import math
import sys

class globeplotter(object):

    def __init__(self,latitude0,longitude0,r):
        self.latitude0 = latitude0
        self.elevation0 = self.to_elevation(latitude0)
        self.longitude0 = longitude0
        self.azimuth0 = self.to_azimuth(longitude0)
        self.r = r

    def to_elevation(self,latitude):
        return ((latitude + 90.0) / 180.0) * math.pi - math.pi/2

    def to_azimuth(self,longitude):
        return ((longitude + 180.0) / 360.0) * math.pi*2 - math.pi

    def plot(self,region):
        points = []
        ignore = True
        for (latitude,longitude) in region:
            elevation = self.to_elevation(latitude)
            azimuth = self.to_azimuth(longitude)
           
            # work out if the point is visible
            cosc = math.sin(elevation)*math.sin(self.elevation0)+math.cos(self.elevation0)*math.cos(elevation)*math.cos(azimuth-self.azimuth0)
            if cosc >= 0.0:
                # this point is visible, so do not ignore this region
                ignore = False
            # orthographic projection
            xo = self.r*math.cos(elevation)*math.sin(azimuth-self.azimuth0)
            yo = -self.r*(math.cos(self.elevation0)*math.sin(elevation)-math.sin(self.elevation0)*math.cos(elevation)*math.cos(azimuth-self.azimuth0))
            x = self.r + xo
            y = self.r + yo
            if cosc < 0:
                # this point is on the far side of the globe.  Truncate it to lie on the rim.
                theta = math.atan2(yo,xo)
                x1 = self.r + self.r * math.cos(theta)
                y1 = self.r + self.r * math.sin(theta)
                points.append((x1,y1))
            else:
                points.append((x,y))
        if ignore:
            return None
        return points