Module src.util.cubic_polynomial

Module for handling and finding roots of cubic polynomaials
Used for bezier interpolation.

Classes

class CubicPolynomial (a: float, b: float, c: float, d: float)

Args

a

Coefficient for the third degree term.

b

Coefficient for the second degree term.

c

Coefficient for the first degree term.

d

Coefficient for the constant term.

Methods

def get_function(self) ‑> Callable[[float], float]

Makes a callable function from the coefficients

Gives the function $f(t) = at^3 + bt^2 + ct + d$

Returns

f

A callable function float $\to$ float.

def solve(self, x: Union[float, NoneType] = 0) ‑> Tuple[complex, complex, complex]

Solves the equation $$at^3 +bt^2 + ct + d = x$$ by depressing the coefficients into a general cubic and using the substitution $t = u - \frac{b}{3a}$.

Args

x

The right hand side of the equation

Returns

A tuple of the three solutions, either real or complex