ostk.mathematics.geometry.Angle¶

class Angle( self: ostk.mathematics.geometry.Angle, value: ostk.core.type.Real, unit: ostk::mathematics::geometry::Angle::Unit, )¶

Bases: pybind11_object

Create an angle with specified value and unit.

Parameters:

value (float) -- The numerical value of the angle.
unit (Angle.Unit) -- The unit of the angle (Radian, Degree, etc.).

Example

>>> angle = Angle(3.14159, Angle.Unit.Radian)
>>> angle = Angle(180.0, Angle.Unit.Degree)

Methods

`arcminutes`	Create an angle from a value in arcminutes.
`arcseconds`	Create an angle from a value in arcseconds.
`between`	Overloaded function.
`degrees`	Create an angle from a value in degrees.
`get_unit`	Get the unit of the angle.
`half_pi`	Create an angle of π/2 radians (90 degrees).
`in_arcminutes`	Overloaded function.
`in_arcseconds`	Overloaded function.
`in_degrees`	Overloaded function.
`in_radians`	Overloaded function.
`in_revolutions`	Get the angle value in revolutions.
`in_unit`	Get the angle value in a specific unit.
`is_defined`	Check if the angle is defined.
`is_near`	Check if this angle is near another angle within a tolerance.
`is_negative`	Check if the angle is negative.
`is_zero`	Check if the angle is zero.
`pi`	Create an angle of π radians (180 degrees).
`radians`	Create an angle from a value in radians.
`revolutions`	Create an angle from a value in revolutions.
`string_from_unit`	Get the string representation of an angle unit.
`symbol_from_unit`	Get the symbol representation of an angle unit.
`to_string`	Convert the angle to a string representation.
`two_pi`	Create an angle of 2π radians (360 degrees).
`undefined`	Create an undefined angle.
`zero`	Create a zero angle.

class Unit(self: ostk.mathematics.geometry.Angle.Unit, value: int)¶

Bases: pybind11_object

Members:

Undefined

Radian

Degree

Arcminute

Arcsecond

Revolution

property name¶

__add__( self: ostk.mathematics.geometry.Angle, arg0: ostk.mathematics.geometry.Angle, ) → ostk.mathematics.geometry.Angle¶

__mul__( self: ostk.mathematics.geometry.Angle, arg0: ostk.core.type.Real, ) → ostk.mathematics.geometry.Angle¶

static arcminutes(value: ostk.core.type.Real) → ostk.mathematics.geometry.Angle¶

Create an angle from a value in arcminutes.

Parameters:: value (float) -- The angle value in arcminutes.
Returns:: An angle with the specified value in arcminutes.
Return type:: Angle

Example

>>> angle = Angle.arcminutes(60.0)
>>> angle.in_degrees()  # 1.0

static arcseconds(value: ostk.core.type.Real) → ostk.mathematics.geometry.Angle¶

Create an angle from a value in arcseconds.

Parameters:: value (float) -- The angle value in arcseconds.
Returns:: An angle with the specified value in arcseconds.
Return type:: Angle

Example

>>> angle = Angle.arcseconds(3600.0)
>>> angle.in_degrees()  # 1.0

static between(*args, **kwargs)¶

Overloaded function.

between(first_vector: numpy.ndarray[numpy.float64[2, 1]], second_vector: numpy.ndarray[numpy.float64[2, 1]]) -> ostk.mathematics.geometry.Angle
Calculate the angle between two 2D vectors.
Args:
first_vector (numpy.array): The first vector. second_vector (numpy.array): The second vector.

Returns:
Angle: The angle between the vectors.

Example:
>>> v1 = numpy.array([1.0, 0.0]) >>> v2 = numpy.array([0.0, 1.0]) >>> angle = Angle.between(v1, v2) >>> angle.in_degrees() # 90.0
between(first_vector: numpy.ndarray[numpy.float64[3, 1]], second_vector: numpy.ndarray[numpy.float64[3, 1]]) -> ostk.mathematics.geometry.Angle
Calculate the angle between two 3D vectors.
Args:
first_vector (numpy.array): The first vector. second_vector (numpy.array): The second vector.

Returns:
Angle: The angle between the vectors.

Example:
>>> v1 = numpy.array([1.0, 0.0, 0.0]) >>> v2 = numpy.array([0.0, 1.0, 0.0]) >>> angle = Angle.between(v1, v2) >>> angle.in_degrees() # 90.0

static degrees(value: ostk.core.type.Real) → ostk.mathematics.geometry.Angle¶

Create an angle from a value in degrees.

Parameters:: value (float) -- The angle value in degrees.
Returns:: An angle with the specified value in degrees.
Return type:: Angle

Example

>>> angle = Angle.degrees(180.0)
>>> angle.in_radians()  # ~3.14159

get_unit( self: ostk.mathematics.geometry.Angle, ) → ostk::mathematics::geometry::Angle::Unit¶

Get the unit of the angle.

Returns:: The unit of the angle.
Return type:: Angle.Unit

Example

>>> angle = Angle.degrees(90.0)
>>> angle.get_unit()  # Angle.Unit.Degree

static half_pi() → ostk.mathematics.geometry.Angle¶

Create an angle of π/2 radians (90 degrees).

Returns:: An angle of π/2 radians.
Return type:: Angle

Example

>>> half_pi = Angle.half_pi()
>>> half_pi.in_degrees()  # 90.0

in_arcminutes(*args, **kwargs)¶

Overloaded function.

in_arcminutes(self: ostk.mathematics.geometry.Angle) -> ostk.core.type.Real
Get the angle value in arcminutes.
Returns:
float: The angle value in arcminutes.

Example:
>>> angle = Angle.degrees(1.0) >>> angle.in_arcminutes() # 60.0
in_arcminutes(self: ostk.mathematics.geometry.Angle, lower_bound: ostk.core.type.Real, upper_bound: ostk.core.type.Real) -> ostk.core.type.Real

Get the angle value in arcminutes within specified bounds.

Args:
lower_bound (float): The lower bound in arcminutes. upper_bound (float): The upper bound in arcminutes.

Returns:
float: The angle value in arcminutes, wrapped within bounds.

in_arcseconds(*args, **kwargs)¶

Overloaded function.

in_arcseconds(self: ostk.mathematics.geometry.Angle) -> ostk.core.type.Real
Get the angle value in arcseconds.
Returns:
float: The angle value in arcseconds.

Example:
>>> angle = Angle.degrees(1.0) >>> angle.in_arcseconds() # 3600.0
in_arcseconds(self: ostk.mathematics.geometry.Angle, lower_bound: ostk.core.type.Real, upper_bound: ostk.core.type.Real) -> ostk.core.type.Real

Get the angle value in arcseconds within specified bounds.

Args:
lower_bound (float): The lower bound in arcseconds. upper_bound (float): The upper bound in arcseconds.

Returns:
float: The angle value in arcseconds, wrapped within bounds.

in_degrees(*args, **kwargs)¶

Overloaded function.

in_degrees(self: ostk.mathematics.geometry.Angle) -> ostk.core.type.Real
Get the angle value in degrees.
Returns:
float: The angle value in degrees.

Example:
>>> angle = Angle.radians(3.14159) >>> angle.in_degrees() # ~180.0
in_degrees(self: ostk.mathematics.geometry.Angle, lower_bound: ostk.core.type.Real, upper_bound: ostk.core.type.Real) -> ostk.core.type.Real
Get the angle value in degrees within specified bounds.
Args:
lower_bound (float): The lower bound in degrees. upper_bound (float): The upper bound in degrees.

Returns:
float: The angle value in degrees, wrapped within bounds.

Example:
>>> angle = Angle.degrees(450.0) >>> angle.in_degrees(-180.0, 180.0) # 90.0

in_radians(*args, **kwargs)¶

Overloaded function.

in_radians(self: ostk.mathematics.geometry.Angle) -> ostk.core.type.Real
Get the angle value in radians.
Returns:
float: The angle value in radians.

Example:
>>> angle = Angle.degrees(180.0) >>> angle.in_radians() # ~3.14159
in_radians(self: ostk.mathematics.geometry.Angle, lower_bound: ostk.core.type.Real, upper_bound: ostk.core.type.Real) -> ostk.core.type.Real
Get the angle value in radians within specified bounds.
Args:
lower_bound (float): The lower bound in radians. upper_bound (float): The upper bound in radians.

Returns:
float: The angle value in radians, wrapped within bounds.

Example:
>>> angle = Angle.radians(7.0) >>> angle.in_radians(-3.14159, 3.14159) # Wrapped to [-π, π]

in_revolutions(self: ostk.mathematics.geometry.Angle) → ostk.core.type.Real¶

Get the angle value in revolutions.

Returns:: The angle value in revolutions.
Return type:: float

Example

>>> angle = Angle.degrees(360.0)
>>> angle.in_revolutions()  # 1.0

in_unit( self: ostk.mathematics.geometry.Angle, unit: ostk::mathematics::geometry::Angle::Unit, ) → ostk.core.type.Real¶

Get the angle value in a specific unit.

Parameters:: unit (Angle.Unit) -- The unit to convert to.
Returns:: The angle value in the specified unit.
Return type:: float

Example

>>> angle = Angle.degrees(180.0)
>>> angle.in_unit(Angle.Unit.Radian)  # ~3.14159

is_defined(self: ostk.mathematics.geometry.Angle) → bool¶

Check if the angle is defined.

Returns:: True if the angle is defined, False otherwise.
Return type:: bool

Example

>>> angle = Angle.radians(1.0)
>>> angle.is_defined()  # True

is_near( self: ostk.mathematics.geometry.Angle, angle: ostk.mathematics.geometry.Angle, tolerance: ostk.mathematics.geometry.Angle, ) → bool¶

Check if this angle is near another angle within a tolerance.

Parameters:

angle (Angle) -- The angle to compare with.
tolerance (Angle) -- The tolerance for comparison.

Returns:

True if angles are within tolerance, False otherwise.

Return type:

bool

Example

>>> angle1 = Angle.degrees(30.0)
>>> angle2 = Angle.degrees(30.1)
>>> tolerance = Angle.degrees(0.2)
>>> angle1.is_near(angle2, tolerance)  # True

is_negative(self: ostk.mathematics.geometry.Angle) → bool¶

Check if the angle is negative.

Returns:: True if the angle is negative, False otherwise.
Return type:: bool

Example

>>> angle = Angle.degrees(-30.0)
>>> angle.is_negative()  # True

is_zero(self: ostk.mathematics.geometry.Angle) → bool¶

Check if the angle is zero.

Returns:: True if the angle is zero, False otherwise.
Return type:: bool

Example

>>> angle = Angle.zero()
>>> angle.is_zero()  # True

static pi() → ostk.mathematics.geometry.Angle¶

Create an angle of π radians (180 degrees).

Returns:: An angle of π radians.
Return type:: Angle

Example

>>> pi = Angle.pi()
>>> pi.in_degrees()  # 180.0

static radians(value: ostk.core.type.Real) → ostk.mathematics.geometry.Angle¶

Create an angle from a value in radians.

Parameters:: value (float) -- The angle value in radians.
Returns:: An angle with the specified value in radians.
Return type:: Angle

Example

>>> angle = Angle.radians(3.14159)
>>> angle.in_degrees()  # ~180.0

static revolutions(value: ostk.core.type.Real) → ostk.mathematics.geometry.Angle¶

Create an angle from a value in revolutions.

Parameters:: value (float) -- The angle value in revolutions.
Returns:: An angle with the specified value in revolutions.
Return type:: Angle

Example

>>> angle = Angle.revolutions(1.0)
>>> angle.in_degrees()  # 360.0

static string_from_unit( unit: ostk::mathematics::geometry::Angle::Unit, ) → ostk.core.type.String¶

Get the string representation of an angle unit.

Parameters:: unit (Angle.Unit) -- The angle unit.
Returns:: String representation of the unit.
Return type:: str

Example

>>> Angle.string_from_unit(Angle.Unit.Degree)  # "Degree"

static symbol_from_unit( unit: ostk::mathematics::geometry::Angle::Unit, ) → ostk.core.type.String¶

Get the symbol representation of an angle unit.

Parameters:: unit (Angle.Unit) -- The angle unit.
Returns:: Symbol representation of the unit.
Return type:: str

Example

>>> Angle.symbol_from_unit(Angle.Unit.Degree)  # "deg"
>>> Angle.symbol_from_unit(Angle.Unit.Radian)  # "rad"

to_string( self: ostk.mathematics.geometry.Angle, precision: ostk.core.type.Integer = Integer.undefined(), ) → ostk.core.type.String¶

Convert the angle to a string representation.

Parameters:: precision (int, optional) -- The precision for floating point numbers. Defaults to Integer.undefined().
Returns:: String representation of the angle.
Return type:: str

Example

>>> angle = Angle.degrees(90.0)
>>> angle.to_string()  # "90.0 [deg]"

static two_pi() → ostk.mathematics.geometry.Angle¶

Create an angle of 2π radians (360 degrees).

Returns:: An angle of 2π radians.
Return type:: Angle

Example

>>> two_pi = Angle.two_pi()
>>> two_pi.in_degrees()  # 360.0

static undefined() → ostk.mathematics.geometry.Angle¶

Create an undefined angle.

Returns:: An undefined angle.
Return type:: Angle

Example

>>> undefined_angle = Angle.undefined()
>>> undefined_angle.is_defined()  # False

static zero() → ostk.mathematics.geometry.Angle¶

Create a zero angle.

Returns:: A zero angle (0 radians).
Return type:: Angle

Example

>>> zero_angle = Angle.zero()
>>> zero_angle.is_zero()  # True