def make_map( filename ):
def _sphere_to_cart( theta, phi ):
return vector_3d( \
s.sin( theta ) * s.cos( phi ), \
s.cos( theta ), \
s.sin( theta ) * s.sin( phi ) )
def _draw_this_circle( c, Circle ):
pass
def _draw_latitude_circle( c, latitude ):
pass
def _draw_longitude_circle( c, longitude ):
pass
# set up our triangle
c = get_letter_canvas( filename )
# hex grid
c.setStrokeColor( (0.75, 0.75, 1) )
# c.setLineWidth( 0.001 )
# draw_hexes( c, 2 )
c.setLineWidth( 0.0005 )
draw_hexes( c, 10 )
c.setStrokeColor( (0.75,0.75,0.75) )
d20 = Icosahedron( numeric = True )
d20.rotate_vertices( rot_x( -s.atan2( s.GoldenRatio-1, s.GoldenRatio ).evalf() ) )
d20.make_faces()
mappings = face_mappings( d20 )
face_plane = d20.faces[0].plane
rot_mat = mappings.face_dict['a'][0]
for lat in range( 0, 40, 5 ):
if lat % 5:
c.setLineWidth( 0.0005 )
else:
c.setLineWidth( 0.001 )
lat_rad = to_rad( lat ).evalf()
try:
point = line_plane_intersect( two_point_line( zero_3d, _sphere_to_cart( lat_rad, 0 ) ), face_plane )
mp1 = point.multiply( rot_mat )
point = line_plane_intersect( two_point_line( zero_3d, _sphere_to_cart( lat_rad, _pi/2 ) ), face_plane )
mp2 = point.multiply( rot_mat )
point = line_plane_intersect( two_point_line( zero_3d, _sphere_to_cart( lat_rad, -_pi/2 ) ), face_plane )
mp3 = point.multiply( rot_mat )
the_circle = three_point_circle( mp1[0], mp1[1], mp2[0], mp2[1], mp3[0], mp3[1] )
c.circle( the_circle.x0, the_circle.y0, the_circle.radius, fill=0, stroke=1 )
except:
pass
for lon in range( 0, 360, 5 ):
if lon % 5:
c.setLineWidth( 0.0005 )
else:
c.setLineWidth( 0.001 )
try:
point = line_plane_intersect( two_point_line( _sphere_to_cart( _pi/4, to_rad( lon).evalf() ), zero_3d ), face_plane )
mp1 = point.multiply( rot_mat )
end_pt = _pi/9
if (lon % 5) == 0:
end_pt = _pi/18
if (lon % 10) == 0:
end_pt = _pi/36
if (lon % 30) == 0:
end_pt = 0
point = line_plane_intersect( two_point_line( _sphere_to_cart( end_pt, to_rad( lon).evalf() ), zero_3d ), face_plane )
mp2 = point.multiply( rot_mat )
c.line( mp1[0], mp1[1], mp2[0], mp2[1] )
except:
pass
c.showPage()
c.save()
def make_map( filename ):
def _sphere_to_cart( theta, phi ):
return vector_3d( \
s.sin( theta ) * s.cos( phi ), \
s.cos( theta ), \
s.sin( theta ) * s.sin( phi ) )
def _draw_this_circle( c, Circle ):
pass
def _draw_latitude_circle( c, latitude ):
pass
def _draw_longitude_circle( c, longitude ):
pass
# set up our triangle
c = get_letter_canvas( filename )
# hex grid
c.setStrokeColor( (0.75, 0.75, 1) )
# c.setLineWidth( 0.001 )
# draw_hexes( c, 2 )
c.setLineWidth( 0.0005 )
draw_hexes( c, 10 )
c.setStrokeColor( (0.75,0.75,0.75) )
d20 = Icosahedron( numeric = True )
d20.rotate_vertices( rot_x( -s.atan2( s.GoldenRatio-1, s.GoldenRatio ).evalf() ) )
d20.make_faces()
mappings = face_mappings( d20 )
face_plane = d20.faces[16].plane
rot_mat = mappings.face_dict['q'][0]
bag_o_points = dict()
for lat in range( 90, 171, 5 ):
for lon in range( 210, 331, 5 ):
point = line_plane_intersect( two_point_line( \
_sphere_to_cart( to_rad( lat ).evalf(), to_rad( lon ).evalf() ), zero_3d), face_plane, ray=True )
mp = point.multiply( rot_mat )
# c.circle( mp[0],mp[1],0.002,fill=1,stroke=0)
bag_o_points[(lat,lon)] = mp
for lat in range( 90, 169, 5 ):
for lon in range( 210, 330, 5 ):
p0 = bag_o_points[(lat, lon)]
p1 = bag_o_points[(lat+5,lon)]
p2 = bag_o_points[(lat,lon+5)]
if lon % 5:
c.setLineWidth( 0.0005 )
else:
c.setLineWidth( 0.001 )
c.line( p0[0],p0[1],p1[0],p1[1] )
if lat % 5:
c.setLineWidth( 0.0005 )
else:
c.setLineWidth( 0.001 )
c.line( p0[0],p0[1],p2[0],p2[1] )
c.showPage()
c.save()
def make_map( filename ):
# = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
# helpers
# = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
def _map_point( point ):
line = two_point_line( point, zero_3d )
for hit in d20.face_hit( line ):
# print hit[0]
mapped_point = mappings.map_point( hit[0], hit[1] )
if mapped_point:
new_x, new_y = mapped_point
c.circle( sx(new_x), sy(new_y), 0.5, stroke=0, fill=1 )
def _sphere_to_cart( theta, phi ):
return vector_3d( \
s.sin( theta ) * s.cos( phi ), \
s.cos( theta ), \
s.sin( theta ) * s.sin( phi ) )
def _arc_azimuth( start_az, end_az, inclin, step ):
for azimuth in range( start_az, end_az, step ):
_map_point( _sphere_to_cart( to_rad( inclin ).evalf(), to_rad(azimuth).evalf() ))
def _arc_inclin( start_inc, end_inc, azimuth, step ):
for inclin in range( start_inc, end_inc, step ):
_map_point( _sphere_to_cart( to_rad( inclin ).evalf(), to_rad(azimuth).evalf() ))
def _plot_skeleton():
th = (s.sqrt(3)/2).evalf()
c.line( sx(0), sy(2 * th) , sx(0.5), sy(3 * th) )
c.line( sx(0.5), sy(th) , sx(1.5), sy(3 * th) )
c.line( sx(1), sy(0) , sx(2.5), sy(3 * th) )
c.line( sx(2), sy(0) , sx(3.5), sy(3 * th) )
c.line( sx(3), sy(0) , sx(4.5), sy(3 * th) )
c.line( sx(4), sy(0) , sx(5), sy(2 * th) )
c.line( sx(5), sy(0) , sx(5.5), sy(th) )
c.line( sx(0), sy( 2 * th ), sx(1), sy(0) )
c.line( sx(0.5), sy( 3 * th ), sx(2), sy(0) )
c.line( sx(1.5), sy( 3 * th ), sx(3), sy(0) )
c.line( sx(2.5), sy( 3 * th ), sx(4), sy(0) )
c.line( sx(3.5), sy( 3 * th ), sx(5), sy(0) )
c.line( sx(4.5), sy( 3 * th ), sx(5.5), sy( th ) )
c.line( sx(0), sy( 2 * th), sx( 5 ), sy( 2*th ) )
c.line( sx(0.5), sy(th), sx( 5.5 ), sy( th ) )
# = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
# main
# = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
c = canvas.Canvas( filename, pagesize=( 17*72, 11*72 ) )
d20 = Icosahedron( numeric = True )
d20.rotate_vertices( rot_x( -s.atan2( s.GoldenRatio-1, s.GoldenRatio ).evalf() ) )
d20.make_faces()
mappings = face_mappings( d20 )
inc_factor = (s.pi/180).evalf()
az_factor = (s.pi/180).evalf()
c.setFillColorRGB( .5,.5, 1 )
for azimuth in range( 0, 360, 5 ):
_arc_inclin( 20, 161, azimuth, 1 )
for inclin in range( 20, 161, 5 ):
_arc_azimuth( 0, 360, inclin, 1 )
c.setStrokeColorRGB( .5,.5, .5 )
_plot_skeleton()
c.showPage()
c.save()
