how to decide point is between two points on compass

Question

Hi All

Given any two points on compass (Start range and End Range) to form a range. Example from 270(Start range) degrees to 45(End range)degrees and given another point say 7 , how can I work out if that point is between Start and End range ?

I'm trying to write some code to work out if the Wind (in the above point 3) is blowing from the sea or from the land , where the land is defind by Start range and End range .

Many Thanks Andy

Update:11/10/2010 18:46BST From @sth's solution the following seems to work for as expected.

#!/usr/bin/perl -w

sub isoffshore {

        my ( $beachstart,$beachend,$wind) = @_;

        if( $beachend < $beachstart) {
                $beachend += 360;
        }

        if ($wind < $beachstart){
                $wind += 360;
        }

        if ($wind <= $beachend){
                print ("Wind is Onshore\n");
                return 0;
        }else{
                print ("Wind is Offshore\n");
                return 1;

        }

}

isoffshore ("0","190","3"); #Should be onshore
isoffshore ("350","10","11"); #Should be offshore
isoffshore ("270","90","180");#Should be offshore
isoffshore ("90","240","0"); #Should be offshore
isoffshore ("270","90","180");#Should be offshore
isoffshore ("0","180","90"); #Should be onshore
isoffshore ("190","0","160"); #Should be offshore
isoffshore ("110","240","9"); #Should be offshore
isoffshore ("0","180","9"); #Should be onshore
isoffshore ("0","180","179"); #Should be onshore

Results

@localhost ~]$ ./offshore2.pl
Wind is Onshore
Wind is Offshore
Wind is Offshore
Wind is Offshore
Wind is Offshore
Wind is Onshore
Wind is Offshore
Wind is Offshore
Wind is Onshore
Wind is Onshore

Answer 1

This should work if all your points are like 0 <= point < 360:

def between(lower, upper, point):
   if upper < lower:
      upper += 360
   if point < lower:
      point += 360
   return (point <= upper)

Answer 2

By points on a compass, I assume that you mean points on the unit circle. And by "between" two points on the unit circle, you mean that you have described an arc on the unit circle and want to know if a given point is in that arc.

Assume that all points on the unit circle are described by angles and for such an angle t describing a point on the unit circle we require that 0 <= t < 2 * pi.

Let's say that your arc is described as the arc (t_1, t_2) (that is, traverse counterclockwise from the point on the unit circle corresponding to the angle t_1 to the point on the unit circle corresponding to the angle t_2^*). Then, given a point on the unit circle with corresponding angle t, it is true that t is on the counterclockwise arc from t_1 to t_2 if t_2 > t_1 and t_1 <= t <= t_2 or t_1 > t_2 and not t_2 <= t <= t_1.

Thus,

public bool IsInArc(double t1, double t2, double t) {
     Guard.Against<ArgumentOutOfRangeException>(t1 < 0 || t1 >= 2 * Math.PI);
     Guard.Against<ArgumentOutOfRangeException>(t2 < 0 || t2 >= 2 * Math.PI);
     Guard.Against<ArgumentOutOfRangeException>(t < 0 || t >= 2 * Math.PI);
     return t2 > t1 ? IsInArcInternal(t1, t2, t) : !IsInArcInternal(t2, t1, t);
}

private bool IsInArcInternal(double t1, double t2, double t) {
     Guard.Against<ArgumentException>(t2 < t1);
     return t1 <= t && t <= t2;
}

Answer 3

Here's a one line function which uses the modulo (%) operator to handle the wraparound case. Input values are assumed to be in the range 0..359 (degrees):

int inRange(int start, int end, int point)
{
    return (point + 360 - start) % 360 <= (end + 360 - start) % 360;
}

//
// Test harness
//

#include <assert.h>
#include <stdlib.h>
#include <stdio.h>

int main(int argc, char *argv[])
{
    assert(inRange(90, 270, 0) == 0);
    assert(inRange(90, 270, 45) == 0);
    assert(inRange(90, 270, 180) == 1);
    assert(inRange(90, 270, 315) == 0);
    assert(inRange(270, 90, 0) == 1);
    assert(inRange(270, 90, 45) == 1);
    assert(inRange(270, 90, 180) == 0);
    assert(inRange(270, 90, 315) == 1);

    if (argc >= 4)
    {
        int start = atoi(argv[1]);
        int end = atoi(argv[2]);
        int point = atoi(argv[3]);
        int result = inRange(start, end, point);

        printf("start = %d, end = %d, point = %d -> result = %d\n", start, end, point, result);
    }
    return 0;
}

Note that the + 360 term on each side of the test is required in C/C++ due to the unfortunate way that % treats negative values.