Module: geodesic/Math

Some useful mathematical constants and functions (mainly for internal use).

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Members

(static) atanh

Inverse hyperbolic tangent.

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(static) cbrt

Cube root function.

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(static, constant) degree :number

The factor to convert degrees to radians.

Type:
  • number
Source:

(static, constant) digits :number

The number of digits of precision in floating-point numbers.

Type:
  • number
Source:

(static, constant) epsilon :number

The machine epsilon.

Type:
  • number
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(static) log1p

The log1p function.

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Methods

(static) AngDiff(x, y) → {object}

The exact difference of two angles reduced to [−180°, 180°]

Parameters:
Name Type Description
x number

the first angle in degrees.
y number

the second angle in degrees.
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Returns:

diff the exact difference, diff.d + diff.e = y − x mod 360°.

This computes z = y − x exactly, reduced to [−180°, 180°]; and then sets z = d + e where d is the nearest representable number to z and e is the truncation error. If z = ±0° or ±180°, then the sign of d is given by the sign of y − x. The maximum absolute value of e is 2−26 (for doubles).

Type
object

(static) AngNormalize(x) → {number}

Normalize an angle.

Parameters:
Name Type Description
x number

the angle in degrees.
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Returns:

the angle reduced to the range [−180°, 180°].

The range of x is unrestricted. If the result is ±0° or ±180° then the sign is the sign of \e x.

Type
number

(static) AngRound(x) → {number}

Coarsen a value close to zero.

Parameters:
Name Type Description
x number
Source:
Returns:

the coarsened value.

Type
number

(static) LatFix(x) → {number}

Normalize a latitude.

Parameters:
Name Type Description
x number

the angle in degrees.
Source:
Returns:

x if it is in the range [−90°, 90°], otherwise return NaN.

Type
number

(static) atan2d(y, x)

Evaluate the atan2 function with the result in degrees

Parameters:
Name Type Description
y number
x number
Source:
Returns:

atan2(y, x) in degrees, in the range [−180° 180°].

(static) copysign(x, y) → {number}

Copy the sign.

Parameters:
Name Type Description
x number

gives the magitude of the result.
y number

gives the sign of the result.
Source:
Returns:

value with the magnitude of x and with the sign of y.

Type
number

(static) hypot(x, y) → {number}

The hypotenuse function.

Parameters:
Name Type Description
x number

the first side.
y number

the second side.
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Returns:

the hypotenuse.

Type
number

(static) polyval(N, p, x) → {number}

Evaluate a polynomial.

Parameters:
Name Type Description
N integer

the order of the polynomial.
p array

the coefficient array (of size N + 1) (leading order coefficient first)
x number

the variable.
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Returns:

the value of the polynomial.

Type
number

(static) remainder(x, y) → {number}

The remainder function.

Parameters:
Name Type Description
x number

the numerator of the division
y number

the denominator of the division
Source:
Returns:

the remainder in the range [−y/2, y/2].

The range of x is unrestricted; y must be positive.

Type
number

(static) sincosd(x) → {object}

Evaluate the sine and cosine function with the argument in degrees

Parameters:
Name Type Description
x number

in degrees.
Source:
Returns:

r with r.s = sin(x) and r.c = cos(x).

Type
object

(static) sincosde(x, t) → {object}

Evaluate the sine and cosine with reduced argument plus correction

Parameters:
Name Type Description
x number

reduced angle in degrees.
t number

correction in degrees.
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Returns:

r with r.s = sin(x + t) and r.c = cos(x + t).

Type
object

(static) sq(x) → {number}

Square a number.

Parameters:
Name Type Description
x number

the number.
Source:
Returns:

the square.

Type
number

(static) sum(u, v) → {object}

An error-free sum.

Parameters:
Name Type Description
u number
v number
Source:
Returns:

sum with sum.s = round(u + v) and sum.t is u + v − round(u + v)

Type
object