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1.3.2 Arithmetic operations of polynomials in Bernstein form
Arithmetic operations between polynomials are often required for shape
interrogation (see for example Chaps. 4,
5, etc.). Farouki and Rajan [106] provide formulae
for such arithmetic operations of polynomials in Bernstein form. Let
the two polynomials
and
of degree
and
with
Bernstein coefficients
and
be as follows:
(1.25)
Addition and subtraction
If the degrees of the two polynomials are the same, i.e.
, we simply
add or subtract the coefficients
(1.26)
If
, we need to first degree elevate
times using
(1.23) and then add
or subtract the coefficients
(1.27)
Multiplication
Multiplication of two polynomials of degree
and
yields a degree
polynomial
(1.28)
Next: 1.3.3 Numerical condition of
Up: 1.3 Bézier curves and
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December 2009