DEF UnitSphere=MAP:[COS~S1 * COS~S1,
                    COS~S1 * SIN~S2,
                    -~SIN~S1]
                   :((intervals:(2*PI):12)*(intervals:(2*PI):12));

DEF OUT=@1:UnitSphere;

DEF myProfileProdSurface (profile, section::IsSeqOf:IsFun) =
  < fx, fy, fz > 
WHERE
  fx = s1:profile * s1:section ~ [S2],
  fy = s1:profile * s2:section ~ [S2],
  fz = s3:profile
END;

        
DEF myRuledSurface (alpha,beta::IsSeqOf:IsFun) =
    alpha vectSum (S2 scalarVectProd beta);
    
DEF alpha = Bezier:S1:<<0.1,0,0>,<2,0,0>,<0,0,4>,<1,0,5>>;  
DEF beta = Bezier:S1:<<0,0,0>,<3,-0.5,0>,<3,3.5,0>,<0,3,0>>;  
DEF out = STRUCT:<
          MAP:alpha:(Intervals:1:20),  
          MAP:beta :(Intervals:1:20),  
          MAP:(ProfileProdSurface:< alpha, beta >):(Intervals:1:20 * Intervals:1:20)  
          >;  

    
DEF myRotationalSurface (ProfileCurve::IsSeqOf:IsFun) = 
  < f * cos ~ s2, f * sin ~ s2, g >
WHERE
  f = s1:ProfileCurve,
  g = s2:ProfileCurve
END;

DEF myProfileCurve = Blend:(BsplineBasis:4:<0,0,0,0,1,2,3,4,4,4,4>):    
                    <<0.1,0>,<2,0>,<6,1.5>,<6,4>,<2,5.5>,<2,6>,<3.5,6.5>>;  
DEF mydomain = Intervals:4:32 * Intervals:(2*PI):32;  
DEF out = MAP:(myRotationalSurface:myProfileCurve):mydomain; 

DEF myRuledSurface (alpha,beta::IsSeqOf:IsFun) = 
  alpha vectSum (S2 scalarVectProd beta);

DEF myv1 = BezierCurve:<<1,1,0>,<-1,1,0>,<1,-1,0>,<-1,-1,0>>;  
DEF myv2 = < COS ~ (K:(3*PI/2) * S1), SIN ~ (K:(3*PI/2) * S1), K:1 >;  
DEF mydomain = Intervals:1:10;  
DEF out = MAP:(myRuledSurface:< myv1, myv2 vectDiff myv1 >):(mydomain * mydomain);  


DEF CylindricalSurface (alpha::IsSeqOf:IsFun; beta::IsSeqOf:IsReal) = 
  RuledSurface:< alpha, AA:K:beta >;

DEF alpha = BezierCurve:<<1,1,0>,<-1,1,0>,<1,-1,0>,<-1,-1,0>>;  
DEF Udomain = Intervals:1:20;  
DEF Vdomain = Intervals:1:6;  
DEF surfaceDomain  = Udomain * Vdomain;  
DEF out = MAP:(CylindricalSurface:< alpha, <0,1,1> >):surfaceDomain;  

%-----------------------------------------------------------------%
%----Conical surface generator------------------------------------%
%-----------------------------------------------------------------%


DEF ConicalSurface (alpha::IsSeqOf:IsReal; beta::IsSeqOf:IsFun) = 
  RuledSurface:< AA:K:alpha, beta vectDiff AA:K:alpha >;

DEF beta = BezierCurve:<<1,1,0>,<-1,1,0>,<1,-1,0>,<-1,-1,0>>;  
DEF surfaceDomain  = Intervals:1:20 * Intervals:1:6;  
DEF out = MAP:(ConicalSurface:< <0,0,1>, beta >):surfaceDomain;