com.bbn.openmap.proj.coords
Class VHTransform

java.lang.Object
  com.bbn.openmap.proj.coords.VHTransform

All Implemented Interfaces:

GeoCoordTransformation

public class VHTransform
extends java.lang.Object
implements GeoCoordTransformation

The VH coordinate system is used by ATT to compute distance used in determining phone call costs.

VH coordinates can be used to compute distance simply, see distance().

This code is based on C code provided by the authors mentioned below, as well as Lisp code by Larry Denenberg of BBN.

I have ported this code to Java, unified the forward and inverse transformations and added some comments. I've left basic code and comments mostly intact.

The url's to the original emails are:

http://x11.dejanews.com/getdoc.xp?AN=177302113&CONTEXT=895858362.931528704& hitnum=1
http://x11.dejanews.com/getdoc.xp?AN=223540739&CONTEXT=895858362.931528704& hitnum=5

Field Summary

static double	EX
static double	EY
static double	EZ
static double	K1
static double	K10
static double	K2
static double	K3
static double	K4
static double	K5
static double	K9
static double	M_PI_2
static double	PX
static double	PY
static double	PZ
static double	RADIUS radius of earth in sqrt(0.1)-mile units, minus 0.3 percent
static double	rot
static double	ROTC
static double	ROTS
static double	TRANSH
static double	TRANSV
static double	WX
static double	WY
static double	WZ

Constructor Summary

VHTransform()

Method Summary

static double	distance(double v1, double h1, double v2, double h2) Return the distance in miles between 2 VH pairs.
java.awt.geom.Point2D	forward(double lat, double lon)
java.awt.geom.Point2D	forward(double lat, double lon, java.awt.geom.Point2D ret)
double	getH() Return the H corresponding to the most recent toVH().
double	getLat() Return the latitude corresponding to the most recent toLatLon().
double	getLon() Return the longitude corresponding to the most recent toLatLon().
double	getV() Return the V corresponding to the most recent toVH().
LatLonPoint	inverse(double v, double h)
LatLonPoint	inverse(double v, double h, LatLonPoint ret)
static void	main(java.lang.String[] args)
void	toLatLon(double v0, double h0) V&H is a system of coordinates (V and H) for describing locations of rate centers in the United States.
void	toLatLon(int v0, int h0)
void	toVH(double lat, double lon) lat and lon are in degrees, positive north and east.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

K1

public static final double K1

See Also:

Constant Field Values

K2

public static final double K2

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Constant Field Values

K3

public static final double K3

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Constant Field Values

K4

public static final double K4

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Constant Field Values

K5

public static final double K5

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Constant Field Values

M_PI_2

public static final double M_PI_2

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Constant Field Values

EX

public static final double EX

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Constant Field Values

EY

public static final double EY

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Constant Field Values

EZ

public static final double EZ

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Constant Field Values

WX

public static final double WX

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Constant Field Values

WY

public static final double WY

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Constant Field Values

WZ

public static final double WZ

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Constant Field Values

PX

public static final double PX

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Constant Field Values

PY

public static final double PY

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Constant Field Values

PZ

public static final double PZ

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Constant Field Values

rot

public static final double rot

ROTC

public static final double ROTC

ROTS

public static final double ROTS

TRANSV

public static final double TRANSV

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Constant Field Values

TRANSH

public static final double TRANSH

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Constant Field Values

RADIUS

public static final double RADIUS

radius of earth in sqrt(0.1)-mile units, minus 0.3 percent

See Also:

Constant Field Values

K9

public static final double K9

K10

public static final double K10

Constructor Detail

VHTransform

public VHTransform()

Method Detail

getV

public double getV()

Return the V corresponding to the most recent toVH(). *

getH

public double getH()

Return the H corresponding to the most recent toVH(). *

getLat

public double getLat()

Return the latitude corresponding to the most recent toLatLon(). *

getLon

public double getLon()

Return the longitude corresponding to the most recent toLatLon(). *

distance

public static double distance(double v1,
                              double h1,
                              double v2,
                              double h2)

Return the distance in miles between 2 VH pairs. *

toVH

public void toVH(double lat,
                 double lon)

lat and lon are in degrees, positive north and east.

toLatLon

public void toLatLon(double v0,
                     double h0)

V&H is a system of coordinates (V and H) for describing locations of rate centers in the United States. The projection, devised by J. K. Donald, is an "elliptical," or "doubly equidistant" projection, scaled down by a factor of 0.003 to balance errors.

The foci of the projection, from which distances are measured accurately (except for the scale correction), are at 37d 42m 14.69s N, 82d 39m 15.27s W (in Floyd Co., Ky.) and 41d 02m 55.53s N, 112d 03m 39.35 W (in Webster Co., Utah). They are just 0.4 radians apart.

Here is the transformation from latitude and longitude to V&H: First project the earth from its ellipsoidal surface to a sphere. This alters the latitude; the coefficients bi in the program are the coefficients of the polynomial approximation for the inverse transformation. (The function is odd, so the coefficients are for the linear term, the cubic term, and so on.) Also subtract 52 degrees from the longitude.

For the rest, compute the arc distances of the given point to the reference points, and transform them to the coordinate system in which the line through the reference points is the X-axis and the origin is the eastern reference point. The solution is

h = (square of distance to E - square of distance to W + square of distance between E and W) / twice distance between E and W;
v = square root of absolute value of (square of distance to E - square of h).

Reduce by three-tenths of a percent, rotate by 76.597497 degrees, and add 6363.235 to V and 2250.7 to H.

To go the other way, as this program does, undo the final translation, rotation, and scaling. The z-value Pz of the point on the x-y-z sphere satisfies the quadratic Azz+Bz+c=0, where

A = (ExWz-EzWx)^2 + (EyWzx-EzWy)^2 + (ExWy-EyWx)^2;
B = -2[(Ex cos(arc to W) - Wx cos(arc to E))(ExWz-EzWx) - (Ey cos(arc to W) -Wy cos(arc to E))(EyWz-EzWy)];
C = (Ex cos(arc to W) - Wx cos(arc to E))^2 + (Ey cos(arc to W) - Wy cos(arc to E))^2 - (ExWy - EyWx)^2.

Solve with the quadratic formula. The latitude is simply the arc sine of Pz. Px and Py satisfy

ExPx + EyPy + EzPz = cos(arc to E);
WxPx + WyPy + WzPz = cos(arc to W).

Substitute Pz's value, and solve linearly to get Px and Py. The longitude is the arc tangent of Px/Py. Finally, this latitude and longitude are spherical; use the inverse polynomial approximation on the latitude to get the ellipsoidal earth latitude, and add 52 degrees to the longitude.

toLatLon

public void toLatLon(int v0,
                     int h0)

forward

public java.awt.geom.Point2D forward(double lat,
                                     double lon)

Specified by:

forward in interface GeoCoordTransformation

forward

public java.awt.geom.Point2D forward(double lat,
                                     double lon,
                                     java.awt.geom.Point2D ret)

Specified by:

forward in interface GeoCoordTransformation

inverse

public LatLonPoint inverse(double v,
                           double h)

Specified by:

inverse in interface GeoCoordTransformation

inverse

public LatLonPoint inverse(double v,
                           double h,
                           LatLonPoint ret)

Specified by:

inverse in interface GeoCoordTransformation

main

public static void main(java.lang.String[] args)