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### Cubic Spline Curve

The diagram shows a geometric construction
for a cubic spline curve.

The curve is parametrized by t. Given A, B, C, D. the following constraints are set:

AE = t AB ; BF = t BC; CG = t CD; EH = t EF; FI = t FG; HJ = t HI

The curve created by tracing J as t goes from 0 to 1 has the following
properties:

It is tangent to AB at A. It lies inside the convex hull of A,B,C,D. (The convex hull is the
smallest convex polygon containing the points)

In fact the curve is a cubic in t. Can you use a computer algebra
system to work out its coefficients in terms of the coordinates of A,
B, C, D?

If you are interested in this applet, you may like our Interactive Symbolic Geometry software Geometry Expressions.