// Last edited on 2024-05-01 18:31:46 by stolfi

#include "bez.inc"

#macro retalho_p(P, U, V)

  #local p0 =  bez_pos(V, P[0][0], P[0][1], P[0][2], P[0][3]);
  #local p1 =  bez_pos(V, P[1][0], P[1][1], P[1][2], P[1][3]);
  #local p2 =  bez_pos(V, P[2][0], P[2][1], P[2][2], P[2][3]);
  #local p3 =  bez_pos(V, P[3][0], P[3][1], P[3][2], P[3][3]);

  #local p = bez_pos(U, p0, p1, p2, p3);

  p
#end

#macro retalho_dpdV(P, U, V)
 
  #local dp0dV =  bez_diff(V, P[0][0], P[0][1], P[0][2], P[0][3]);
  #local dp1dV =  bez_diff(V, P[1][0], P[1][1], P[1][2], P[1][3]);
  #local dp2dV =  bez_diff(V, P[2][0], P[2][1], P[2][2], P[2][3]);
  #local dp3dV =  bez_diff(V, P[3][0], P[3][1], P[3][2], P[3][3]);

  #local dpdV = bez_pos(U, dp0dV, dp1dV, dp2dV, dp3dV);

  dpdV
#end

#macro retalho_dpdU(P, U, V)
 
  #local dp0dU =  bez_diff(U, P[0][0], P[1][0], P[2][0], P[3][0]);
  #local dp1dU =  bez_diff(U, P[0][1], P[1][1], P[2][1], P[3][1]);
  #local dp2dU =  bez_diff(U, P[0][2], P[1][2], P[2][2], P[3][2]);
  #local dp3dU =  bez_diff(U, P[0][3], P[1][3], P[2][3], P[3][3]);

  #local dpdU = bez_pos(v, dp0dU, dp1dU, dp2dU, dp3dU);

  dpdU
#end

#macro retalho_normal(P, U, V)

  #local dpdU = retalho_dpdU(P, U, V);
  #local dpdV = retalho_dpdV(P, U, V);
  
  #local norm = vnormalize(vcross(dpdU, dpdV))
  
  norm
#end