< cpp‎ | numeric‎ | complex
Defined in header <complex>
template< class T >
complex<T> proj( const complex<T>& z );
(1) (since C++11)
std::complex<long double> proj( long double z );
(2) (since C++11)
template< class DoubleOrIngeter >
std::complex<double> proj( DoubleOrInteger z );
(3) (since C++11)
std::complex<float> proj( float z );
(4) (since C++11)

Returns the projection of the complex number z onto the Riemann sphere.

For most z, std::proj(z)==z, but all complex infinities, even the numbers where one component is infinite and the other is NaN, become positive real infinity, (INFINITY, 0) or (INFINITY, -0). The sign of the imaginary (zero) component is the sign of std::imag(z).

(since C++11)Additional overloads are provided for float, double, long double, and all integer types, which are treated as complex numbers with zero imaginary component.


[edit] Parameters

z - complex value

[edit] Return value

the projection of z onto the Riemann sphere

[edit] Example

#include <iostream>
#include <complex>
int main()
    std::complex<double> c1(1, 2);
    std::cout << "proj" << c1 << " = " << std::proj(c1) << '\n';
    std::complex<double> c2(INFINITY, -1);
    std::cout << "proj" << c2 << " = " << std::proj(c2) << '\n';
    std::complex<double> c3(0, -INFINITY);
    std::cout << "proj" << c3 << " = " << std::proj(c3) << '\n';


proj(1,2) = (1,2)
proj(inf,-1) = (inf,-0)
proj(0,-inf) = (inf,-0)

[edit] See also

returns the magnitude of a complex number
(function template) [edit]
returns the squared magnitude
(function template) [edit]
constructs a complex number from magnitude and phase angle
(function template) [edit]
C documentation for cproj