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Cell["Bezier Curves via G.M.T", "Title"],

Cell["Joseph O'Rourke", "Subtitle",
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Illustrates how to compute a Bezier curve from four input points, using a \
matrix formulation.  The powers of t for the polynomial are placed in T.  The \
coordinates of the four points are placed in the geometric array G.  M is a \
\"magic matrix\" that encodes already the solution of the simultaneous \
equations to find the coefficients.  Then G.M.T gives the Bezier curves \
directly.

At the end of the file, there is an exploration of the \"best\" Bezier curve \
to match the circle, and an analysis of how different they are.\
\>", "Subsubtitle",
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M is the fixed matrix that encodes the solution of the system of eqs.\
\>", "Text",
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Cell["\<\
G is the geometric data, the four points.  In this case:
p0=(0,0), p1=(1,0), p2=(1/2,0), p3=(1,1)
So curve runs from origin to (2,1).
All the x-coords are in the 1st row, all the y-coords in the 2nd row.  A bit \
awkward format...\
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If one were doing this by hand, probably easiest to first compute G.M:\
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Here is a plot of the resulting curve:
(AspectRatio->Automatic means draw it without distortion)\
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Note: 
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In this version, a variable u is used for the length of the tangent vector.
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Cell["\<\
Figure out how different the two curves are by evaluating the absolute value \
of the differences at many t values. (The variable tt is used because t is \
used in the curve and circle equations.)  Just check the x-coordinate.\
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