Bzier curve via subdivision

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Bézier curve via subdivision
Every polynomial curve of degree
can be associated with a unique n-variate
symmetric polynomial such
that The polynomial is referred to as the polar
form or blossom of
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Bézier curve via subdivision
Any polynomial curve defined over
interval a,b can be considered as a Bézier
curve with control points
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Bézier curve via subdivision
0½1
001
011
½½½
0½½
½½1
00½
½11
000
111
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Bézier curve via subdivision
Theorem
Proof of the theorem it is enough to show that
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Bézier curve via subdivision
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Bézier curve via subdivision
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Bézier curve via subdivision