sorbetto.geometry.conic module

class sorbetto.geometry.conic.Conic(a, b, c, d, e, f, name: str | None = None)[source]

Bases: AbstractGeometricObject2D

This class is used to represent conic sections. \(a x^2 + b x y + c y^2 + d x + e y + f = 0\) See https://en.wikipedia.org/wiki/Conic_section

property a: float

The coefficient \(a\) that multiplies \(x^2 y^0\) in the equation of the conic section.

Returns:: The paramater \(a\) of the conic section.
Return type:: float

property b: float

The coefficient \(b\) that multiplies \(x^1 y^1\) in the equation of the conic section.

Returns:: The paramater \(b\) of the conic section.
Return type:: float

property c: float

The coefficient \(c\) that multiplies \(x^0 y^2\) in the equation of the conic section.

Returns:: The paramater \(c\) of the conic section.
Return type:: float

classify(tol: float = 1e-08) → str[source]

Classify the conic section.

Parameters:: tol (float, optional) – the numerical tolerance, positive. Defaults to 1e-8.
Returns:: a name, in english, for the conic section type
Return type:: str

property d: float

The coefficient \(d\) that multiplies \(x^1 y^0\) in the equation of the conic section.

Returns:: The paramater \(d\) of the conic section.
Return type:: float

draw(fig: Figure, ax: Axes, extent, **plt_kwargs)[source]

Draws the part of the conic section that is within some axis-aligned box in some given Pyplot axes.

Parameters:

fig (_type_) – a Pyplot Figure object
ax (_type_) – a Pyplot Axes object
extent (_type_) – the axis-aligned box \((x_{min}, x_{max}, y_{min}, y_{max})\)
plt_kwargs – options for Pyplot’s plot command.

property e: float

The coefficient \(e\) that multiplies \(x^0 y^1\) in the equation of the conic section.

Returns:: The paramater \(e\) of the conic section.
Return type:: float

property f: float

The coefficient \(a\) that multiplies \(x^0 y^0\) in the equation of the conic section.

Returns:: The paramater \(f\) of the conic section.
Return type:: float

getLargestX(y)[source]

Computes the largest value of \(x\), for any given \(y\).

Parameters:: y (_type_) – \(y\)
Returns:: the largest value of \(x\), for the given \(y\).
Return type:: _type_

getLargestY(x)[source]

Computes the largest value of \(y\), for any given \(x\).

Parameters:: x (_type_) – \(x\)
Returns:: the largest value of \(y\), for the given \(x\).
Return type:: _type_

getMatrixRepresentation() → ndarray[source]

Computes the 3 by 3 matrix representation of the conic section. See https://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections

Returns:: the matrix representation
Return type:: np.nparray

getSmallestX(y)[source]

Computes the smallest value of \(x\), for any given \(y\).

Parameters:: y (_type_) – \(y\)
Returns:: the smallest value of \(x\), for the given \(y\).
Return type:: _type_

getSmallestY(x)[source]

Computes the smallest value of \(y\), for any given \(x\).

Parameters:: x (_type_) – \(x\)
Returns:: the smallest value of \(y\), for the given \(x\).
Return type:: _type_

isCircle(tol: float = 1e-08) → bool[source]

Test if the conic section is a circle.

Parameters:: tol (float, optional) – the numerical tolerance, positive. Defaults to 1e-8.
Returns:: True if the conic section is a circle; False otherwise
Return type:: bool

isDegenerate(tol: float = 1e-08) → bool[source]

See https://en.wikipedia.org/wiki/Degenerate_conic

Parameters:: tol (float, optional) – the numerical tolerance, positive. Defaults to 1e-8.
Returns:: True if the conic section is degenerate; False otherwise
Return type:: bool

isEllipse(tol: float = 1e-08) → bool[source]

Test if the conic section is an ellipse.

Parameters:: tol (float, optional) – the numerical tolerance, positive. Defaults to 1e-8.
Returns:: True if the conic section is an ellipse; False otherwise
Return type:: bool

isHyperbola(tol: float = 1e-08) → bool[source]

Test if the conic section is a hyperbola.

Parameters:: tol (float, optional) – the numerical tolerance, positive. Defaults to 1e-8.
Returns:: True if the conic section is a hyperbola; False otherwise
Return type:: bool

isParabola(tol: float = 1e-08) → bool[source]

Test if the conic section is a parabola.

Parameters:: tol (float, optional) – the numerical tolerance, positive. Defaults to 1e-8.
Returns:: True if the conic section is a parabola; False otherwise
Return type:: bool

isRectangularHyperbola(tol: float = 1e-08) → bool[source]

Test if the conic section is a rectangular hyperbola.

Parameters:: tol (float, optional) – the numerical tolerance, positive. Defaults to 1e-8.
Returns:: True if the conic section is a rectangular hyperbola; False otherwise
Return type:: bool