] = PTa[0][2];
  #local PTa[0][3] = (PTa[1][3] + PBa[1][3])/2; #local PBa[0][3] = PTa[0][3];
  
  #local PTa[3][1] = (PTa[2][1] + PBa[2][1])/2; #local PBa[3][1] = PTa[3][1];
  #local PTa[3][2] = (PTa[2][2] + PBa[2][2])/2; #local PBa[3][2] = PTa[3][2];
  #local PTa[3][3] = (PTa[2][3] + PBa[2][3])/2; #local PBa[3][3] = PTa[3][3];
  
  #local PTb[0][1] = (PTb[1][1] + PBb[1][1])/2; #local PBb[0][1] = PTb[0][1];
  #local PTb[0][2] = (PTb[1][2] + PBb[1][2])/2; #local PBb[0][2] = PTb[0][2];
  #local PTb[0][3] = (PTb[1][3] + PBb[1][3])/2; #local PBb[0][3] = PTb[0][3];

  #local PTb[3][0] = (PTb[2][0] + PBb[2][0])/2; #local PBb[3][0] = PTb[3][0];
  #local PTb[3][1] = (PTb[2][1] + PBb[2][1])/2; #local PBb[3][1] = PTb[3][1];
  #local PTb[3][2] = (PTb[2][2] + PBb[2][2])/2; #local PBb[3][2] = PTb[3][2];
  #local PTb[3][3] = (PTb[2][3] + PBb[2][3])/2; #local PBb[3][3] = PTb[3][3];
  
  // Control points at singular corners:
  #local Psing = (PTa[2][0] + PTb[1][0] + PBa[2][0] + PBb[1][0])/4;
  #local PTa[3][0] = Psing;
  #local PTb[0][0] = Psing;
  #local PBa[3][0] = Psing;
  #local PBb[0][0] = Psing;

  union{
    #debug "\nposfork Ta\n"
    object{ bzpatch(PTa, txT, rad, txg) }
    #debug "\nposfork Tb\n"
    object{ bzpatch(PTb, txT, rad, txg) }
    #debug "\nposfork Ba\n"
    object{ bzpatch(PBa, txB, rad, txg) }
    #debug "\nposfork Bb\n"
    object{ bzpatch(PBb, txB, rad, txg) }
  }

#end