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 _precalculate( self ):
num_vertices = len( self.vertices )
if num_vertices < 3:
raise InvalidPolygon
# we don't check for planarity
vert_list = list( self.vertices )
vert_list.append( vert_list[0] )
# calculate the polygon normal
self.plane = three_point_plane( vert_list[0], vert_list[1], vert_list[2] )
self.normal = self.plane.normal
# calculate the (directed) edges
self.edges = list()
self.edge_normals = list()
for x in range( num_vertices ):
self.edges.append( two_point_line( vert_list[x], vert_list[x+1] ) )
self.edge_normals.append( self.edges[x].v.cross( self.normal ) )
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 test_cube_hits( self ):
d6 = Icosahedron( numeric = True )
d6.rotate_vertices( rot_x( -s.atan2( s.GoldenRatio-1, s.GoldenRatio ).evalf() ) )
d6.make_faces()
print d6.face_hit( two_point_line( v_x, zero_3d))
print d6.face_hit( two_point_line( -v_x, zero_3d))
print d6.face_hit( two_point_line( v_y, zero_3d))
print d6.face_hit( two_point_line( -v_y, zero_3d))
print d6.face_hit( two_point_line( v_z, zero_3d))
print d6.face_hit( two_point_line( -v_z, zero_3d))
print d6.face_hit( two_point_line( v_x+v_y+v_z, zero_3d))
print d6.face_hit( two_point_line( v_x+v_y-v_z, zero_3d))
print d6.face_hit( two_point_line( v_x-v_y+v_z, zero_3d))
print d6.face_hit( two_point_line( v_x-v_y-v_z, zero_3d))
print d6.face_hit( two_point_line( -v_x+v_y+v_z, zero_3d))
print d6.face_hit( two_point_line( -v_x+v_y-v_z, zero_3d))
print d6.face_hit( two_point_line( -v_x-v_y+v_z, zero_3d))
print d6.face_hit( two_point_line( -v_x-v_y-v_z, zero_3d))
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()
