The geodesic Reference Manual

This is the geodesic Reference Manual, generated automatically by Declt version 4.0 beta 2 "William Riker" on Thu Sep 15 04:53:34 2022 GMT+0.

1 Introduction

* geodesic

  A Common lisp library to solve direct and inverse geodesic
  problem. It implements Charles Karney's method from this paper:
  https://doi.org/10.1007/s00190-012-0578-z

#+BEGIN_SRC lisp
  ;; Two examples from the paper
  (geodesic:direct (geodesic:radians 40) (geodesic:radians 30) 1e7)
   -> 0.7294308683855781d0
   ->  2.405847362846288d0
   ->  2.6021143369561823d0

  (geodesic:inverse (geodesic:radians -30) (geodesic:radians 29.9) (geodesic:radians 179.8))
   -> 1.9989832879260477d7
   -> 0.3160648483358468d0
   -> 2.825854840938509d0
#+END_SRC

2 Systems

The main system appears first, followed by any subsystem dependency.

geodesic

2.1 `geodesic`

Library for geodesic calculations.

Author

Manuel Giraud <manuel@ledu-giraud.fr>

License

ISC

Source

geodesic.asd.

Child Components

package.lisp (file).
util.lisp (file).
poly.lisp (file).
geodesic.lisp (file).

3 Files

Files are sorted by type and then listed depth-first from the systems components trees.

Lisp

3.1.1 `geodesic/geodesic.asd`

Source: geodesic.asd.
Parent Component: geodesic (system).
ASDF Systems: geodesic.

3.1.2 `geodesic/package.lisp`

Source: geodesic.asd.
Parent Component: geodesic (system).
Packages: geodesic.

3.1.3 `geodesic/util.lisp`

Dependency

package.lisp (file).

Source

geodesic.asd.

Parent Component

geodesic (system).

Public Interface

degrees (function).
parse-float (function).
radians (function).

Internals

normalize (function).
normalize-azimuth (function).
plusp-and-value (function).

3.1.4 `geodesic/poly.lisp`

Dependency

util.lisp (file).

Source

geodesic.asd.

Parent Component

geodesic (system).

Public Interface

cubic-roots (function).
quartic-roots (function).

Internals

3rt (function).
best-2-roots (function).
horner (function).

3.1.5 `geodesic/geodesic.lisp`

Dependency

poly.lisp (file).

Source

geodesic.asd.

Parent Component

geodesic (system).

Public Interface

direct (function).
inverse (function).

Internals

*a* (special variable).
*b* (special variable).
*f* (special variable).
*f-a-3* (special variable).
*n* (special variable).
*p-c-3* (special variable).
*square-e* (special variable).
*square-e-prime* (special variable).
a-1 (function).
a-2 (function).
ac-3 (function).
alpha-beta (function).
alpha0 (function).
alpha2 (function).
c-1 (function).
c-2 (function).
c-prime-1 (function).
delta-alpha1 (function).
dereduce-latitude (function).
i (function).
init-alpha1 (function).
j (function).
longitude (function).
m12 (function).
nearly-antipodal-p (function).
normalize-latitudes (function).
omega (function).
omega-bar (function).
reduce-latitude (function).
sigma (function).
sigma-tau (function).
sigma12 (function).
solve-triangle (function).
z1 (function).
z2 (function).

4 Packages

Packages are listed by definition order.

geodesic

4.1 `geodesic`

Source

package.lisp.

Use List

common-lisp.

Public Interface

cubic-roots (function).
degrees (function).
direct (function).
inverse (function).
parse-float (function).
quartic-roots (function).
radians (function).

Internals

*a* (special variable).
*b* (special variable).
*f* (special variable).
*f-a-3* (special variable).
*n* (special variable).
*p-c-3* (special variable).
*square-e* (special variable).
*square-e-prime* (special variable).
3rt (function).
a-1 (function).
a-2 (function).
ac-3 (function).
alpha-beta (function).
alpha0 (function).
alpha2 (function).
best-2-roots (function).
c-1 (function).
c-2 (function).
c-prime-1 (function).
delta-alpha1 (function).
dereduce-latitude (function).
horner (function).
i (function).
init-alpha1 (function).
j (function).
longitude (function).
m12 (function).
nearly-antipodal-p (function).
normalize (function).
normalize-azimuth (function).
normalize-latitudes (function).
omega (function).
omega-bar (function).
plusp-and-value (function).
reduce-latitude (function).
sigma (function).
sigma-tau (function).
sigma12 (function).
solve-triangle (function).
z1 (function).
z2 (function).

5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.

Public Interface
Internals

5.1 Public Interface

Ordinary functions

5.1.1 Ordinary functions

Function: cubic-roots (a b c d) ¶

Roots of a·z³ + b·z² + c·z + d.

Package: geodesic.
Source: poly.lisp.

Function: degrees (angle) ¶

Package: geodesic.
Source: util.lisp.

Function: direct (latitude azimuth distance) ¶

LATITUDE and AZIMUTH in radians. DISTANCE in meters.

Package: geodesic.
Source: geodesic.lisp.

Function: inverse (lat1 lat2 lon12) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: parse-float (string) ¶

Parse float STRING into an exact rational. XXX it is really simple and the form should be "{-}[0-9]+" or "{-}[0-9]*.[0-9]+"

Package: geodesic.
Source: util.lisp.

Function: quartic-roots (a b c d e) ¶

Package: geodesic.
Source: poly.lisp.

Function: radians (angle) ¶

Package: geodesic.
Source: util.lisp.

5.2 Internals

Special variables
Ordinary functions

5.2.1 Special variables

Special Variable: *a* ¶

WGS84 equatorial Earth radius in meter.

Package: geodesic.
Source: geodesic.lisp.

Special Variable: *b* ¶

Package: geodesic.
Source: geodesic.lisp.

Special Variable: *f* ¶

WGS84 ellipsoid flattening.

Package: geodesic.
Source: geodesic.lisp.

Special Variable: *f-a-3* ¶

Factors for A-3.

Package: geodesic.
Source: geodesic.lisp.

Special Variable: *n* ¶

Package: geodesic.
Source: geodesic.lisp.

Special Variable: *p-c-3* ¶

Polynomial factors for C-3.

Package: geodesic.
Source: geodesic.lisp.

Special Variable: *square-e* ¶

Package: geodesic.
Source: geodesic.lisp.

Special Variable: *square-e-prime* ¶

Package: geodesic.
Source: geodesic.lisp.

5.2.2 Ordinary functions

Function: 3rt (number) ¶

Cubic root that handles negative numbers.

Package: geodesic.
Source: poly.lisp.

Function: a-1 (epsilon) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: a-2 (epsilon) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: ac-3 (epsilon) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: alpha-beta (alpha0 sigma) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: alpha0 (beta azimuth) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: alpha2 (alpha1 beta1 beta2) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: best-2-roots (roots) ¶

Package: geodesic.
Source: poly.lisp.

Function: c-1 (epsilon) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: c-2 (epsilon) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: c-prime-1 (epsilon) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: delta-alpha1 (delta-l12 m12 alpha2 beta2) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: dereduce-latitude (beta) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: horner (x &rest p) ¶

Horner’s method of P at X.

Package: geodesic.
Source: poly.lisp.

Function: i (sigma an cn) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: init-alpha1 (lat1 lat2 lon12 beta1 beta2 omega12) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: j (sigma epsilon) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: longitude (omega alpha0 i3) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: m12 (k2 sigma1 sigma2 epsilon) ¶

Returns m12 and M12.

Package: geodesic.
Source: geodesic.lisp.

Function: nearly-antipodal-p (lat1 lat2 lon12) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: normalize (angle) ¶

Normalize angle between -π and π.

Package: geodesic.
Source: util.lisp.

Function: normalize-azimuth (angle) ¶

Normalize angle between 0 and π.

Package: geodesic.
Source: util.lisp.

Function: normalize-latitudes (lat1 lat2) ¶

lat1 <= 0 and lat1 <= lat2 <= -lat1 (i.e. lat2 is closest to zero).

Package: geodesic.
Source: geodesic.lisp.

Function: omega (alpha0 sigma) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: omega-bar (beta1 beta2) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: plusp-and-value (string) ¶

Package: geodesic.
Source: util.lisp.

Function: reduce-latitude (latitude) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: sigma (beta azimuth) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: sigma-tau (tau c-prime-1) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: sigma12 (beta1 beta2 omega12 z1) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: solve-triangle (alpha1 beta1 beta2) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: z1 (beta1 beta2 omega12) ¶

Package: geodesic.
Source: geodesic.lisp.

Function: z2 (beta1 beta2 omega12) ¶

Package: geodesic.
Source: geodesic.lisp.

Appendix A Indexes

Concepts
Functions
Variables
Data types

A.1 Concepts

A.2 Functions

Jump to:	3 A B C D F H I J L M N O P Q R S Z

	Index Entry	Section

3
	`3rt`:	Private ordinary functions

A
	`a-1`:	Private ordinary functions
	`a-2`:	Private ordinary functions
	`ac-3`:	Private ordinary functions
	`alpha-beta`:	Private ordinary functions
	`alpha0`:	Private ordinary functions
	`alpha2`:	Private ordinary functions

B
	`best-2-roots`:	Private ordinary functions

C
	`c-1`:	Private ordinary functions
	`c-2`:	Private ordinary functions
	`c-prime-1`:	Private ordinary functions
	`cubic-roots`:	Public ordinary functions

D
	`degrees`:	Public ordinary functions
	`delta-alpha1`:	Private ordinary functions
	`dereduce-latitude`:	Private ordinary functions
	`direct`:	Public ordinary functions

F
	`Function, 3rt`:	Private ordinary functions
	`Function, a-1`:	Private ordinary functions
	`Function, a-2`:	Private ordinary functions
	`Function, ac-3`:	Private ordinary functions
	`Function, alpha-beta`:	Private ordinary functions
	`Function, alpha0`:	Private ordinary functions
	`Function, alpha2`:	Private ordinary functions
	`Function, best-2-roots`:	Private ordinary functions
	`Function, c-1`:	Private ordinary functions
	`Function, c-2`:	Private ordinary functions
	`Function, c-prime-1`:	Private ordinary functions
	`Function, cubic-roots`:	Public ordinary functions
	`Function, degrees`:	Public ordinary functions
	`Function, delta-alpha1`:	Private ordinary functions
	`Function, dereduce-latitude`:	Private ordinary functions
	`Function, direct`:	Public ordinary functions
	`Function, horner`:	Private ordinary functions
	`Function, i`:	Private ordinary functions
	`Function, init-alpha1`:	Private ordinary functions
	`Function, inverse`:	Public ordinary functions
	`Function, j`:	Private ordinary functions
	`Function, longitude`:	Private ordinary functions
	`Function, m12`:	Private ordinary functions
	`Function, nearly-antipodal-p`:	Private ordinary functions
	`Function, normalize`:	Private ordinary functions
	`Function, normalize-azimuth`:	Private ordinary functions
	`Function, normalize-latitudes`:	Private ordinary functions
	`Function, omega`:	Private ordinary functions
	`Function, omega-bar`:	Private ordinary functions
	`Function, parse-float`:	Public ordinary functions
	`Function, plusp-and-value`:	Private ordinary functions
	`Function, quartic-roots`:	Public ordinary functions
	`Function, radians`:	Public ordinary functions
	`Function, reduce-latitude`:	Private ordinary functions
	`Function, sigma`:	Private ordinary functions
	`Function, sigma-tau`:	Private ordinary functions
	`Function, sigma12`:	Private ordinary functions
	`Function, solve-triangle`:	Private ordinary functions
	`Function, z1`:	Private ordinary functions
	`Function, z2`:	Private ordinary functions

H
	`horner`:	Private ordinary functions

I
	`i`:	Private ordinary functions
	`init-alpha1`:	Private ordinary functions
	`inverse`:	Public ordinary functions

J
	`j`:	Private ordinary functions

L
	`longitude`:	Private ordinary functions

M
	`m12`:	Private ordinary functions

N
	`nearly-antipodal-p`:	Private ordinary functions
	`normalize`:	Private ordinary functions
	`normalize-azimuth`:	Private ordinary functions
	`normalize-latitudes`:	Private ordinary functions

O
	`omega`:	Private ordinary functions
	`omega-bar`:	Private ordinary functions

P
	`parse-float`:	Public ordinary functions
	`plusp-and-value`:	Private ordinary functions

Q
	`quartic-roots`:	Public ordinary functions

R
	`radians`:	Public ordinary functions
	`reduce-latitude`:	Private ordinary functions

S
	`sigma`:	Private ordinary functions
	`sigma-tau`:	Private ordinary functions
	`sigma12`:	Private ordinary functions
	`solve-triangle`:	Private ordinary functions

Z
	`z1`:	Private ordinary functions
	`z2`:	Private ordinary functions

Jump to:	3 A B C D F H I J L M N O P Q R S Z

A.3 Variables

Jump to:	* S

	Index Entry	Section

*
	`a`:	Private special variables
	`b`:	Private special variables
	`f`:	Private special variables
	`f-a-3`:	Private special variables
	`n`:	Private special variables
	`p-c-3`:	Private special variables
	`square-e`:	Private special variables
	`square-e-prime`:	Private special variables

S
	`Special Variable, a`:	Private special variables
	`Special Variable, b`:	Private special variables
	`Special Variable, f`:	Private special variables
	`Special Variable, f-a-3`:	Private special variables
	`Special Variable, n`:	Private special variables
	`Special Variable, p-c-3`:	Private special variables
	`Special Variable, square-e`:	Private special variables
	`Special Variable, square-e-prime`:	Private special variables

Jump to:	* S

A.4 Data types

Jump to:	F G P S U

	Index Entry	Section

F
	`File, geodesic.asd`:	The geodesic/geodesic․asd file
	`File, geodesic.lisp`:	The geodesic/geodesic․lisp file
	`File, package.lisp`:	The geodesic/package․lisp file
	`File, poly.lisp`:	The geodesic/poly․lisp file
	`File, util.lisp`:	The geodesic/util․lisp file

G
	`geodesic`:	The geodesic system
	`geodesic`:	The geodesic package
	`geodesic.asd`:	The geodesic/geodesic․asd file
	`geodesic.lisp`:	The geodesic/geodesic․lisp file

P
	`Package, geodesic`:	The geodesic package
	`package.lisp`:	The geodesic/package․lisp file
	`poly.lisp`:	The geodesic/poly․lisp file

S
	`System, geodesic`:	The geodesic system

U
	`util.lisp`:	The geodesic/util․lisp file

Jump to:	F G P S U

The geodesic Reference Manual

The geodesic Reference Manual

Table of Contents

1 Introduction

2 Systems

2.1 geodesic

3 Files

3.1 Lisp

3.1.1 geodesic/geodesic.asd

3.1.2 geodesic/package.lisp

3.1.3 geodesic/util.lisp

3.1.4 geodesic/poly.lisp

3.1.5 geodesic/geodesic.lisp

4 Packages

4.1 geodesic

5 Definitions

5.1 Public Interface

5.1.1 Ordinary functions

5.2 Internals

5.2.1 Special variables

5.2.2 Ordinary functions

Appendix A Indexes

A.1 Concepts

A.2 Functions

A.3 Variables

A.4 Data types

2.1 `geodesic`

3.1.1 `geodesic/geodesic.asd`

3.1.2 `geodesic/package.lisp`

3.1.3 `geodesic/util.lisp`

3.1.4 `geodesic/poly.lisp`

3.1.5 `geodesic/geodesic.lisp`

4.1 `geodesic`