math::trig.3

视频监控网络部分的协议ddns,的模块的实现代码,请大家大胆指正.

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.\" ========================================================================
.\"
.IX Title "Math::Trig 3"
.TH Math::Trig 3 "2007-12-18" "perl v5.10.0" "Perl Programmers Reference Guide"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
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.SH "NAME"
Math::Trig \- trigonometric functions
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&    use Math::Trig;
\&
\&    $x = tan(0.9);
\&    $y = acos(3.7);
\&    $z = asin(2.4);
\&
\&    $halfpi = pi/2;
\&
\&    $rad = deg2rad(120);
\&
\&    # Import constants pi2, pip2, pip4 (2*pi, pi/2, pi/4).
\&    use Math::Trig \*(Aq:pi\*(Aq;
\&
\&    # Import the conversions between cartesian/spherical/cylindrical.
\&    use Math::Trig \*(Aq:radial\*(Aq;
\&
\&        # Import the great circle formulas.
\&    use Math::Trig \*(Aq:great_circle\*(Aq;
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
\&\f(CW\*(C`Math::Trig\*(C'\fR defines many trigonometric functions not defined by the
core Perl which defines only the \f(CW\*(C`sin()\*(C'\fR and \f(CW\*(C`cos()\*(C'\fR.  The constant
\&\fBpi\fR is also defined as are a few convenience functions for angle
conversions, and \fIgreat circle formulas\fR for spherical movement.
.SH "TRIGONOMETRIC FUNCTIONS"
.IX Header "TRIGONOMETRIC FUNCTIONS"
The tangent
.IP "\fBtan\fR" 4
.IX Item "tan"
.PP
The cofunctions of the sine, cosine, and tangent (cosec/csc and cotan/cot
are aliases)
.PP
\&\fBcsc\fR, \fBcosec\fR, \fBsec\fR, \fBsec\fR, \fBcot\fR, \fBcotan\fR
.PP
The arcus (also known as the inverse) functions of the sine, cosine,
and tangent
.PP
\&\fBasin\fR, \fBacos\fR, \fBatan\fR
.PP
The principal value of the arc tangent of y/x
.PP
\&\fBatan2\fR(y, x)
.PP
The arcus cofunctions of the sine, cosine, and tangent (acosec/acsc
and acotan/acot are aliases).  Note that atan2(0, 0) is not well-defined.
.PP
\&\fBacsc\fR, \fBacosec\fR, \fBasec\fR, \fBacot\fR, \fBacotan\fR
.PP
The hyperbolic sine, cosine, and tangent
.PP
\&\fBsinh\fR, \fBcosh\fR, \fBtanh\fR
.PP
The cofunctions of the hyperbolic sine, cosine, and tangent (cosech/csch
and cotanh/coth are aliases)
.PP
\&\fBcsch\fR, \fBcosech\fR, \fBsech\fR, \fBcoth\fR, \fBcotanh\fR
.PP
The arcus (also known as the inverse) functions of the hyperbolic
sine, cosine, and tangent
.PP
\&\fBasinh\fR, \fBacosh\fR, \fBatanh\fR
.PP
The arcus cofunctions of the hyperbolic sine, cosine, and tangent
(acsch/acosech and acoth/acotanh are aliases)
.PP
\&\fBacsch\fR, \fBacosech\fR, \fBasech\fR, \fBacoth\fR, \fBacotanh\fR
.PP
The trigonometric constant \fBpi\fR and some of handy multiples
of it are also defined.
.PP
\&\fBpi, pi2, pi4, pip2, pip4\fR
.Sh "\s-1ERRORS\s0 \s-1DUE\s0 \s-1TO\s0 \s-1DIVISION\s0 \s-1BY\s0 \s-1ZERO\s0"
.IX Subsection "ERRORS DUE TO DIVISION BY ZERO"
The following functions
.PP
.Vb 10
\&    acoth
\&    acsc
\&    acsch
\&    asec
\&    asech
\&    atanh
\&    cot
\&    coth
\&    csc
\&    csch
\&    sec
\&    sech
\&    tan
\&    tanh
.Ve
.PP
cannot be computed for all arguments because that would mean dividing
by zero or taking logarithm of zero. These situations cause fatal
runtime errors looking like this
.PP
.Vb 3
\&    cot(0): Division by zero.
\&    (Because in the definition of cot(0), the divisor sin(0) is 0)
\&    Died at ...
.Ve
.PP
or
.PP
.Vb 2
\&    atanh(\-1): Logarithm of zero.
\&    Died at...
.Ve
.PP
For the \f(CW\*(C`csc\*(C'\fR, \f(CW\*(C`cot\*(C'\fR, \f(CW\*(C`asec\*(C'\fR, \f(CW\*(C`acsc\*(C'\fR, \f(CW\*(C`acot\*(C'\fR, \f(CW\*(C`csch\*(C'\fR, \f(CW\*(C`coth\*(C'\fR,
\&\f(CW\*(C`asech\*(C'\fR, \f(CW\*(C`acsch\*(C'\fR, the argument cannot be \f(CW0\fR (zero).  For the
\&\f(CW\*(C`atanh\*(C'\fR, \f(CW\*(C`acoth\*(C'\fR, the argument cannot be \f(CW1\fR (one).  For the
\&\f(CW\*(C`atanh\*(C'\fR, \f(CW\*(C`acoth\*(C'\fR, the argument cannot be \f(CW\*(C`\-1\*(C'\fR (minus one).  For the
\&\f(CW\*(C`tan\*(C'\fR, \f(CW\*(C`sec\*(C'\fR, \f(CW\*(C`tanh\*(C'\fR, \f(CW\*(C`sech\*(C'\fR, the argument cannot be \fIpi/2 + k *
pi\fR, where \fIk\fR is any integer.
.PP
Note that atan2(0, 0) is not well-defined.
.Sh "\s-1SIMPLE\s0 (\s-1REAL\s0) \s-1ARGUMENTS\s0, \s-1COMPLEX\s0 \s-1RESULTS\s0"
.IX Subsection "SIMPLE (REAL) ARGUMENTS, COMPLEX RESULTS"
Please note that some of the trigonometric functions can break out
from the \fBreal axis\fR into the \fBcomplex plane\fR. For example
\&\f(CWasin(2)\fR has no definition for plain real numbers but it has
definition for complex numbers.
.PP
In Perl terms this means that supplying the usual Perl numbers (also
known as scalars, please see perldata) as input for the
trigonometric functions might produce as output results that no more
are simple real numbers: instead they are complex numbers.
.PP
The \f(CW\*(C`Math::Trig\*(C'\fR handles this by using the \f(CW\*(C`Math::Complex\*(C'\fR package
which knows how to handle complex numbers, please see Math::Complex
for more information. In practice you need not to worry about getting
complex numbers as results because the \f(CW\*(C`Math::Complex\*(C'\fR takes care of
details like for example how to display complex numbers. For example:
.PP
.Vb 1
\&    print asin(2), "\en";
.Ve
.PP
should produce something like this (take or leave few last decimals):
.PP
.Vb 1
\&    1.5707963267949\-1.31695789692482i
.Ve
.PP
That is, a complex number with the real part of approximately \f(CW1.571\fR
and the imaginary part of approximately \f(CW\*(C`\-1.317\*(C'\fR.
.SH "PLANE ANGLE CONVERSIONS"
.IX Header "PLANE ANGLE CONVERSIONS"
(Plane, 2\-dimensional) angles may be converted with the following functions.
.IP "deg2rad" 4
.IX Item "deg2rad"
.Vb 1
\&    $radians  = deg2rad($degrees);
.Ve
.IP "grad2rad" 4
.IX Item "grad2rad"
.Vb 1
\&    $radians  = grad2rad($gradians);