The geodesic Reference Manual

This is the geodesic Reference Manual, generated automatically by Declt version 3.0 "Montgomery Scott" on Sun May 15 04:51:58 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.

2.1 `geodesic`

Author

Manuel Giraud <manuel@ledu-giraud.fr>

License

ISC

Description

Library for geodesic calculations.

Source

geodesic.asd (file)

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.

3.1 Lisp

3.1.1 `geodesic.asd`

Location: geodesic.asd
Systems: geodesic (system)

3.1.2 `geodesic/package.lisp`

Parent: geodesic (system)
Location: package.lisp
Packages: geodesic

3.1.3 `geodesic/util.lisp`

Dependency

package.lisp (file)

Parent

geodesic (system)

Location

util.lisp

Exported Definitions

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

Internal Definitions

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

3.1.4 `geodesic/poly.lisp`

Dependency

util.lisp (file)

Parent

geodesic (system)

Location

poly.lisp

Exported Definitions

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

Internal Definitions

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

3.1.5 `geodesic/geodesic.lisp`

Dependency

poly.lisp (file)

Parent

geodesic (system)

Location

geodesic.lisp

Exported Definitions

direct (function)
inverse (function)

Internal Definitions

*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.

4.1 `geodesic`

Source

package.lisp (file)

Use List

common-lisp

Exported Definitions

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

Internal Definitions

*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.

5.1 Exported definitions

5.1.1 Functions

Function: cubic-roots A B C D

Roots of a·z³ + b·z² + c·z + d.

Package: geodesic
Source: poly.lisp (file)

Function: degrees ANGLE

Package: geodesic
Source: util.lisp (file)

Function: direct LATITUDE AZIMUTH DISTANCE

LATITUDE and AZIMUTH in radians. DISTANCE in meters.

Package: geodesic
Source: geodesic.lisp (file)

Function: inverse LAT1 LAT2 LON12

Package: geodesic
Source: geodesic.lisp (file)

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 (file)

Function: quartic-roots A B C D E

Package: geodesic
Source: poly.lisp (file)

Function: radians ANGLE

Package: geodesic
Source: util.lisp (file)

5.2 Internal definitions

5.2.1 Special variables

Special Variable: *a*

WGS84 equatorial Earth radius in meter.

Package: geodesic
Source: geodesic.lisp (file)

Special Variable: *b*

Package: geodesic
Source: geodesic.lisp (file)

Special Variable: *f*

WGS84 ellipsoid flattening.

Package: geodesic
Source: geodesic.lisp (file)

Special Variable: *f-a-3*

Factors for A-3.

Package: geodesic
Source: geodesic.lisp (file)

Special Variable: *n*

Package: geodesic
Source: geodesic.lisp (file)

Special Variable: *p-c-3*

Polynomial factors for C-3.

Package: geodesic
Source: geodesic.lisp (file)

Special Variable: *square-e*

Package: geodesic
Source: geodesic.lisp (file)

Special Variable: *square-e-prime*

Package: geodesic
Source: geodesic.lisp (file)

5.2.2 Functions

Function: 3rt NUMBER

Cubic root that handles negative numbers.

Package: geodesic
Source: poly.lisp (file)

Function: a-1 EPSILON

Package: geodesic
Source: geodesic.lisp (file)

Function: a-2 EPSILON

Package: geodesic
Source: geodesic.lisp (file)

Function: ac-3 EPSILON

Package: geodesic
Source: geodesic.lisp (file)

Function: alpha-beta ALPHA0 SIGMA

Package: geodesic
Source: geodesic.lisp (file)

Function: alpha0 BETA AZIMUTH

Package: geodesic
Source: geodesic.lisp (file)

Function: alpha2 ALPHA1 BETA1 BETA2

Package: geodesic
Source: geodesic.lisp (file)

Function: best-2-roots ROOTS

Package: geodesic
Source: poly.lisp (file)

Function: c-1 EPSILON

Package: geodesic
Source: geodesic.lisp (file)

Function: c-2 EPSILON

Package: geodesic
Source: geodesic.lisp (file)

Function: c-prime-1 EPSILON

Package: geodesic
Source: geodesic.lisp (file)

Function: delta-alpha1 DELTA-L12 M12 ALPHA2 BETA2

Package: geodesic
Source: geodesic.lisp (file)

Function: dereduce-latitude BETA

Package: geodesic
Source: geodesic.lisp (file)

Function: horner X &rest P

Horner’s method of P at X.

Package: geodesic
Source: poly.lisp (file)

Function: i SIGMA AN CN

Package: geodesic
Source: geodesic.lisp (file)

Function: init-alpha1 LAT1 LAT2 LON12 BETA1 BETA2 OMEGA12

Package: geodesic
Source: geodesic.lisp (file)

Function: j SIGMA EPSILON

Package: geodesic
Source: geodesic.lisp (file)

Function: longitude OMEGA ALPHA0 I3

Package: geodesic
Source: geodesic.lisp (file)

Function: m12 K2 SIGMA1 SIGMA2 EPSILON

Returns m12 and M12.

Package: geodesic
Source: geodesic.lisp (file)

Function: nearly-antipodal-p LAT1 LAT2 LON12

Package: geodesic
Source: geodesic.lisp (file)

Function: normalize ANGLE

Normalize angle between -π and π.

Package: geodesic
Source: util.lisp (file)

Function: normalize-azimuth ANGLE

Normalize angle between 0 and π.

Package: geodesic
Source: util.lisp (file)

Function: normalize-latitudes LAT1 LAT2

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

Package: geodesic
Source: geodesic.lisp (file)

Function: omega ALPHA0 SIGMA

Package: geodesic
Source: geodesic.lisp (file)

Function: omega-bar BETA1 BETA2

Package: geodesic
Source: geodesic.lisp (file)

Function: plusp-and-value STRING

Package: geodesic
Source: util.lisp (file)

Function: reduce-latitude LATITUDE

Package: geodesic
Source: geodesic.lisp (file)

Function: sigma BETA AZIMUTH

Package: geodesic
Source: geodesic.lisp (file)

Function: sigma-tau TAU C-PRIME-1

Package: geodesic
Source: geodesic.lisp (file)

Function: sigma12 BETA1 BETA2 OMEGA12 Z1

Package: geodesic
Source: geodesic.lisp (file)

Function: solve-triangle ALPHA1 BETA1 BETA2

Package: geodesic
Source: geodesic.lisp (file)

Function: z1 BETA1 BETA2 OMEGA12

Package: geodesic
Source: geodesic.lisp (file)

Function: z2 BETA1 BETA2 OMEGA12

Package: geodesic
Source: geodesic.lisp (file)

Appendix A Indexes

A.1 Concepts

Jump to:	F G L

	Index Entry	Section

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

G
	`geodesic.asd`:	The geodesic․asd file
	`geodesic/geodesic.lisp`:	The geodesic/geodesic․lisp file
	`geodesic/package.lisp`:	The geodesic/package․lisp file
	`geodesic/poly.lisp`:	The geodesic/poly․lisp file
	`geodesic/util.lisp`:	The geodesic/util․lisp file

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

Jump to:	F G L

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`:	Internal functions

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

B
	`best-2-roots`:	Internal functions

C
	`c-1`:	Internal functions
	`c-2`:	Internal functions
	`c-prime-1`:	Internal functions
	`cubic-roots`:	Exported functions

D
	`degrees`:	Exported functions
	`delta-alpha1`:	Internal functions
	`dereduce-latitude`:	Internal functions
	`direct`:	Exported functions

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

H
	`horner`:	Internal functions

I
	`i`:	Internal functions
	`init-alpha1`:	Internal functions
	`inverse`:	Exported functions

J
	`j`:	Internal functions

L
	`longitude`:	Internal functions

M
	`m12`:	Internal functions

N
	`nearly-antipodal-p`:	Internal functions
	`normalize`:	Internal functions
	`normalize-azimuth`:	Internal functions
	`normalize-latitudes`:	Internal functions

O
	`omega`:	Internal functions
	`omega-bar`:	Internal functions

P
	`parse-float`:	Exported functions
	`plusp-and-value`:	Internal functions

Q
	`quartic-roots`:	Exported functions

R
	`radians`:	Exported functions
	`reduce-latitude`:	Internal functions

S
	`sigma`:	Internal functions
	`sigma-tau`:	Internal functions
	`sigma12`:	Internal functions
	`solve-triangle`:	Internal functions

Z
	`z1`:	Internal functions
	`z2`:	Internal 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`:	Internal special variables
	`b`:	Internal special variables
	`f`:	Internal special variables
	`f-a-3`:	Internal special variables
	`n`:	Internal special variables
	`p-c-3`:	Internal special variables
	`square-e`:	Internal special variables
	`square-e-prime`:	Internal special variables

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

Jump to:	* S

A.4 Data types

Jump to:	G P S

	Index Entry	Section

G
	`geodesic`:	The geodesic system
	`geodesic`:	The geodesic package

P
	`Package, geodesic`:	The geodesic package

S
	`System, geodesic`:	The geodesic system

Jump to:	G P S

• Introduction		What geodesic is all about
• Systems		The systems documentation
• Files		The files documentation
• Packages		The packages documentation
• Definitions		The symbols documentation
• Indexes		Concepts, functions, variables and data types

• The geodesic.asd file
• The geodesic/package.lisp file
• The geodesic/util.lisp file
• The geodesic/poly.lisp file
• The geodesic/geodesic.lisp file

• Concept index
• Function index
• Variable index
• Data type index

The geodesic Reference Manual

Table of Contents

The geodesic Reference Manual

1 Introduction

2 Systems

2.1 geodesic

3 Files

3.1 Lisp

3.1.1 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 Exported definitions

5.1.1 Functions

5.2 Internal definitions

5.2.1 Special variables

5.2.2 Functions

Appendix A Indexes

A.1 Concepts

A.2 Functions

A.3 Variables

A.4 Data types

2.1 `geodesic`

3.1.1 `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`