GeographicLib: GeographicLib::AuxAngle Class Reference (original) (raw)

An accurate representation of angles. More...

#include <[GeographicLib/AuxAngle.hpp](AuxAngle%5F8hpp%5Fsource.html)>

An accurate representation of angles.

This class is an implementation of the methods described in

• C. F. F. Karney, On auxiliary latitudes, Survey Review 56(395), 165–180 (2024); preprint arXiv:2212.05818.

An angle is represented be the y and x coordinates of a point in the 2d plane. The two coordinates are proportional to the sine and cosine of the angle. This allows angles close to the cardinal points to be represented accurately. It also saves on unnecessary recomputations of trigonometric functions of the angle. Only angles in [−180°, 180°] can be represented. (A possible extension would be to keep count of the number of turns.)

Example of use:

#include

#include

#include

int main(int argc, const char* const argv[]) {

try {

double f = 0.5;

std::cout << std::fixed << std::setprecision(4);

for (int d = 0; d <= 90; d+=10) {

angle phi(angle::degrees(d)), beta(phi);

beta.y() *= (1 - f);

std::cout << d << " " << beta.degrees() << "\n";

}

}

catch (const std::exception& e) {

std::cerr << "Caught exception: " << e.what() << "\n";

return 1;

}

}

Header for the GeographicLib::AuxAngle class.

int main(int argc, const char *const argv[])

Header for GeographicLib::Utility class.

An accurate representation of angles.

Definition at line 47 of file AuxAngle.hpp.

The constructor.

Parameters

Note

the y coordinate is specified first.

Warning

either x or y can be infinite, but not both.

The defaults (x = 1 and y = 0) are such that

• no arguments gives an angle of 0;
• 1 argument specifies the tangent of the angle.

Definition at line 65 of file AuxAngle.hpp.

Referenced by copyquadrant(), degrees(), lam(), lamd(), NaN(), normalized(), and radians().

◆ y() [1/2]

Returns

the y component. This is the sine of the angle if the AuxAngle has been normalized.

Definition at line 70 of file AuxAngle.hpp.

Referenced by GeographicLib::AuxLatitude::Authalic(), GeographicLib::Ellipsoid::CircleHeight(), GeographicLib::AuxLatitude::Convert(), copyquadrant(), GeographicLib::DAuxLatitude::DConvert(), degrees(), GeographicLib::AuxLatitude::FromAuxiliary(), GeographicLib::AuxLatitude::Geocentric(), normalized(), GeographicLib::AuxLatitude::Parametric(), and GeographicLib::AuxLatitude::Rectifying().

◆ x() [1/2]

Returns

the x component. This is the cosine of the angle if the AuxAngle has been normalized.

Definition at line 75 of file AuxAngle.hpp.

Referenced by GeographicLib::AuxLatitude::Authalic(), GeographicLib::Ellipsoid::CircleRadius(), GeographicLib::AuxLatitude::Conformal(), GeographicLib::AuxLatitude::Convert(), copyquadrant(), GeographicLib::DAuxLatitude::DConvert(), degrees(), GeographicLib::AuxLatitude::FromAuxiliary(), GeographicLib::AuxLatitude::Geocentric(), normalized(), operator+=(), GeographicLib::AuxLatitude::Parametric(), and GeographicLib::AuxLatitude::Rectifying().

◆ y() [2/2]

Returns

a reference to the y component. This allows this component to be altered.

Definition at line 80 of file AuxAngle.hpp.

◆ x() [2/2]

Returns

a reference to the x component. This allows this component to be altered.

Definition at line 85 of file AuxAngle.hpp.

◆ degrees() [1/2]

◆ radians() [1/2]

◆ lam() [1/2]

◆ lamd() [1/2]

◆ tan()

Returns

the tangent of the angle.

Definition at line 113 of file AuxAngle.hpp.

Referenced by GeographicLib::AuxLatitude::Authalic(), GeographicLib::AuxLatitude::Conformal(), GeographicLib::DAuxLatitude::DIsometric(), GeographicLib::DAuxLatitude::DParametric(), GeographicLib::DAuxLatitude::DRectifying(), GeographicLib::AuxLatitude::FromAuxiliary(), GeographicLib::Rhumb::GenInverse(), GeographicLib::RhumbLine::GenPosition(), lam(), lamd(), normalized(), operator+=(), and GeographicLib::AuxLatitude::Rectifying().

◆ normalized()

◆ normalize()

Normalize the AuxAngle in place so that the y and x components are equal to the sine and cosine of the angle.

Definition at line 124 of file AuxAngle.hpp.

◆ copyquadrant()

◆ operator+=()

Add an AuxAngle.

Parameters

Returns

a reference to the new AuxAngle.

The addition is done in place, altering the current AuxAngle.

Warning

Neither *this nor p should have an infinite component. If necessary, invoke AuxAngle::normalize on these angles first.

Definition at line 48 of file AuxAngle.cpp.

References tan(), and x().

◆ degrees() [2/2]

◆ radians() [2/2]

Construct and return an AuxAngle specied as an angle in radians.

Parameters

Returns

the corresponding AuxAngle.

This allows a new AuxAngle to be initialized as an angle in radians with

Math::real radians() const

Definition at line 209 of file AuxAngle.hpp.

References AuxAngle().

◆ lam() [2/2]

Construct and return an AuxAngle specied by the lambertian of the angle.

Parameters

Returns

the corresponding AuxAngle.

This allows a new AuxAngle to be initialized given the lambertian with

Note

this sets the angle χ to gd(ψ) = atan(sinh(ψ)).

Definition at line 214 of file AuxAngle.hpp.

References AuxAngle().

◆ lamd() [2/2]

Construct and return an AuxAngle specied by the lambertian of the angle in degrees.

Parameters

Returns

the corresponding AuxAngle.

This allows a new AuxAngle to be initialized given the lambertian with

Note

this sets the angle χ to gd(ψ) = atan(sinh(ψ)).

Definition at line 219 of file AuxAngle.hpp.

References AuxAngle(), and GeographicLib::Math::degree().

◆ NaN()

The documentation for this class was generated from the following files:

• AuxAngle.hpp
• AuxAngle.cpp