%-----------------------------------------------------------------%
%----Tensor product toolbox---------------------------------------%
%-----------------------------------------------------------------%
DEF UDOMAIN=(INTERVALS:1:16);
DEF UVDOMAIN=(INTERVALS:1:16)*(INTERVALS:1:16);

DEF ConstFunTensor = IF:<IsSeq, AA:ConstFunTensor, K>;  
DEF TensorInnerProd = InnerProd ~ AA:FlatTensor ;  
DEF FlatTensor = IF:<IsSeqOf:IsFun, ID,CAT ~ AA:FlatTensor> ;  
DEF TensorProd = AA:DistlTerm ~ DISTR;  
DEF DistlTerm = IF:<IsFun ~ S2, FunProd, AA:DistlTerm ~ DISTL>;  
DEF FunProd (f,g::IsFun) = f ~ [S1] * g ~ TAIL;  

DEF myTensorProdSurface 
	(uBasis,vBasis::IsSeq)(ControlPoints::IsMatOf:IsPoint) = 
(AA:TensorInnerProd ~ DISTL):
  < BivariateBasis, AA:ConstFunTensor:CoordTensors >
WHERE
  CoordTensors = (TRANS~AA:TRANS):controlPoints,
  BivariateBasis = TensorProd:< uBasis, vBasis >
END;

%-----------------------------------------------------------------%
%----Bilinear                     --------------------------------%
%-----------------------------------------------------------------%


DEF myBilinearSurface (ControlPoints::IsMatOf:IsPoint) = 
  TensorProdSurface:< BernsteinBasis:S1:1, BernsteinBasis:S1:1>:ControlPoints;


DEF OUT=STRUCT:<MAP:(myBilinearSurface:<<<0,0,0>,<1,1,0>>,<<0,1,1>,<1,1,1>>>):UVDOMAIN,
                MKFRAME>;  
  
DEF OUT=STRUCT:<MAP:(myBilinearSurface:<<<0,0,0>,<1,1,0>>,<<1,0,1>,<1,1,1>>>):UVDOMAIN,
                MKFRAME>;

%-----------------------------------------------------------------%
%----Biquadratic surface generator--------------------------------%
%-----------------------------------------------------------------%

DEF myBiquadraticSurface (ControlPoints::IsMatOf:IsPoint) = 
  TensorProdSurface:< Basis, Basis >:ControlPoints
  WHERE
    Basis = < u2, u1, u0 >,
    u2 = (k:2 * uu) - (K:3 * u) + K:1,
    u1 = (k:4 * u) - (k:4 * uu),
    u0 = (k:2 * uu) - u,  uu = u * u,  u = s1
  END;


DEF Mapping = myBiquadraticSurface:<  
     <<0,0,1>, <1,0,0>,<2,0,1>>,   
     <<0,1,-1>, <1,1,0>,<2,1,2>>,  
     <<0,2,0>, <1,2,1>,<2,2,0>> >;  
DEF out = STRUCT:<MAP:Mapping:UVDOMAIN,mkframe>;

DEF Mapping = myBiquadraticSurface:<  
     <<0,0,1>, <1,0,0>,<2,0,1>>,   
     <<0,1,0.5>, <1,1,0.5>,<2,1,0.5>>,  
     <<0,2,0>, <1,2,1>,<2,2,0>> >;  
DEF out = STRUCT:<MAP:Mapping:UVDOMAIN,mkframe>;    

DEF Mapping = BiquadraticSurface:<  
      <<0,0,0>, <2,0,1>,<3,1,1>>,   
      <<1,3,-1>,<3,2,0>,<4,2,0>>,  
      <<0,9,0>, <2,5,1>,<3,3,2>> >;  
DEF out = MAP:Mapping:(Intervals:1:10 * Intervals:1:10);  

%-----------------------------------------------------------------%
%---Bicubic Hermite surface generator-----------------------------%
%-----------------------------------------------------------------%


DEF HermiteSurface (ControlPoints::IsMatOf:IsPoint) =  
  TensorProdSurface:< HermiteBasis:S1, HermiteBasis:S1 >:ControlPoints;

DEF Mapping1 = HermiteSurface: <  
    <<0,0,0>, <1,0,0>, <0,0,1>, <0,0,-1>>,   
    <<0,1,0>, <1,1,0>, <0,0,-1>,<0,0,1>>,  
    <<0,0,1>, <0,0,-1>,<0,0,1>, <0,0,-1>>,  
    <<0,0,-1>,<0,0,1>, <0,0,-1>, <0,0,1>> >;  
DEF out1 = STRUCT:<MAP:Mapping1:UVDOMAIN,
                  MKFRAME>; 

DEF Mapping2 = HermiteSurface: <  
    <<0,0,0>, <1,0,0>, <0,0,1>, <0,0,-1>>,   
    <<0,1,0>, <1,1,0>, <0,0,-1>,<0,0,1>>,  
    <<0,0,1>, <0,0,-1>,<1,1,0>, <-1,1,0>>,  
    <<0,0,-1>,<0,0,1>, <1,-1,0>, <-1,-1,0>> >;  
DEF out2 = STRUCT:<MAP:Mapping2:UVDOMAIN,
                  MKFRAME>; 
                  
DEF Mapping3 = HermiteSurface: <  
    <<0,0,0>, <1,0,0>, <0,0,1>, <0,0,-1>>,   
    <<0,1,0>, <1,1,0>, <0,0,-1>,<0,0,1>>,  
    <<0,0,1>, <0,0,-1>,<0,0,-1>, <0,0,1>>,  
    <<0,0,-1>,<0,0,1>, <0,0,1>, <0,0,-1>> >;
      
DEF out3 = STRUCT:<MAP:Mapping3:UVDOMAIN,
                  MKFRAME>;
    
CLASS MATERIAL_T(color::IsRGBColor) ISA BASEMATERIAL =<color,color,0.2,BLACK,0.2,0.8>;
      
DEF out=STRUCT:<out1 MATERIAL MATERIAL_T:BLUE,
               % out2 MATERIAL MATERIAL_T:RED,%
                out3 MATERIAL MATERIAL_T:GREEN>;

DEF Mapping = HermiteSurface: <  
    <<0,0,0>, <2,0,1>, <3,1,1>, <4,1,1>>,   
    <<1,3,-1>,<3,2,0>, <4,2,0>, <4,2,0>>,  
    <<0,4,0>, <2,4,1>, <3,3,2>, <5,3,2>>,  
    <<0,6,0>, <2,5,1>, <3,4,1>, <4,4,0>> >;  
DEF out = MAP:Mapping:(Intervals:1:10 * Intervals:1:10);  

%-----------------------------------------------------------------%
%----Bezier surface generator (arbitrary degrees)-----------------%
%-----------------------------------------------------------------%

DEF BezierSurface (ControlPoints::IsMatOf:IsPoint) = TensorProdSurface:
  < BernsteinBasis:S1:m, BernsteinBasis:S1:n >:ControlPoints
WHERE
  m = LEN:ControlPoints - 1,
  n = (LEN ~ S1):ControlPoints - 1
END;


DEF points1 = <<0,0,0>,<1,0,1>>; 
DEF points2 = <<0,1,1>,<1,1,0>>; 
DEF pointArray = < points1, points2 >;  
DEF surf = MAP:(BezierSurface:pointArray):UVDOMAIN;
DEF OUT = STRUCT:<surf,
                  polymarker:1:(CAT:pointArray),
                  mkframe>;

                
DEF points1 = <<0,0,0>,<1,0,1>,<2,0,0>>; 
DEF points2 = <<0,1,1>,<1,1,2>,<2,1,1>>; 
DEF points3 = <<0,2,0>,<1,2,1>,<2,2,0>>; 
DEF pointArray = < points1, points2,points3 >;  
DEF surf = MAP:(BezierSurface:pointArray):UVDOMAIN;
DEF OUT = STRUCT:<surf,
				  MAP:(CONS:(Bezier:S1:points2)):UDOMAIN,
                  polymarker:1:(CAT:pointArray),
                  mkframe>;

DEF points1 = <<0,0,0>,<1,0,1>,<2,0,0>>; 
DEF points2 = <<0,1,0.5>,<1,1,0.5>,<2,1,0.5>>; 
DEF points3 = <<0,2,1>,<1,2,0>,<2,2,1>>; 
DEF pointArray = < points1, points2,points3 >;  
DEF surf = MAP:(BezierSurface:pointArray):UVDOMAIN;
DEF OUT = STRUCT:<surf,
				  MAP:(CONS:(Bezier:S1:points2)):UDOMAIN,
                  polymarker:1:(CAT:pointArray),
                  mkframe>;
  
                  
DEF points1 = <<0,0,0>,<1,0,1>,<2,0,-1>,<3,0,0>>; 
DEF points2 = <<0,1,-1>,<1,1,2>,<2,1,-2>,<3,1,1>>; 
DEF points3 = <<0,2,1>,<1,2,-2>,<2,2,2>,<3,2,-1>>; 
DEF points4 = <<0,3,0>,<1,3,-1>,<2,3,1>,<3,3,0>>; 
DEF pointArray = < points1, points2,points3,points4 >;  
DEF surf = MAP:(BezierSurface:pointArray):UVDOMAIN;
DEF OUT = STRUCT:<surf,
				  MAP:(CONS:(Bezier:S1:points2)):UDOMAIN,
				  MAP:(CONS:(Bezier:S1:points3)):UDOMAIN,
                  polymarker:1:(CAT:pointArray),
                  mkframe>;

DEF points1 = <<0,0,0>,<0,3,4>,<0,6,3>,<0,10,0>>; 
DEF points2 = <<3,0,2>,<2,2.5,5>,<3,6,5>,<4,8,2>>;  
DEF points3 = <<6,0,2>,<8,3,5>,<7,6,4.5>,<6,10,2.5>>;  
DEF points4 = <<10,0,0>,<11,3,4>,<11,6,3>,<10,9,0>>;  
DEF pointArray = < points1, points2, points3, points4 >;  
DEF out = MAP:(BezierSurface:pointArray):UVDOMAIN;