 NCL Home > Documentation > Functions > Lat/Lon functions

# gc_dangle

Finds the directed angle between two great circles having a specified intersection point. Available in version 4.3.1 and later.

## Prototype

```	function gc_dangle (
lat  : numeric,
lon  : numeric
)

return_val  :  numeric
```

## Arguments

lat
lon

Latitudes and longitudes, in degrees, of vertices. These can be multi-dimensional arrays, but the rightmost dimension size must be 3, for the vertices of three points defining two arcs and an intersection point. In the simple case of scalars, where A=(lat,lon), B=(lat,lon), and C=(lat,lon), AB and AC define arcs of great circles that intersect at A. If lat and lon have more than one dimension, then they must agree in number of dimensions and dimension sizes.

## Return value

The angle, in degrees, between the great circles defined by the arcs as describe above. The returned angle is positive if C is in the hemisphere to the left of the great circle through A and B, negative otherwise. If the input arrays are singly dimensioned, then the return value will be a scalar. If the input arrays are multi-dimensional, then the returned array will have one less dimension than the number of dimensions of the input arrays and the dimension sizes of the returned array will agree with those of the input arrays up through their penultimate dimension. The return value will be of type double if either of the input arguments is of type double and type float otherwise.

## Description

This function finds the directed angle between two great circles, given three points A, B, C on the globe where AB and AC are arcs on the great circles. The returned angle is positive if C is in the hemisphere to the left of the great circle through A and B, negative otherwise.

Missing values are not honored as such, since it does not make sense to have a vertex specified as a missing value.

## Examples

Example 1

The following:

```  begin
angle = gc_dangle((/0.0, 0.0, 10.0/), (/0.0, 10.0, 0.0/))
print (angle)
end
```
produces:

```Variable: angle
Type: float
Total Size: 4 bytes
1 values
Number of Dimensions: 1
Dimensions and sizes:   
Coordinates:
(0)     90
```
Example 2

The following:

```  begin
angle = gc_dangle((/0.0d, 0.0d, 10.0d/), (/0.0d, 10.0d, -10.0d/))
print (angle)
end
```
produces:

```Variable: angle
Type: double
Total Size: 8 bytes
1 values
Number of Dimensions: 1
Dimensions and sizes:   
Coordinates:
(0)     134.5614514132577
```
Example 3

The following:

```begin
lat = (/                                              \
(/ (/  0.,  0.,  10./) , (/22., 40., 10./) /),  \
(/ (/-20., 40., -60./) , (/ 0.,  1., 45./) /)   \
/)
lon = (/                                               \
(/ (/ 0.,  10.,   0./) , (/40., 50.,  30./) /), \
(/ (/30., -40., -80./) , (/ 0., -1.,  45./) /)  \
/)
angles = gc_dangle(lat, lon)
print(angles)
end
```
produces:

```Variable: angles
Type: float
Total Size: 16 bytes
4 values
Number of Dimensions: 2
Dimensions and sizes:    x 
Coordinates:
(0,0)   90
(0,1)   162.7924
(1,0)   105.629
(1,1)   -80.26003
```