The gcd_hf function calculates the great circle distance, Haversine formula.

Synopsis

gcd_hf(radius,lat1,lon1,lat2,lon2)

Latitude and longitude are given in radians.

Summary

Geographical distances are given in changes in latitude and longitude:

The Haversine formula for great-circle distances is:

Example

This example uses Haversine's formula to find the great circle distance between two points assuming a mean earth radius of 6371 kilometers. The example is published in Wikipedia.

The latitude and longitude for Los Angeles International Airport (LAX) is N 33.94°, W 118.4°. In radians, these values are .5924 and -2.0665. The latitude and longitude for Nashville International Airport (BNA) in Nashville, Tennessee is N 36.12°, W 86.67°. In radians, these values are .6304 and -1.5127. Create an input array to contain these values:
```
AFL% store(build(<airport:string, lat:double, lon:double>[i=0:1],
                 '[(\'LAX\', .5924, -2.0665), (\'BNA\', 0.6304, -1.5127)]', true), airports);
```
The output is:
```
{i} airport,lat,lon
{0} 'LAX',0.5924,-2.0665
{1} 'BNA',0.6304,-1.5127
```

The input attribute arguments for the gcd_hf function must be from the same cell. From the airports array, use filter and cross_join to build a trip array describing the airport entries we care about. The cast operator is used to rename the lat and lon attributes:

AFL% store(cast(cross_join(filter(airports, airport='LAX'),
                           filter(airports, airport='BNA')),
                <from:string, latf:double, lonf:double, to:string, latt:double, lont:double>[i;j]),
           trip);

The output is:

{i,j} from,latf,lonf,to,latt,lont
{0,1} 'LAX',0.5924,-2.0665,'BNA',0.6304,-1.5127

Use apply and gcd_hf to add the Haversine great circle distance attribute:

AFL% apply(trip, distance, gcd_hf(6371.0, latf, lonf, latt, lont));

The output is:

{i,j} from,latf,lonf,to,latt,lont,distance
{0,1} 'LAX',0.5924,-2.0665,'BNA',0.6304,-1.5127,2886.43

Remove the example arrays:
```
AFL% remove(airports); remove(trip);
```

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