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Bézier Curves
Urs Oswald osurs@bluewin.ch http://www.ursoswald.ch September 11, 2002
Quadratic Bézier curves
From the above equations, it follows that
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Cubic Bézier curves
From (2), we get
![]() From (1), ![]() In fig. 2, if ![]() ![]() ![]() ![]() ![]() ![]()
Bézier curves of arbitrary order
For distinct points
![]()
Theorem 1 (Bézier curves of order 1)
For points
![]() ![]()
PROOF: By the above definition,
Theorem 2
For any non-negative integer
![]() ![]() ![]()
PROOF: By induction on ![]() which is correct by the first part of the definition. For ![]() ![]() ![]() ![]() We get
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