Drawing irregular concentric circles using Google Maps

Question

I have a bit of a problem. I am trying to do the following using Javascript & the Google Maps API v2:

I can draw individual circles just fine using formulas found all over the Internet. The problem I am facing is that the circles must:

A. Be concentric, and B. Must have different radius for each "quadrant", i.e., NE, NW, SE & SW

I've searched almost everywhere I can think of on the Internet, and have come up with no way on how to do this. Clearly someone has done this before, and thus why I'm asking in a forum of programmers. :)

Thanks!

UPDATE: I have drawn out, using the following code, what I think the coordinates for each of the points would be. for the drawing below:

This was obtained using the following JS:

http://gist.github.com/181290

NOTE: This javascript is from (slightly modified) the following site, which may hold more answers in terms of what the algorithm may end up being: http://www.movable-type.co.uk/scripts/latlong.html

UPDATE 2: I was able to get this in Google Maps:

Created using the following code:

var NEQ = [0, 90];
var SEQ = [90, 180];
var SWQ = [180, 270];
var NWQ = [270, 0];

// var centrePoint = new LatLon(25.0, -83.1);
// pointsForWindQuadrant(NEQ, centrePoint, 50);
function pointsForWindQuadrant(quadrantDegrees, centrePoint, radius){
  var points = [];

  // Points must be pushed into the array in order
  points.push(new google.maps.LatLng(centrePoint.lat, centrePoint.lon));

  for(i = quadrantDegrees[0]; i <= quadrantDegrees[1]; i++){
    var point = centrePoint.destPoint(i, radius * 1.85);
    points.push(new google.maps.LatLng(point.lat, point.lon)); // Radius should be in nautical miles from NHC
  }

  points.push(new google.maps.LatLng(centrePoint.lat, centrePoint.lon));

  return points;
}

UPDATE 3: I should probably also point out that this is for a geographic coordinate system (as this whole thing is for tropical cyclone wind radii), not the Cartesian coordinate system. Thanks!

Answer 1

Basically, calculate the circle as the x,y = (cos(a), sin(a)), and then multiple this (both terms) by a radius that's the appropriate function of the angle. I don't know Javascript well, or Google maps, so I'll do this in Python, hopefully it's clear enough from this.

from pylab import *

def Rscale(a):
    if a>3*pi/2:  # lower right, and then work CW around the circle
        return 1.
    elif a>pi:  # lower left
        return .9
    elif a>pi/2:   # upper left
        return .8
    else:       # upper right
        return 1.

def step_circle(R):
    return array([(R*Rscale(a))*array([cos(a), sin(a)]) for a in arange(0, 2*pi, .001)])

for R in (.5, .7, .9):  # make three concentric circles
    c = step_circle(R)
    plot(c[:,0], c[:,1])

show()

Which gives

I couldn't really follow your sketch, so I just guessed at the numbers. Also, I made the two rightmost quadrants to be the same since that's what your plot looked like, but that is, of course, optional.

Answer 2

I figured it out. Here is the final code. Maybe it can be refactored a bit?

// Returns points for a wind field for a cyclone. Requires
// a LatLon centre point, and an array of wind radii, starting
// from the northeast quadrant (NEQ), i.e., [200, 200, 150, 175]
//
// Returns points to be used in a GPolyline object.
function pointsForWindQuadrant(centrePoint, radii){
  if(radii.length != 4){ return false; }

  var points = [];
  var angles = [0, 90, 180, 270];

  // For each angle 0, 90, 180, 270...
  for(a = 0; a < angles.length; a++){
    // For each individual angle within the range, create a point...
    for(i = angles[a]; i <= angles[a] + 90; i++){
      var point = centrePoint.destPoint(i, radii[a] * 1.85); // Radius should be in nautical miles from NHC
      points.push(new google.maps.LatLng(point.lat, point.lon));
    }
  }

  // Add the first point again, to be able to close the GPolyline
  var point = centrePoint.destPoint(0, radii[0] * 1.85);
  points.push(new google.maps.LatLng(point.lat, point.lon));

  return points;
}

This results in the following: