Splines.html

Splines

Example from the PscFunctions package

With the help of routines of the PscFunctions package one can obtain general parametric equations of splines.
The CPscSpline routine generates a sequence of two or three functions that represents parametric equation of the spline with specified end conditions. The spline curve passes through the given point set (first argument of the procedure). The type of end conditions is determined by the second (optional) argument.

`>`	restart; with(PscFunctions): x,y:=CPscSpline([[0,0],[-12,4],[-9,6],[-15,14],[-6,12],[-15/2,18],[-3,16],[0,22],[3,16],[15/2,18],[6,12],[15,14],[9,6],[12,4],[0,0]],endpoints=natural): plot([x(t),y(t),t=0..14],thickness=2,scaling=CONSTRAINED,color=BLACK); X=x(t); Y=y(t);

The fPscSpline routine computes an expression that represents explicit equation of the polynomial spline of any degre.
In the following example equations of some splines of different degree passing through the same points constructed.

> LL:=[[-5,-2],[-3,-3],[1,2],[3,2],[4,0],[5,-1],[6,0],[8,-2],[9,4],[12,-1],[15,4],[20,3],[24,-1],[25,0]]:
Z2:=x->fPscSpline(LL,x,degree=2):
Z3:=x->fPscSpline(LL,x,degree=3):
Z4:=x->fPscSpline(LL,x,degree=4):
Z5:=x->fPscSpline(LL,x,degree=5):
pnts:=plots[pointplot](LL,symbolsize=20):
pys:=plot([Z2(x),Z3(x),Z4(x),Z5(x)],x=LL[1,1]..LL[nops(LL),1],thickness=2,scaling=CONSTRAINED,color=[BLACK,BLUE,GREEN,RED]):
plots[display](pnts,pys);
'Z3'=Z3(x);