Polynomial Classes in Monomial and Bezier Bases

Polynomial Classes in Monomial and Bezier Bases ***

This section of the implementation utilizes the basic arithmetic operations of a "Numeric" implementation to represent polynomials. Two representations are available: the standard monomial base and the Bezier representation. These are implemented in the classes PolynomialStandard and PolynomialBezier, respectively.

Both classes implement many smaller algorithms later needed for implementing the three root finding algorithms. Among the base algorithms are:

• conversion between the two polynomial representations
• constructing a polynomial from given roots
• finding the roots of quadratic and cubic polynomial using the direct formulas.
• evaluation of the polynomial at a give position (using Horner or de Casteljau)
• splitting a Bezier representation using de Castljau's algorithm
• calculating the convex hull of the Bezier polygon using Jarvis's march