calculate latitude and longitude along a circumference of a known circle with known distance - vb.net

Question

I dont need help with a programming language, I need help from someone to calculate the gps coordinates of points of a specific distance, namely 22 feet apart, on the circumference of a circle. I know the beginning gps coordinates and the radius. I am pretty sure the haversine, or the speherical law of cosines has the answer, but its been a long time since I have used any trig formulas and I cant figure it out. I am using decimal degrees and am programing in this vb.net. If someone could dumb this down for me it would be a great help.

Answer 1

As I understand you have:
Coordinate of the center of
circumference.
Distance between
two point on the circumference of a
circle.
Radius of circumference.
In my opinion this is not enough for calculating other point's coordinates. You should have as minimum yet one point coordinate, because we only can guess where points are placed on the circumference.

Answer 2

Here's the basic algorithm:
Calculate the angular measure whose arc length is 22 feet, with the given radius
numPoints = Math.PI * 2 / angularMeasure
for i in range(numPoints):
calculate proportion around the circle we are, in terms of degrees or radians
calculate the location of the endpoint of a great circle or rhumb arc from the center point moving in the specific azimuth direction (from the proportion around the circle) the given radius
This last point is the hardest part. Here's code from the WorldWind SDK (available: http://worldwind.arc.nasa.gov/java/) (Note- you'll have to calculate the radius in terms of angles, which you can do pretty easily given the radius / circumference of the earth)
/*
Copyright (C) 2001, 2006 United States Government
as represented by the Administrator of the
National Aeronautics and Space Administration.
All Rights Reserved.
*/
/**
* Computes the location on a rhumb line with the given starting location, rhumb azimuth, and arc distance along the
* line.
*
* #param p LatLon of the starting location
* #param rhumbAzimuth rhumb azimuth angle (clockwise from North)
* #param pathLength arc distance to travel
*
* #return LatLon location on the rhumb line.
*/
public static LatLon rhumbEndPosition(LatLon p, Angle rhumbAzimuth, Angle pathLength)
{
if (p == null)
{
String message = Logging.getMessage("nullValue.LatLonIsNull");
Logging.logger().severe(message);
throw new IllegalArgumentException(message);
}
if (rhumbAzimuth == null || pathLength == null)
{
String message = Logging.getMessage("nullValue.AngleIsNull");
Logging.logger().severe(message);
throw new IllegalArgumentException(message);
}
double lat1 = p.getLatitude().radians;
double lon1 = p.getLongitude().radians;
double azimuth = rhumbAzimuth.radians;
double distance = pathLength.radians;
if (distance == 0)
return p;
// Taken from http://www.movable-type.co.uk/scripts/latlong.html
double lat2 = lat1 + distance * Math.cos(azimuth);
double dPhi = Math.log(Math.tan(lat2 / 2.0 + Math.PI / 4.0) / Math.tan(lat1 / 2.0 + Math.PI / 4.0));
double q = (lat2 - lat1) / dPhi;
if (Double.isNaN(dPhi) || Double.isNaN(q) || Double.isInfinite(q))
{
q = Math.cos(lat1);
}
double dLon = distance * Math.sin(azimuth) / q;
// Handle latitude passing over either pole.
if (Math.abs(lat2) > Math.PI / 2.0)
{
lat2 = lat2 > 0 ? Math.PI - lat2 : -Math.PI - lat2;
}
double lon2 = (lon1 + dLon + Math.PI) % (2 * Math.PI) - Math.PI;
if (Double.isNaN(lat2) || Double.isNaN(lon2))
return p;
return new LatLon(
Angle.fromRadians(lat2).normalizedLatitude(),
Angle.fromRadians(lon2).normalizedLongitude());
}

Answer 3

You are looking for the equation of what is called a "small circle". Look at this book for the equation of the small circle and the arc length equation for that small circle. However, because your distances are so small, you could consider your area flat and use simpler geometry. Using UTM coordinates would make the calculations much simpler than using lat/long.
The Haversine formula relates to great circles, not small circles...