> restart;
> with(plots): with(linalg):
> deboor1 :=proc(degree,coeff1,knot,u)
> # De Boor Agorithmus zur Berechnung einer Koordinate der 
> # B-spline-Kurve fuer den Parameterwert u im Intervall i
> #	degree:	Polynomgrad der B-spline-Kurve s
> # coeff1:	Kontrollpunkte der B-spline-Kurve s
> # knot:	Knotenfolge 
> # u:	Parameterwert, berechnet wird s(u)
> #	i:	u's interval: knot[i]<= u < knot[i+1]
> # output:	s(u)
> #option trace;
> local k,j,t1,t2,coeffa,kn,i;
>  coeffa:=vector(30);
>  kn:=vectdim(knot);
>  i:=degree;
>  for j from 2 to kn-1 do if u > knot[j] then i:=j fi od;
> 	for j from i-degree+1 to i+1 do coeffa[j] :=coeff1[j] od;
> 	for k from 1 to degree do
>    for j from i+1 by (-1) to i-degree+k+1 do
>     t1 := (knot[j+degree-k] - u )/(knot[j+degree-k]-knot[j-1]);
> 		  t2 := 1.0-t1;
>     coeffa[j] :=t1* coeffa[j-1]+t2* coeffa[j];
> 	  od	
>  od;
> 	RETURN(coeffa[i+1])
> end:
> 
> # Grad 3 (kubische Splinekurve)
> knot:=vector(19,[-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10]): #
> Knotenvektor 
> coeff1:=vector(14): coeff0:=vector(14):
> # y-Koordinate der Kontrollpunkte
> for j from 1 to 14 do
> coeff1[j]:=evalf(sin(2*knot[j+3]+1)+cos(knot[j+3]-3/2)) od:
> # spezielle x-Koordinate fŸr kubische Splines
> for j from 1 to 14 do
> coeff0[j]:=evalf((knot[j+3]+knot[j+4]+knot[j+5])/3) od: 
> m:=101:
> z:= vector(m):
> a:=-5: b:=5: h:=(b-a)/(m-1):
>  for j from 1 to m do z[j]:=evalf(a+ (j-1)*h) od:
> #Anwendung des DeBoor Algorithmus fŸr y-Koordinate und x-Koordinate
>  for j from 1 to m do s[j]:=deboor1(3,coeff1,knot,z[j]);
>                       s0[j]:=deboor1(3,coeff0,knot,z[j]) od:
> # plotsetup(ps,plotoutput=`plot1.ps`,plotoptions=`noborder`);
>  F:=listplot([seq([s0[t],s[t]],t=1..m)],axes=NONE): #Druck der
> B-Spline-Kurve
>  G:=listplot([seq([coeff0[t],coeff1[t]],t=1..14)],axes=NONE): #Druck
> des Kontrollpolygons
> 
> H:=pointplot([seq([coeff0[t],coeff1[t]],t=1..14)],axes=NONE,symbol=CIR
> CLE): #Druck der Kontrollpunkte
>  display({F,G,H});
> 
> 
> #Grad 2 (quadratische Splinekurve)
> knot:=vector(18,[-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9]): #
> Knotenvektor 
> coeff1:=vector(15): coeff0:=vector(15):
> # y-Koordinate der Kontrollpunkte
> for j from 1 to 15 do
> coeff1[j]:=evalf(sin(2*knot[j+2]+1)+cos(knot[j+2]-3/2)) od:
> # spezielle x-Koordinate fŸr quadratische Splines
> for j from 1 to 15 do coeff0[j]:=evalf((knot[j+2]+knot[j+3])/2) od: 
> m:=101:
> z:= vector(m):
> a:=-6: b:=6: h:=(b-a)/(m-1):
> for j from 1 to m do z[j]:=evalf(a+ (j-1)*h) od:
> #Anwendung des DeBoor Algorithmus fŸr y-Koordinate und x-Koordinate
>  for j from 1 to m do s[j]:=deboor1(2,coeff1,knot,z[j]);
>                       s0[j]:=deboor1(2,coeff0,knot,z[j]) od:
>  # plotsetup(ps,plotoutput=`plot1.ps`,plotoptions=`noborder`);
>  F:=listplot([seq([s0[t],s[t]],t=1..m)],axes=NONE):
>  G:=listplot([seq([coeff0[t],coeff1[t]],t=1..15)],axes=NONE):
> 
> H:=pointplot([seq([coeff0[t],coeff1[t]],t=1..15)],axes=NONE,symbol=CIR
> CLE):
>  display({F,G,H});
Warning, new definition for norm
Warning, new definition for trace


>