DEF myBlend (Basis::IsSeq) (ControlPoints::IsSeq) = 
   (AA:innerProd ~ DISTL): 
      < Basis, (AA:(AA:K) ~ TRANS):ControlPoints >;  

DEF subsets (h::IsIntPos)(seq::IsSeq) = 
    (CONS ~ AA:(AS:SEL ~ FROMTO ~ [ID - K:h + K:1,ID])):(h..LEN:seq):seq;
    
subsets:4:(1..10);

subsets:5:(1..10);

DEF mySpline (Curve::IsFun) = STRUCT ~ AA:Curve ~ subsets:4;


%------------------------------------------------------------%
%----Cubic cardinal------------------------------------------%
%------------------------------------------------------------%

DEF CubicCardinalBasis = < C0,C1,C2,C3 >
WHERE
    C0 = ((k:0 - a) * u3) + ((k:2  *  a) * u2) - (a  *  u),
    C1 = ((k:2 - a) * u3) + ((a - k:3) * u2) + (k:1),
    C2 = ((a - k:2) * u3) + ((k:3 - k:2 * a) * u2) + (a * u),
    C3 = (a * u3) - (a * u2),
    u = s1, u2 = u * u, u3 = u2 * u, a = k:1
END;

DEF CubicCardinalGraph =
	STRUCT ~ [box,MAP:[u,C3], k:(T:1:1), 
	          box,MAP:[u,C2], k:(T:1:1),
              box,MAP:[u,C1], k:(T:1:1), 
              box,MAP:[u,C0]]
WHERE 
    C0 = ((k:0 - a) * u3) + ((k:2  *  a) * u2) - (a  *  u),
    C1 = ((k:2 - a) * u3) + ((a - k:3) * u2) + (k:1),
    C2 = ((a - k:2) * u3) + ((k:3 - k:2 * a) * u2) + (a * u),
    C3 = (a * u3) - (a * u2),
    u = s1, u2 = u * u, u3 = u2 * u, a = k:1,
    Box = K:(@1:(CUBOID:<1,1>))
END;

DEF OUT=CubicCardinalGraph:(intervals:1:24);


DEF myCubicCardinal (segmentDomain::IsPol) (q1,q2,q3,q4::IsSeq) = 
  MAP:(Blend:CubicCardinalBasis:<q1,q2,q3,q4>):segmentDomain;
 
DEF myCubicCardinal (segmentDomain::IsPol) (q1,q2,q3,q4::IsSeq) = 
  MAP:(Blend:CubicCardinalBasis:<q1,q2,q3,q4>):segmentDomain
WHERE 
  segmentDomain = Intervals:1:splineSampling
END; 
  
DEF CubicCardinalSpline(segmentDomain::IsPol)=
     ((mySpline:myCubicCardinal):segmentDomain);


DEF out = ( STRUCT~
	        [ polyline, polymarker:2 ,mySpline:(myCubicCardinal:domain) ]):
  <<0,-1>,<-1,0>,<-2,1>,<0,3>,<2,1>,<1,0>,<0,-1>>
WHERE
  domain = intervals:1:20
END;
out;

DEF CubicUBspline (segmentDomain::IsPol) (q1,q2,q3,q4::IsSeq) = 
  MAP:(Blend:CubicUBsplineBasis:<q1,q2,q3,q4>):segmentDomain;

DEF out = ( STRUCT~
	        [ polyline, polymarker:2 ,Spline:(CubicUBspline:domain) ]):
  <<0,-1>,<-1,0>,<-2,1>,<0,3>,<2,1>,<1,0>,<0,-1>>
WHERE
  domain = intervals:1:20
END;


%------------------------------------------------------------%
%-----Cubic uniform B-spline---------------------------------%
%------------------------------------------------------------%

DEF myCubicUBsplineBasis = < B0,B1,B2,B3 >
WHERE
    B0 = a  *  ((k:3 * u2) - (k:1 * u3) - (k:3 * u) + (k:1)),
    B1 = a  *  ((k:3 * u3) - (k:6 * u2) + (k:4)),
    B2 = a  *  ((k:3 * u2) - (k:3 * u3) + (k:3 * u) + (k:1)),
    B3 = a  *  u3,
    u = s1, u2 = u * u, u3 = u2 * u, a = k:1/k:6
END;

DEF CubicUBsplineGraph = 
	STRUCT ~ [Box, MAP:[u,B3], k:(T:1:1), 
	          Box, MAP:[u,B2], k:(T:1:1),
              Box, MAP:[u,B1], k:(T:1:1), 
              Box, MAP:[u,B0]]
WHERE
    B0 = a  *  ((k:3 * u2) - (k:1 * u3) - (k:3 * u) + (k:1)),
    B1 = a  *  ((k:3 * u3) - (k:6 * u2) + (k:4)),
    B2 = a  *  ((k:3 * u2) - (k:3 * u3) + (k:3 * u) + (k:1)),
    B3 = a  *  u3,
    u = s1, u2 = u * u, u3 = u2 * u, a = k:1/k:6,
    Box = (K ~ @1 ~ CUBOID):<1,1>
END;

DEF OUT=CubicUBsplineGraph:(intervals:1:24);

DEF myCubicUBspline (segmentDomain::IsPol) (q1,q2,q3,q4::IsSeq) = 
  MAP:(Blend:CubicUBsplineBasis:<q1,q2,q3,q4>):segmentDomain;

DEF out = ( STRUCT~
	        [ polyline, polymarker:2 ,Spline:(CubicUBspline:domain) ]):
  <<0,-1>,<-1,0>,<-2,1>,<0,3>,<2,1>,<1,0>,<0,-1>>
WHERE
  domain = intervals:1:20
END;
out;

DEF out = ( STRUCT~
	        [ polyline, polymarker:2 ,Spline:(CubicUBspline:domain) ]):
  <<0,-1>,<-2,1>,<0,3>,<2,1>,<0,-1>>
WHERE
  domain = intervals:1:20
END;
out;

DEF out = ( STRUCT~
	        [ polyline,   polymarker:2 ,Spline:(CubicUBspline:domain), Spline:(CubicCardinal:domain) ]):
  <<-3,6,0>,<-4,2,2>,<-3,-1,4>,<-1,1,-1>,<1.5,1.5,-2>,<3,4,2>,<5,5,0>,
  <7,2,3>,<6,-2,0>,<2,-3,0>>
WHERE
  domain = intervals:1:20
END;
out;