### 1. distance point to point revisited

```--
-- distance.e
--
include std/math.e

-- Great Circle Method
global function distance(atom LA1, atom LO1, atom LA2, atom LO2, integer miles = 1)
-- given starting and destination lattitude and longitude coordinates in degrees
-- returns distance between the two points (default: miles = 1, or km (miles = 0)
-- South latitudes are negative / East longitudes are positive
-- uses spherical law of cosines

atom D, DLO, R =  6371.02   -- mean earth radius in km

D = arccos( sin(LA1) * sin(LA2) + cos(LA1) * cos(LA2) * cos(DLO)) * R

if miles then
D = D / 1.609 -- convert km to miles
end if

return D
end function

-- test
? distance(41.3, 174.7, 37.0, 174.7)    -- Wellington-Auckland
? distance(41.3, 174.7, 33.7, 151.3)    -- Wellington-Sydney

atom LA1, LA2, LO1, LO2
LA1 =  32.204287  LO1 =  82.322732  -- Lyons, GA -- starting location
LA2 =  51.5074    LO2 =   0.1278    -- London, UK
? distance(LA1,LO1, LA2, LO2)
LA2 = 33.7490 LO2= 84.3880   -- Lyons, GA to Atlanta, GA
? distance(LA1,LO1,LA2,LO2)
LA2 = 32.8407 LO2 = 83.6324  -- Lyons, GA to Macon, GA
? distance(LA1,LO1,LA2,LO2)
LA2 = 32.2177 LO2 = 82.4135  -- Lyons, GA to Vidalia, GA
? distance(LA1,LO1,LA2,LO2)
LA2 = 32.0522 LO2 = 118.2437 -- Lyons, GA to Los Angeles, California
? distance(LA1,LO1,LA2,LO2)

```

### 2. Re: distance point to point revisited

This function seems to be a more accurate than the Great Circle Method. See: Haversine Formula and Calc-Distance

```global function distance(atom LA1, atom LO1, atom LA2, atom LO2, integer miles = 1)
-- Haversine Formula

atom a, c, D, DLO,  DLA, R = 6371.02 -- mean earth radius in km

a = power(sin(DLA/2),2)  + cos(LA1) * cos(LA2) * power(sin(DLO/2),2)
c = 2 * arcsin(min({1,sqrt(a)}))
D = R * c

if miles then
D/=1.609      -- convert km to miles
end if

return D
end function

-- test
-- the distance reading refers to the Haversine Formula

LA1=32.204287 LO1=82.322732 -- Lyons, GA - starting location

LA2=32.0835 LO2=81.0998   -- Savannah, GA USA  -- 72.0542
? Great_Circle_Distance(LA1,LO1, LA2, LO2,u)   -- 72.12361789
? distance(LA1,LO1, LA2, LO2,u)                -- 72.04468674

LA2=21.3069 LO2=157.8583 -- Honolulu, USA      -- 4627
? Great_Circle_Distance(LA1,LO1, LA2, LO2,u)   -- 4636
? distance(LA1,LO1, LA2, LO2,u)                -- 4631

LA2=51.5074 LO2=0.1278 -- Lyons, GA to London, UK -- 4195
? Great_Circle_Distance(LA1,LO1, LA2, LO2,u)      -- 4202
? distance(LA1,LO1, LA2, LO2,u)                   -- 4198

LA2=-22.9068 LO2=43.1729-- Lyons, GA to Rio de Janero -- 4599
? Great_Circle_Distance(LA1,LO1, LA2, LO2,u)          -- 4608.276053
? distance(LA1,LO1, LA2, LO2,u)                       -- 4603.232816

```

### 3. Re: distance point to point revisited

Senator said...

but I didn't know how to translate min(1,sqrt(a)) to euphoria

OE has a min function, so at a guess it is just

```min({1,sqrt(a)})
```

### 4. Re: distance point to point revisited

Thanks, Pete!

I edited the Haversine code in the previous post and included some sample run data.

The first number I got from a search engine The second number is the Great Circle code results The third number is the Haversine code results

The Haversine code appears to run 3-4 miles over the results obtained from the web for distances 4000+ miles

Regards, Ken