How do I draw the points in an ESRI Polyline, given the bounding box as lat/long and the “points” as radians?

Question

I'm using OpenMap and I'm reading a ShapeFile using com.bbn.openmap.layer.shape.ShapeFile. The bounding box is read in as lat/long points, for example 39.583642,-104.895486. The bounding box is a lower-left point and an upper-right point which represents where the points are contained. The "points," which are named "radians" in OpenMap, are in a different format, which looks like this: [0.69086486, -1.8307719, 0.6908546, -1.8307716, 0.6908518, -1.8307717, 0.69085056, -1.8307722, 0.69084936, -1.8307728, 0.6908477, -1.8307738, 0.69084626, -1.8307749, 0.69084185, -1.8307792].

How do I convert the points like "0.69086486, -1.8307719" into x,y coordinates that are usable in normal graphics?

I believe all that's needed here is some kind of conversion, because bringing the points into Excel and graphing them creates a line whose curve matches the curve of the road at the given location (lat/long). However, the axises need to be adjusted manually and I have no reference as how to adjust the axises, since the given bounding box appears to be in a different format than the given points.

The ESRI Shapefile technical description doesn't seem to mention this (http://www.esri.com/library/whitepapers/pdfs/shapefile.pdf).

Answer 1

0.69086486, -1.8307719 is a latitude and a longitude in radians.

First, convert to degrees (multiply by (180/pi)), then you will have common units between your bounding box and your coordinates.

Then you can plot all of it in a local frame with the following :

x = (longitude-longitude0)*(6378137*pi/180)*cos(latitude0*pi/180)
y = (latitude-latitude0)*(6378137*pi/180)

(latitude0, longitude0) are the coordinates of a reference point (e.g. the lower-left corner of the bounding box) units are degrees for angles and meters for distances

Edit -- explanation : This is an orthographic projection of the Earth considered as a sphere whose radius is 6378137.0 m (semi-major axis of the WGS84 ellipsoid), centered on the point (lat0, lon0)

Answer 2

In OpenMap, there are a number of ways to convert from radians to decimal degrees:

Length.DECIMAL_DEGREE.fromRadians(radVal);
Math.toDegrees(radVal)  // Standard java library

For an array, you can use ProjMath.arrayDegToRad(double[] radvals);

Be careful with that last one, it does the conversion in place. So if you grab a lat/lon array from an OMPoly, make a copy of it first before converting it. Otherwise, you'll mess up the internal coordinates of the OMPoly, which it expects to be in radians.