PlaneOutline.html

Airplane outline

Example from the PscFunctions package

The CPscHermite routine computes a parametric equation of a piecewise-cubic interpolating Hermite polynomial of degree 3. This Hermite polynomial approximates 2D or 3D set of points. Coordinates of two ending points and tangent vectors to them uniquely determine segments of the curve. In some nodes left-hand and right-hand tangent vectors can not coincide.
The most of the following example contains a code of input data preparation.

> with(PscFunctions):
Lxy:=[[1,0],[1,2],[4,0],[4,2],[1,4],[2,12],[12,10],[12,12],[2,16],\
[2,22],[0,26],[-2,22],[-2,16],[-12,12],[-12,10],[-2,12],\
[-1,4],[-4,2],[-4,0],[-1,2],[-1,0],[1,0]]:
Lt:=[0,2,5,7,10,18,28,30,40,46,50,\
54,60,70,72,82,90,93,95,98,100,102]:
DER:=[[0,1],[[0,1],[3,-2]],[[3,-2],[0,1]],[[0,1],[-3,2]],\
[[-3,2],[1/2,1/2]],[[0,1],[5,-1]],[[5,-1],[0,1]],\
[[0,1],[-5,2]],[[-5,2],[0,1]],[0,1],\
[[-1,1],[-1,-1]],[0,-1],[[0,-1],[-5,-2]],[[-5,-2],[0,-1]],\
[[0,-1],[5,1]],[[5,1],[0,-1]],[[1/2,-1/2],[-3,-2]],\
[[-3,-2],[0,-1]],[[0,-1],[3,2]],[[3,2],[0,-1]],\
[[0,-1],[1,0]],[1,0]]:
xe,ye:=CPscHermite(Lxy,param=Lt,t,tanvectors=DER):
pp:=plot([xe,ye,t=0..102],thickness=2,color=BLACK,scaling=CONSTRAINED,numpoints=1000):
pnts:=plots[pointplot](Lxy,symbolsize=20):
plots[display](pnts,pp);

Here is a parametric equation of this curve.

`>`	'X'=xe; 'Y'=ye;