def theta2014(d):
"""
Convert Julian Day into a rotation angle of the sky about the NCP at midnight, relative to spring equinox.
:param d:
Julian day
:return:
Rotation angle, radians
"""
return (d - calendar.julian_day(year=2014, month=3, day=20, hour=16, minute=55, sec=0)) / 365.25 * unit_rev
def do_rendering(self, settings, context):
"""
This method is required to actually render this item.
:param settings:
A dictionary of settings required by the renderer.
:param context:
A GraphicsContext object to use for drawing
:return:
None
"""
is_southern = settings['latitude'] < 0
language = settings['language']
latitude = abs(settings['latitude'])
theme = themes[settings['theme']]
context.set_font_size(1.2)
# Radius of outer edge of star chart
r_2 = r_1 - r_gap
# Radius of day-of-month ticks from centre of star chart
r_3 = r_1 * 0.1 + r_2 * 0.9
# Radius of every fifth day-of-month tick from centre of star chart
r_4 = r_1 * 0.2 + r_2 * 0.8
# Radius of lines between months on date scale
r_5 = r_1
# Radius for writing numeric labels for days of the month
r_6 = r_1 * 0.4 + r_2 * 0.6
# Shade background to month scale
shading_inner_radius = r_1 * 0.55 + r_2 * 0.45
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_1)
context.circle(centre_x=0, centre_y=0, radius=shading_inner_radius)
context.fill(color=theme['shading'])
# Draw the outer edge of planisphere
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_1)
context.fill(color=theme['background'])
# Draw the central hole in the middle of the planisphere
context.begin_sub_path()
context.circle(centre_x=0, centre_y=0, radius=central_hole_size)
context.stroke(color=theme['edge'])
# Combine these two paths to make a clipping path for drawing the star wheel
context.clip()
# Draw lines of constant declination at 15 degree intervals.
for dec in arange(-80, 85, 15):
# Convert declination into radius from the centre of the planisphere
r = radius(dec=dec, latitude=latitude)
if r > r_2:
continue
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r)
context.stroke(color=theme['grid'])
# Draw constellation stick figures
for line in open("raw_data/constellation_stick_figures.dat", "rt"):
line = line.strip()
# Ignore blank lines and comment lines
if (len(line) == 0) or (line[0] == '#'):
continue
# Split line into words.
# These are the names of the constellations, and the start and end points for each stroke.
[name, ra1, dec1, ra2, dec2] = line.split()
# If we're making a southern hemisphere planisphere, we flip the sky upside down
if is_southern:
ra1 = -float(ra1)
ra2 = -float(ra2)
dec1 = -float(dec1)
dec2 = -float(dec2)
# Project RA and Dec into radius and azimuth in the planispheric projection
r_point_1 = radius(dec=float(dec1), latitude=latitude)
if r_point_1 > r_2:
continue
r_point_2 = radius(dec=float(dec2), latitude=latitude)
if r_point_2 > r_2:
continue
p1 = (-r_point_1 * cos(float(ra1) * unit_deg),
-r_point_1 * sin(float(ra1) * unit_deg))
p2 = (-r_point_2 * cos(float(ra2) * unit_deg),
-r_point_2 * sin(float(ra2) * unit_deg))
# Impose a maximum length of 4 cm on constellation stick figures; they get quite distorted at the edge
if hypot(p2[0] - p1[0], p2[1] - p1[1]) > 4 * unit_cm:
continue
# Stroke a line
context.begin_path()
context.move_to(x=p1[0], y=p1[1])
context.line_to(x=p2[0], y=p2[1])
context.stroke(color=theme['stick'], line_width=1, dotted=True)
# Draw stars from Yale Bright Star Catalogue
for star_descriptor in fetch_bright_star_list()['stars'].values():
[ra, dec, mag] = star_descriptor[:3]
# Discard stars fainter than mag 4
if mag == "-" or float(mag) > 4.0:
continue
ra = float(ra)
dec = float(dec)
# If we're making a southern hemisphere planisphere, we flip the sky upside down
if is_southern:
ra *= -1
dec *= -1
r = radius(dec=dec, latitude=latitude)
if r > r_2:
continue
# Represent each star with a small circle
context.begin_path()
context.circle(centre_x=-r * cos(ra * unit_deg),
centre_y=-r * sin(ra * unit_deg),
radius=0.18 * unit_mm * (5 - mag))
context.fill(color=theme['star'])
# Write constellation names
context.set_font_size(0.7)
context.set_color(theme['constellation'])
# Open a list of the coordinates where we place the names of the constellations
for line in open("raw_data/constellation_names.dat"):
line = line.strip()
# Ignore blank lines and comment lines
if (len(line) == 0) or (line[0] == '#'):
continue
# Split line into words
[name, ra, dec] = line.split()[:3]
# Translate constellation name into the requested language, if required
if name in text[language]['constellation_translations']:
name = text[language]['constellation_translations'][name]
ra = float(ra) * 360. / 24
dec = float(dec)
# If we're making a southern hemisphere planisphere, we flip the sky upside down
if is_southern:
ra = -ra
dec = -dec
# Render name of constellation, with _s turned into spaces
name2 = re.sub("_", " ", name)
r = radius(dec=dec, latitude=latitude)
if r > r_2:
continue
p = (-r * cos(ra * unit_deg), -r * sin(ra * unit_deg))
a = atan2(p[0], p[1])
context.text(text=name2,
x=p[0],
y=p[1],
h_align=0,
v_align=0,
gap=0,
rotation=unit_rev / 2 - a)
# Calendar ring counts clockwise in northern hemisphere; anticlockwise in southern hemisphere
s = -1 if not is_southern else 1
def theta2014(d):
"""
Convert Julian Day into a rotation angle of the sky about the north celestial pole at midnight,
relative to spring equinox.
:param d:
Julian day
:return:
Rotation angle, radians
"""
return (d - calendar.julian_day(
year=2014, month=3, day=20, hour=16, minute=55,
sec=0)) / 365.25 * unit_rev
# Write month names around the date scale
context.set_font_size(2.3)
context.set_color(theme['date'])
for mn, (mlen, name) in enumerate(text[language]['months']):
theta = s * theta2014(
calendar.julian_day(year=2014,
month=mn + 1,
day=mlen // 2,
hour=12,
minute=0,
sec=0))
# We supply circular_text with a negative radius here, as a fudge to orientate the text with bottom-inwards
context.circular_text(text=name,
centre_x=0,
centre_y=0,
radius=-(r_1 * 0.65 + r_2 * 0.35),
azimuth=theta / unit_deg + 180,
spacing=1,
size=1)
# Draw ticks for the days of the month
for mn, (mlen, name) in enumerate(text[language]['months']):
# Tick marks for each day
for d in range(1, mlen + 1):
theta = s * theta2014(
calendar.julian_day(year=2014,
month=mn + 1,
day=d,
hour=0,
minute=0,
sec=0))
# Days of the month which are multiples of 5 get longer ticks
R = r_3 if (d % 5) else r_4
# The last day of each month is drawn as a dividing line between months
if d == mlen:
R = r_5
# Draw line
context.begin_path()
context.move_to(x=r_2 * cos(theta), y=-r_2 * sin(theta))
context.line_to(x=R * cos(theta), y=-R * sin(theta))
context.stroke(line_width=1, dotted=False)
# Write numeric labels for the 10th, 20th and last day of each month
for d in [10, 20, mlen]:
theta = s * theta2014(
calendar.julian_day(year=2014,
month=mn + 1,
day=d,
hour=0,
minute=0,
sec=0))
context.set_font_size(1.2)
# First digit
theta2 = theta + 0.15 * unit_deg
context.text(text="%d" % (d / 10),
x=r_6 * cos(theta2),
y=-r_6 * sin(theta2),
h_align=1,
v_align=0,
gap=0,
rotation=-theta + pi / 2)
# Second digit
theta2 = theta - 0.15 * unit_deg
context.text(text="%d" % (d % 10),
x=r_6 * cos(theta2),
y=-r_6 * sin(theta2),
h_align=-1,
v_align=0,
gap=0,
rotation=-theta + pi / 2)
# Draw the dividing line between the date scale and the star chart
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_2)
context.stroke(color=theme['date'], line_width=1, dotted=False)
def do_rendering(self, settings, context):
"""
This method is required to actually render this item.
:param settings:
A dictionary of settings required by the renderer.
:param context:
A GraphicsContext object to use for drawing
:return:
None
"""
language = settings['language']
theme = themes[settings['theme']]
context.set_color(color=theme['lines'])
# Define the radii of all the concentric circles to be drawn on back of mother
# Scale of angles around the rim of the astrolabe
r_2 = r_1 - d_12
r_3 = r_2 - d_12 / 2
# Zodiacal constellations
r_4 = r_3 - d_12
r_5 = r_4 - d_12
# Calendar for 1394
r_6 = r_5 - d_12
r_7 = r_6 - d_12
# Days of the year
r_8 = r_7 - d_12 / 2
# Calendar for 1974
r_9 = r_8 - d_12
r_10 = r_9 - d_12
# Saints' days
r_11 = r_10 - d_12
r_12 = r_11 - d_12
# Radius of the central hole
r_13 = d_12 * centre_scaling
# Draw the handle at the top of the astrolabe
ang = 180 * unit_deg - acos(unit_cm / r_1)
context.begin_path()
context.arc(centre_x=0,
centre_y=-r_1,
radius=2 * unit_cm,
arc_from=-ang - pi / 2,
arc_to=ang - pi / 2)
context.move_to(x=0, y=-r_1 - 2 * unit_cm)
context.line_to(x=0, y=-r_1 + 2 * unit_cm)
context.stroke()
# Draw circles 1-13 onto back of mother
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_1)
context.begin_sub_path()
context.circle(centre_x=0, centre_y=0, radius=r_13)
context.stroke(line_width=1)
context.clip()
for radius, line_width in ((r_2, 1), (r_3, 3), (r_4, 1), (r_5, 3),
(r_6, 1), (r_7, 1), (r_8, 1), (r_9, 1),
(r_10, 3), (r_11, 1), (r_12, 1), (r_13, 1)):
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=radius)
context.stroke(line_width=line_width)
# Label space between circles 1-5 with passage of Sun through zodiacal constellations
# Mark every 30 degrees, where Sun enters new zodiacal constellation
for theta in arange(0 * unit_deg, 359 * unit_deg, 30 * unit_deg):
context.begin_path()
context.move_to(x=r_1 * cos(theta), y=-r_1 * sin(theta))
context.line_to(x=r_5 * cos(theta), y=-r_5 * sin(theta))
context.stroke()
# Mark 5-degree intervals within each zodiacal constellation
for theta in arange(0 * unit_deg, 359 * unit_deg, 5 * unit_deg):
context.begin_path()
context.move_to(x=r_1 * cos(theta), y=-r_1 * sin(theta))
context.line_to(x=r_4 * cos(theta), y=-r_4 * sin(theta))
context.stroke()
# Mark fine scale of 1-degree intervals between circles 2 and 3
for theta in arange(0 * unit_deg, 359.9 * unit_deg, 1 * unit_deg):
context.begin_path()
context.move_to(x=r_2 * cos(theta), y=-r_2 * sin(theta))
context.line_to(x=r_3 * cos(theta), y=-r_3 * sin(theta))
context.stroke()
# Between circles 1 and 2, surround the entire astrolabe with a protractor scale from 0 to 90 degrees
# Radius from centre for writing the text of the protractor scale around the rim
rt_1 = (r_1 + r_2) / 2
for theta in arange(-180 * unit_deg, 179 * unit_deg, 10 * unit_deg):
# Work out angle to display around the rim: counts from 0 to 90 four times, not -180 to 180 degrees!
if theta < -179 * unit_deg:
theta_disp = theta
elif theta < -90 * unit_deg:
theta_disp = theta + 180 * unit_deg
elif theta < 0 * unit_deg:
theta_disp = -theta
elif theta < 90 * unit_deg:
theta_disp = theta
else:
theta_disp = -theta + 180 * unit_deg
# Display angles around rim as rounded integers
theta_disp = floor(theta_disp / unit_deg + 0.01)
context.set_font_size(1.2)
# Display right-hand zero as a simple one-digit zero
if theta_disp == 0:
theta2 = theta
context.text(text="0",
x=rt_1 * cos(theta2),
y=-rt_1 * sin(theta2),
h_align=-1,
v_align=0,
gap=0,
rotation=-theta - 90 * unit_deg)
# Display a cross sign at the left-hand zero
elif theta_disp == -180:
theta2 = theta
context.set_font_size(2.1)
context.text(text="\u2720",
x=rt_1 * cos(theta2),
y=-rt_1 * sin(theta2),
h_align=0,
v_align=0,
gap=0,
rotation=-theta - 90 * unit_deg)
# Display all other angles as two digits, carefully arranged with one digit on either side of the line
else:
theta2 = theta - 0.2 * unit_deg
context.text(text="{:.0f}".format(theta_disp / 10),
x=rt_1 * cos(theta2),
y=-rt_1 * sin(theta2),
h_align=1,
v_align=0,
gap=0,
rotation=-theta - 90 * unit_deg)
theta2 = theta + 0.2 * unit_deg
context.text(text="{:.0f}".format(theta_disp % 10),
x=rt_1 * cos(theta2),
y=-rt_1 * sin(theta2),
h_align=-1,
v_align=0,
gap=0,
rotation=-theta - 90 * unit_deg)
# Between circles 3 and 4, mark 10-, 20-, 30-degree points within each zodiacal constellation
# Radius for writing the 30 degree scales within each zodiacal constellation
rt_2 = (r_3 + r_4) / 2
for theta in arange(-180 * unit_deg, 179 * unit_deg, 10 * unit_deg):
context.set_font_size(1.2)
# Work out what angle to display, which is rotation angle modulo 30 degrees
theta_disp = floor(theta / unit_deg + 380.01) % 30 + 10
# Write two digits separately, with a slight gap between them for the dividing line they label
theta2 = theta - 0.2 * unit_deg
context.text(text="{:.0f}".format(theta_disp / 10),
x=rt_2 * cos(theta2),
y=-rt_2 * sin(theta2),
h_align=1,
v_align=0,
gap=0,
rotation=-theta - 90 * unit_deg)
theta2 = theta + 0.2 * unit_deg
context.text(text="{:.0f}".format(theta_disp % 10),
x=rt_2 * cos(theta2),
y=-rt_2 * sin(theta2),
h_align=-1,
v_align=0,
gap=0,
rotation=-theta - 90 * unit_deg)
# Write names of zodiacal constellations between circles 4 and 5
for i, item in enumerate(text[language]["zodiacal_constellations"]):
i += 1
name = "{} {}".format(item['name'], item['symbol'])
context.circular_text(text=name,
centre_x=0,
centre_y=0,
radius=(r_4 * 0.65 + r_5 * 0.35),
azimuth=(-15 + 30 * i),
spacing=1,
size=1)
# Between circles 5 and 10, display calendars for 1394 and 1974
# The Tuckerman tables provide the longitude of the Sun along the ecliptic on any given day of the year.
# We produce functions which interpolate the tabulated longitudes, so that we can look up the longitude
# of the Sun at any moment in time.
x_1394 = [] # List of Julian day numbers of supplied data points
y_1394 = [] # List of solar longitude values for each data point
x_1974 = []
y_1974 = []
for line in open("raw_data/tuckerman.dat", "rt"):
line = line.strip()
# Ignore blank lines and comment lines
if (len(line) == 0) or (line[0] == '#'):
continue
# Split line into words
columns = [float(i) for i in line.split()]
x_1394.append(
calendar.julian_day(year=1394,
month=int(columns[0]),
day=int(columns[1]),
hour=12,
minute=0,
sec=0))
x_1974.append(
calendar.julian_day(year=1974,
month=int(columns[0]),
day=int(columns[1]),
hour=12,
minute=0,
sec=0))
y_1394.append(30 * unit_deg * (columns[4] - 1) +
columns[5] * unit_deg)
y_1974.append(30 * unit_deg * (columns[6] - 1) +
columns[7] * unit_deg)
# Use scipy to do linear interpolation between the supplied data
theta_1394 = scipy.interpolate.interp1d(x=x_1394,
y=y_1394,
kind='linear')
theta_1974 = scipy.interpolate.interp1d(x=x_1974,
y=y_1974,
kind='linear')
# Mark 365 days around calendar using the solar longitude data we have.
# Write numbers on the 10th, 20th and last day of each month
rt_1 = (r_6 + r_7) / 2 # Radius of text for the 1394 calendar
rt_2 = (r_8 + r_9) / 2 # Radius of text for the 1974 calendar
prev_theta = 30 * unit_deg * (10 - 1) + 9.4 * unit_deg
for line in open("raw_data/tuckerman.dat"):
line = line.strip()
# Ignore blank lines and comment lines
if (len(line) == 0) or (line[0] == "#"):
continue
m, d, interval, last, z1394, a1394, z1974, a1974 = [
float(i) for i in line.split()
]
# *** Calendar for 1974 ***
# Work out azimuth of given date in 1974 calendar
theta = 30 * unit_deg * (z1974 - 1) + a1974 * unit_deg
# Interpolate interval into number of days since last data point in table (normally five)
if prev_theta > theta:
prev_theta = prev_theta - unit_rev
for i in arange(0, interval - 0.1):
theta_day = prev_theta + (theta - prev_theta) * (i +
1) / interval
context.begin_path()
context.move_to(x=r_7 * cos(theta_day),
y=-r_7 * sin(theta_day))
context.line_to(x=r_8 * cos(theta_day),
y=-r_8 * sin(theta_day))
context.stroke()
prev_theta = theta
# Draw a marker line on calendar. Month ends get longer markers
if last:
context.begin_path()
context.move_to(x=r_8 * cos(theta), y=-r_8 * sin(theta))
context.line_to(x=r_10 * cos(theta), y=-r_10 * sin(theta))
context.stroke()
else:
context.begin_path()
context.move_to(x=r_8 * cos(theta), y=-r_8 * sin(theta))
context.line_to(x=r_9 * cos(theta), y=-r_9 * sin(theta))
context.stroke()
# Label 10th and 20th day of month, and last day of month
if ((d % 10) == 0) or (d > 26):
context.set_font_size(1.0)
theta2 = theta - 0.2 * unit_deg
context.text(text="{:.0f}".format(floor(d / 10)),
x=rt_2 * cos(theta2),
y=-rt_2 * sin(theta2),
h_align=1,
v_align=0,
gap=0,
rotation=-theta - 90 * unit_deg)
theta2 = theta + 0.2 * unit_deg
context.text(text="{:.0f}".format(d % 10),
x=rt_2 * cos(theta2),
y=-rt_2 * sin(theta2),
h_align=-1,
v_align=0,
gap=0,
rotation=-theta - 90 * unit_deg)
# *** Calendar for 1394 ***
# Work out azimuth of given date in 1394 calendar
if settings['astrolabe_type'] == 'full':
theta = 30 * unit_deg * (z1394 - 1) + a1394 * unit_deg
if last:
context.begin_path()
context.move_to(x=r_5 * cos(theta), y=-r_5 * sin(theta))
context.line_to(x=r_7 * cos(theta), y=-r_7 * sin(theta))
context.stroke()
else:
context.begin_path()
context.move_to(x=r_6 * cos(theta), y=-r_6 * sin(theta))
context.line_to(x=r_7 * cos(theta), y=-r_7 * sin(theta))
context.stroke()
# Label 10th and 20th day of month, and last day of month
if ((d % 10) == 0) or (d > 26):
context.set_font_size(0.75)
theta2 = theta - 0.2 * unit_deg
context.text(text="{:.0f}".format(d / 10),
x=rt_1 * cos(theta2),
y=-rt_1 * sin(theta2),
h_align=1,
v_align=0,
gap=0,
rotation=-theta - 90 * unit_deg)
theta2 = theta + 0.2 * unit_deg
context.text(text="{:.0f}".format(d % 10),
x=rt_1 * cos(theta2),
y=-rt_1 * sin(theta2),
h_align=-1,
v_align=0,
gap=0,
rotation=-theta - 90 * unit_deg)
# Label names of months
for mn, (mlen, name) in enumerate(text[language]['months']):
theta = theta_1974(
calendar.julian_day(year=1974,
month=mn + 1,
day=mlen // 2,
hour=12,
minute=0,
sec=0))
context.circular_text(text=name,
centre_x=0,
centre_y=0,
radius=r_9 * 0.65 + r_10 * 0.35,
azimuth=theta / unit_deg,
spacing=1,
size=0.9)
if settings['astrolabe_type'] == 'full':
theta = theta_1394(
calendar.julian_day(year=1394,
month=mn + 1,
day=mlen // 2,
hour=12,
minute=0,
sec=0))
context.circular_text(text=name,
centre_x=0,
centre_y=0,
radius=r_5 * 0.65 + r_6 * 0.35,
azimuth=theta / unit_deg,
spacing=1,
size=0.75)
# Add dates of saints days between circles 10 and 12
context.set_font_size(1.0)
for line in open("raw_data/saints_days.dat"):
line = line.strip()
# Ignore blank lines and comment lines
if (len(line) == 0) or (line[0] == "#"):
continue
d, m, name = line.split()
day_week = floor(
calendar.julian_day(year=1974,
month=int(m),
day=int(d),
hour=12,
minute=0,
sec=0) -
calendar.julian_day(
year=1974, month=1, day=1, hour=12, minute=0, sec=0)) % 7
sunday_letter = "abcdefg"[day_week:day_week + 1]
theta = theta_1974(
calendar.julian_day(year=1974,
month=int(m),
day=int(d),
hour=12,
minute=0,
sec=0))
context.circular_text(text=name,
centre_x=0,
centre_y=0,
radius=r_10 * 0.65 + r_11 * 0.35,
azimuth=theta / unit_deg,
spacing=1,
size=1)
context.circular_text(text=sunday_letter,
centre_x=0,
centre_y=0,
radius=r_11 * 0.65 + r_12 * 0.35,
azimuth=theta / unit_deg,
spacing=1,
size=1)
# Shadow scale in middle of astrolabe
if settings['astrolabe_type'] == 'full':
context.begin_path()
# Draw horizontal radial line labelled Occidens
theta_a = 0 * unit_deg
context.move_to(x=r_12 * cos(theta_a), y=-r_12 * sin(theta_a))
context.line_to(x=r_13 * cos(theta_a), y=-r_13 * sin(theta_a))
# Radial line between RECTA and VERSA
theta_b = -45 * unit_deg
context.move_to(x=r_12 * cos(theta_b), y=-r_12 * sin(theta_b))
context.line_to(x=r_13 * cos(theta_b), y=-r_13 * sin(theta_b))
# Radial line between UMBRA and UMBRA
theta_c = -135 * unit_deg
context.move_to(x=r_12 * cos(theta_c), y=-r_12 * sin(theta_c))
context.line_to(x=r_13 * cos(theta_c), y=-r_13 * sin(theta_c))
# Draw horizontal radial line labelled Oriens
theta_d = 180 * unit_deg
context.move_to(x=r_12 * cos(theta_d), y=-r_12 * sin(theta_d))
context.line_to(x=r_13 * cos(theta_d), y=-r_13 * sin(theta_d))
# Vertical line at right edge of shadow scale
context.move_to(x=r_12 * cos(theta_b), y=-r_12 * sin(theta_b))
context.line_to(x=r_12 * cos(theta_b), y=0)
# Horizontal line along bottom of shadow scale
context.move_to(x=r_12 * cos(theta_b), y=-r_12 * sin(theta_b))
context.line_to(x=r_12 * cos(theta_c), y=-r_12 * sin(theta_c))
# Vertical line at left edge of shadow scale
context.move_to(x=r_12 * cos(theta_c), y=-r_12 * sin(theta_c))
context.line_to(x=r_12 * cos(theta_c), y=0)
# Central vertical line down middle of shadow scale
context.move_to(x=0, y=-r_12 * sin(theta_c))
context.line_to(x=0, y=r_13)
context.move_to(x=0, y=-r_12)
context.line_to(x=0, y=-r_13)
rs1 = r_12 - 0.75 * d_12 / 2 # Radius of corners of fine shadow scale
rs2 = rs1 - 0.75 * d_12 # Radius of corners of coarse shadow scale
# Draw horizontal and vertical sides of the fine and coarse shadow scales
context.move_to(x=rs1 * cos(theta_b), y=-rs1 * sin(theta_b))
context.line_to(x=rs1 * cos(theta_b), y=0)
context.move_to(x=rs1 * cos(theta_b), y=-rs1 * sin(theta_b))
context.line_to(x=rs1 * cos(theta_c), y=-rs1 * sin(theta_c))
context.move_to(x=rs1 * cos(theta_c), y=-rs1 * sin(theta_c))
context.line_to(x=rs1 * cos(theta_c), y=0)
context.move_to(x=rs2 * cos(theta_b), y=-rs2 * sin(theta_b))
context.line_to(x=rs2 * cos(theta_b), y=0)
context.move_to(x=rs2 * cos(theta_b), y=-rs2 * sin(theta_b))
context.line_to(x=rs2 * cos(theta_c), y=-rs2 * sin(theta_c))
context.move_to(x=rs2 * cos(theta_c), y=-rs2 * sin(theta_c))
context.line_to(x=rs2 * cos(theta_c), y=0)
context.stroke()
# Write the UMBRA and VERSA labels on the shadow scale
context.set_font_size(0.64)
context.text(text="UMBRA",
x=-1 * unit_mm,
y=-rs2 * sin(theta_c),
h_align=1,
v_align=-1,
gap=0.7 * unit_mm,
rotation=0)
context.text(text="UMBRA",
x=rs2 * cos(theta_c),
y=unit_mm,
h_align=-1,
v_align=-1,
gap=0.7 * unit_mm,
rotation=pi / 2)
context.text(text="RECTA",
x=1 * unit_mm,
y=-rs2 * sin(theta_c),
h_align=-1,
v_align=-1,
gap=0.7 * unit_mm,
rotation=0)
context.text(text="VERSA",
x=rs2 * cos(theta_b),
y=unit_mm,
h_align=1,
v_align=-1,
gap=0.7 * unit_mm,
rotation=-pi / 2)
context.text(text="ORIENS",
x=-r_12 * 0.95,
y=0,
h_align=-1,
v_align=-1,
gap=0.8 * unit_mm,
rotation=0)
context.text(text="OCCIDENS",
x=r_12 * 0.95,
y=0,
h_align=1,
v_align=-1,
gap=0.8 * unit_mm,
rotation=0)
r_label = (rs1 + rs2) / 2
offset = 5 * unit_deg
# Divisions of scale on shadow scale
q = 90 * unit_deg
for i in range(1, 12):
# Decide how long to make this tick
rs = rs2 if (i % 4 == 0) else rs1
# Draw a tick on the shadow scale (right side)
theta = -atan(i / 12)
context.begin_path()
context.move_to(x=rs * cos(theta_b),
y=-rs * cos(theta_b) * tan(theta))
context.line_to(x=r_12 * cos(theta_b),
y=-r_12 * cos(theta_b) * tan(theta))
context.stroke()
# Label every fourth tick
if i % 4 == 0:
context.text(text="{:d}".format(i),
x=r_label * cos(theta_b),
y=-r_label * cos(theta_b) *
tan(theta - offset),
h_align=0,
v_align=0,
gap=0,
rotation=-q - theta)
# Draw a tick on the shadow scale (bottom right)
theta = -atan(12 / i)
context.begin_path()
context.move_to(x=rs * sin(theta_b) / tan(theta),
y=-rs * sin(theta_b))
context.line_to(x=r_12 * sin(theta_b) / tan(theta),
y=-r_12 * sin(theta_b))
context.stroke()
# Label every fourth tick
if i % 4 == 0:
context.text(text="{:d}".format(i),
x=r_label * sin(theta_b) /
tan(theta - offset),
y=-r_label * sin(theta_b),
h_align=0,
v_align=0,
gap=0,
rotation=-q - theta)
# Draw a tick on the shadow scale (bottom left)
theta = -2 * q - theta
context.begin_path()
context.move_to(x=rs * sin(theta_b) / tan(theta),
y=-rs * sin(theta_b))
context.line_to(x=r_12 * sin(theta_b) / tan(theta),
y=-r_12 * sin(theta_b))
context.stroke()
# Label every fourth tick
if i % 4 == 0:
context.text(text="{:d}".format(i),
x=r_label * sin(theta_b) /
tan(theta + offset),
y=-r_label * sin(theta_b),
h_align=0,
v_align=0,
gap=0,
rotation=-q - theta)
# Draw a tick on the shadow scale (left side)
theta = -2 * q + atan(i / 12)
context.begin_path()
context.move_to(x=rs * cos(theta_c),
y=-rs * cos(theta_c) * tan(theta))
context.line_to(x=r_12 * cos(theta_c),
y=-r_12 * cos(theta_c) * tan(theta))
context.stroke()
# Label every fourth tick
if i % 4 == 0:
context.text(text="{:d}".format(i),
x=r_label * cos(theta_c),
y=-r_label * cos(theta_c) *
tan(theta + offset),
h_align=0,
v_align=0,
gap=0,
rotation=-q - theta)
# Add the 12s to the ends of the shadow scale
theta = -45 * unit_deg
context.text(text="12",
x=r_label * sin(theta_b) / tan(theta - offset),
y=-r_label * sin(theta_b),
h_align=0,
v_align=0,
gap=0,
rotation=-pi / 4)
theta = -135 * unit_deg
context.text(text="12",
x=r_label * sin(theta_b) / tan(theta + offset),
y=-r_label * sin(theta_b),
h_align=0,
v_align=0,
gap=0,
rotation=pi / 4)
# Unequal hours scale -- the maths behind this is explained in
# http://adsabs.harvard.edu/abs/1975JBAA...86...18E
# First draw innermost circle, which touches centre of astrolabe and the top of the unequal hours scale
context.begin_path()
context.circle(centre_x=0, centre_y=-r_12 / 2, radius=r_12 / 2)
context.stroke()
# Now draw arcs for the hours 1 to 11
for theta in arange(15 * unit_deg, 75.1 * unit_deg, 15 * unit_deg):
# Vertical position of the centre of the arc
y_centre = r_12 * cos(theta) / 2 + r_12 * sin(theta) / 2 * tan(
theta)
# Size of arc
arc_end = atan2(
r_12 * sin(theta),
r_12 * cos(theta) / 2 - r_12 * sin(theta) / 2 * tan(theta))
context.begin_path()
context.arc(centre_x=0,
centre_y=-y_centre,
radius=y_centre,
arc_from=arc_end - pi / 2,
arc_to=-arc_end - pi / 2)
context.stroke()
# Finish up
context.set_color(color=theme['text'])
context.circular_text(text=text[language]['copyright'],
centre_x=0,
centre_y=0,
radius=r_12 - 2 * unit_mm,
azimuth=270,
spacing=1,
size=0.7)
def do_rendering(self, settings, context):
"""
This method is required to actually render this item.
:param settings:
A dictionary of settings required by the renderer.
:param context:
A GraphicsContext object to use for drawing
:return:
None
"""
language = settings['language']
theme = themes[settings['theme']]
context.set_color(color=theme['lines'])
# Radii of circles to be drawn on back of mother
r_2 = r_1 - d_12
r_3 = r_2 - d_12 / 2
r_4 = r_3 - d_12
r_5 = r_4 - d_12
r_6 = r_5 - d_12
r_7 = r_6 - d_12
r_8 = r_7 - d_12 / 2
r_9 = r_8 - d_12
r_10 = r_9 - d_12
r_11 = r_10 - d_12
r_12 = r_11 - d_12
r_13 = d_12 * centre_scaling
# No need for circle 12 in the Hungarian version
if language == "hu":
r_12=r_11
# Draw the handle at the top of the astrolabe
ang = 180 * unit_deg - acos(unit_cm / r_1)
context.begin_path()
context.arc(centre_x=0, centre_y=-r_1, radius=2 * unit_cm,
arc_from=-ang - pi / 2, arc_to=ang - pi / 2)
context.move_to(x=0, y=-r_1 - 2 * unit_cm)
context.line_to(x=0, y=-r_1 + 2 * unit_cm)
context.stroke()
# Draw circles 1-13 onto back of mother
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_1)
context.begin_sub_path()
context.circle(centre_x=0, centre_y=0, radius=r_13)
context.stroke(line_width=1)
context.clip()
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_2)
context.stroke(line_width=1)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_3)
context.stroke(line_width=3)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_4)
context.stroke(line_width=1)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_5)
context.stroke(line_width=3)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_6)
context.stroke(line_width=1)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_7)
context.stroke(line_width=1)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_8)
context.stroke(line_width=1)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_9)
context.stroke(line_width=1)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_10)
context.stroke(line_width=3)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_11)
context.stroke(line_width=1)
if language != "hu":
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_12)
context.stroke(line_width=1)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_13)
context.stroke(line_width=1)
# Label space between circles 1-5 with passage of Sun through zodiacal constellations
# Mark every 30 degrees, where Sun enters new zodiacal constellation
for theta in arange(0 * unit_deg, 359 * unit_deg, 30 * unit_deg):
context.begin_path()
context.move_to(x=r_1 * cos(theta), y=-r_1 * sin(theta))
context.line_to(x=r_5 * cos(theta), y=-r_5 * sin(theta))
context.stroke()
# Mark five degree intervals within each zodiacal constellation
for theta in arange(0 * unit_deg, 359 * unit_deg, 5 * unit_deg):
context.begin_path()
context.move_to(x=r_1 * cos(theta), y=-r_1 * sin(theta))
context.line_to(x=r_4 * cos(theta), y=-r_4 * sin(theta))
context.stroke()
# Mark fine scale of 1-degree intervals between circles 2 and 3
for theta in arange(0 * unit_deg, 359.9 * unit_deg, 1 * unit_deg):
context.begin_path()
context.move_to(x=r_2 * cos(theta), y=-r_2 * sin(theta))
context.line_to(x=r_3 * cos(theta), y=-r_3 * sin(theta))
context.stroke()
# Between circles 3 and 4 mark each constellation 10, 20, 30 degrees
# Also, between circles 1 and 2, surround entire astrolabe with 0, 10, .. 90 degrees
rt_1 = (r_1 + r_2) / 2
rt_2 = (r_3 + r_4) / 2
for theta in arange(-180 * unit_deg, 179 * unit_deg, 10 * unit_deg):
if theta < -179 * unit_deg:
theta_disp = theta
elif theta < - 90 * unit_deg:
theta_disp = theta + 180 * unit_deg
elif theta < 0 * unit_deg:
theta_disp = -theta
elif theta < 90 * unit_deg:
theta_disp = theta
else:
theta_disp = -theta + 180 * unit_deg
theta_disp = floor(theta_disp / unit_deg + 0.01)
context.set_font_size(1.2)
if theta_disp == 0:
theta2 = theta
context.text(text="0",
x=rt_1 * cos(theta2), y=-rt_1 * sin(theta2),
h_align=-1, v_align=0, gap=0, rotation=-theta - 90 * unit_deg)
elif theta_disp == -180:
theta2 = theta
context.set_font_size(2.1)
context.text(text="\u2720",
x=rt_1 * cos(theta2), y=-rt_1 * sin(theta2),
h_align=0, v_align=0, gap=0, rotation=-theta - 90 * unit_deg)
else:
theta2 = theta - 0.2 * unit_deg
context.text(text="{:.0f}".format(theta_disp / 10),
x=rt_1 * cos(theta2), y=-rt_1 * sin(theta2),
h_align=1, v_align=0, gap=0, rotation=-theta - 90 * unit_deg)
theta2 = theta + 0.2 * unit_deg
context.text(text="{:.0f}".format(theta_disp % 10),
x=rt_1 * cos(theta2), y=-rt_1 * sin(theta2),
h_align=-1, v_align=0, gap=0, rotation=-theta - 90 * unit_deg)
context.set_font_size(1.2)
theta_disp = floor(theta / unit_deg + 380.01) % 30 + 10
theta2 = theta - 0.2 * unit_deg
context.text(text="{:.0f}".format(theta_disp / 10),
x=rt_2 * cos(theta2), y=-rt_2 * sin(theta2),
h_align=1, v_align=0, gap=0, rotation=-theta - 90 * unit_deg)
theta2 = theta + 0.2 * unit_deg
context.text(text="{:.0f}".format(theta_disp % 10),
x=rt_2 * cos(theta2), y=-rt_2 * sin(theta2),
h_align=-1, v_align=0, gap=0, rotation=-theta - 90 * unit_deg)
# Write names of zodiacal constellations
for i, item in enumerate(text[language]["zodiacal_constellations"]):
i += 1
name = "{} {}".format(item['name'], item['symbol'])
context.circular_text(text=name,
centre_x=0, centre_y=0, radius=(r_4 * 0.65 + r_5 * 0.35),
azimuth=(-15 + 30 * i),
spacing=1, size=1)
# Between circles 5 and 10, display calendars for 1394 and 1974
# Produce functions which interpolate the Tuckerman tables
x_1394 = []
y_1394 = []
x_1974 = []
y_1974 = []
for line in open("raw_data/tuckerman.dat", "rt"):
line = line.strip()
# Ignore blank lines and comment lines
if (len(line) == 0) or (line[0] == '#'):
continue
# Split line into words
columns = [float(i) for i in line.split()]
x_1394.append(calendar.julian_day(year=1394, month=int(columns[0]), day=int(columns[1]),
hour=12, minute=0, sec=0))
x_1974.append(calendar.julian_day(year=1974, month=int(columns[0]), day=int(columns[1]),
hour=12, minute=0, sec=0))
y_1394.append(30 * unit_deg * (columns[4] - 1) + columns[5] * unit_deg)
y_1974.append(30 * unit_deg * (columns[6] - 1) + columns[7] * unit_deg)
theta_1394 = scipy.interpolate.interp1d(x=x_1394, y=y_1394, kind='linear')
theta_1974 = scipy.interpolate.interp1d(x=x_1974, y=y_1974, kind='linear')
# Use Tuckerman table to mark 365 days around calendar.
# Write numbers on the 10th, 20th and last day of each month
rt_1 = (r_6 + r_7) / 2
rt_2 = (r_8 + r_9) / 2
last_theta = 30 * unit_deg * (10 - 1) + 9.4 * unit_deg
for line in open("raw_data/tuckerman.dat"):
line = line.strip()
# Ignore blank lines and comment lines
if (len(line) == 0) or (line[0] == "#"):
continue
m, d, interval, last, z1394, a1394, z1974, a1974 = [float(i) for i in line.split()]
# Work out azimuth of given date in 1974 calendar
theta = 30 * unit_deg * (z1974 - 1) + a1974 * unit_deg
# Interpolate interval into number of days since last data point in table (normally five)
if last_theta > theta:
last_theta = last_theta - unit_rev
for i in arange(0, interval - 0.1):
theta_day = last_theta + (theta - last_theta) * (i + 1) / interval
context.begin_path()
context.move_to(x=r_7 * cos(theta_day), y=-r_7 * sin(theta_day))
context.line_to(x=r_8 * cos(theta_day), y=-r_8 * sin(theta_day))
context.stroke()
last_theta = theta
# Draw a marker line on calendar. Month ends get longer markers
if last:
context.begin_path()
context.move_to(x=r_8 * cos(theta), y=-r_8 * sin(theta))
context.line_to(x=r_10 * cos(theta), y=-r_10 * sin(theta))
context.stroke()
else:
context.begin_path()
context.move_to(x=r_8 * cos(theta), y=-r_8 * sin(theta))
context.line_to(x=r_9 * cos(theta), y=-r_9 * sin(theta))
context.stroke()
# Label 10th and 20th day of month, and last day of month
if ((d % 10) == 0) or (d > 26):
context.set_font_size(1.0)
theta2 = theta - 0.2 * unit_deg
context.text(text="{:.0f}".format(d / 10),
x=rt_2 * cos(theta2), y=-rt_2 * sin(theta2),
h_align=1, v_align=0, gap=0, rotation=-theta - 90 * unit_deg)
theta2 = theta + 0.2 * unit_deg
context.text(text="{:.0f}".format(d % 10),
x=rt_2 * cos(theta2), y=-rt_2 * sin(theta2),
h_align=-1, v_align=0, gap=0, rotation=-theta - 90 * unit_deg)
# Work out azimuth of given date in 1394 calendar
theta = 30 * unit_deg * (z1394 - 1) + a1394 * unit_deg
if last:
context.begin_path()
context.move_to(x=r_5 * cos(theta), y=-r_5 * sin(theta))
context.line_to(x=r_7 * cos(theta), y=-r_7 * sin(theta))
context.stroke()
else:
context.begin_path()
context.move_to(x=r_6 * cos(theta), y=-r_6 * sin(theta))
context.line_to(x=r_7 * cos(theta), y=-r_7 * sin(theta))
context.stroke()
# Label 10th and 20th day of month, and last day of month
if ((d % 10) == 0) or (d > 26):
context.set_font_size(0.75)
theta2 = theta - 0.2 * unit_deg
context.text(text="{:.0f}".format(d / 10),
x=rt_1 * cos(theta2), y=-rt_1 * sin(theta2),
h_align=1, v_align=0, gap=0, rotation=-theta - 90 * unit_deg)
theta2 = theta + 0.2 * unit_deg
context.text(text="{:.0f}".format(d % 10),
x=rt_1 * cos(theta2), y=-rt_1 * sin(theta2),
h_align=-1, v_align=0, gap=0, rotation=-theta - 90 * unit_deg)
# Label names of months
for mn, (mlen, name) in enumerate(text[language]['months']):
theta = theta_1974(calendar.julian_day(year=1974, month=mn + 1, day=mlen // 2, hour=12, minute=0, sec=0))
context.circular_text(text=name, centre_x=0, centre_y=0, radius=r_9 * 0.65 + r_10 * 0.35,
azimuth=theta / unit_deg,
spacing=1, size=0.9)
theta = theta_1394(calendar.julian_day(year=1394, month=mn + 1, day=mlen // 2, hour=12, minute=0, sec=0))
context.circular_text(text=name, centre_x=0, centre_y=0, radius=r_5 * 0.65 + r_6 * 0.35,
azimuth=theta / unit_deg,
spacing=1, size=0.75)
# Add significant dates between circles 10 and 12
context.set_font_size(1.0)
# In a Hungarian astrolabe we generate the old names of the months instead
if language != "hu":
data_file = "raw_data/saints_days.dat"
else:
data_file = "raw_data/old_hungarian_months.dat"
for line in open(data_file):
line = line.strip()
# Ignore blank lines and comment lines
if (len(line) == 0) or (line[0] == "#"):
continue
d, m, name = line.split()
day_week = floor(calendar.julian_day(year=1974, month=int(m), day=int(d), hour=12, minute=0, sec=0) -
calendar.julian_day(year=1974, month=1, day=1, hour=12, minute=0, sec=0)) % 7
sunday_letter = "abcdefg"[day_week:day_week + 1]
theta = theta_1974(calendar.julian_day(year=1974, month=int(m), day=int(d), hour=12, minute=0, sec=0))
context.circular_text(text=name, centre_x=0, centre_y=0, radius=r_10 * 0.65 + r_11 * 0.35,
azimuth=theta / unit_deg,
spacing=1, size=1)
if language != "hu":
context.circular_text(text=sunday_letter, centre_x=0, centre_y=0, radius=r_11 * 0.65 + r_12 * 0.35,
azimuth=theta / unit_deg,
spacing=1, size=1)
# Shadow scale in middle of astrolabe
context.begin_path()
theta_a = 0 * unit_deg
context.move_to(x=r_12 * cos(theta_a), y=-r_12 * sin(theta_a))
context.line_to(x=r_13 * cos(theta_a), y=-r_13 * sin(theta_a))
theta_b = - 45 * unit_deg
context.move_to(x=r_12 * cos(theta_b), y=-r_12 * sin(theta_b))
context.line_to(x=r_13 * cos(theta_b), y=-r_13 * sin(theta_b))
theta_c = -135 * unit_deg
context.move_to(x=r_12 * cos(theta_c), y=-r_12 * sin(theta_c))
context.line_to(x=r_13 * cos(theta_c), y=-r_13 * sin(theta_c))
theta_d = 180 * unit_deg
context.move_to(x=r_12 * cos(theta_d), y=-r_12 * sin(theta_d))
context.line_to(x=r_13 * cos(theta_d), y=-r_13 * sin(theta_d))
context.move_to(x=r_12 * cos(theta_b), y=-r_12 * sin(theta_b))
context.line_to(x=r_12 * cos(theta_b), y=0)
context.move_to(x=r_12 * cos(theta_b), y=-r_12 * sin(theta_b))
context.line_to(x=r_12 * cos(theta_c), y=-r_12 * sin(theta_c))
context.move_to(x=r_12 * cos(theta_c), y=-r_12 * sin(theta_c))
context.line_to(x=r_12 * cos(theta_c), y=0)
context.move_to(x=0, y=-r_12 * sin(theta_c))
context.line_to(x=0, y=r_13)
context.move_to(x=0, y=-r_12)
context.line_to(x=0, y=-r_13)
rs1 = r_12 - 0.75 * d_12 / 2
rs2 = rs1 - 0.75 * d_12
context.move_to(x=rs1 * cos(theta_b), y=-rs1 * sin(theta_b))
context.line_to(x=rs1 * cos(theta_b), y=0)
context.move_to(x=rs1 * cos(theta_b), y=-rs1 * sin(theta_b))
context.line_to(x=rs1 * cos(theta_c), y=-rs1 * sin(theta_c))
context.move_to(x=rs1 * cos(theta_c), y=-rs1 * sin(theta_c))
context.line_to(x=rs1 * cos(theta_c), y=0)
context.move_to(x=rs2 * cos(theta_b), y=-rs2 * sin(theta_b))
context.line_to(x=rs2 * cos(theta_b), y=0)
context.move_to(x=rs2 * cos(theta_b), y=-rs2 * sin(theta_b))
context.line_to(x=rs2 * cos(theta_c), y=-rs2 * sin(theta_c))
context.move_to(x=rs2 * cos(theta_c), y=-rs2 * sin(theta_c))
context.line_to(x=rs2 * cos(theta_c), y=0)
context.stroke()
context.set_font_size(0.64)
context.text(text="UMBRA", x=-1 * unit_mm, y=-rs2 * sin(theta_c), h_align=1, v_align=-1, gap=0.7 * unit_mm,
rotation=0)
context.text(text="UMBRA", x=rs2 * cos(theta_c), y=unit_mm, h_align=-1, v_align=-1, gap=0.7 * unit_mm,
rotation=pi / 2)
context.text(text="RECTA", x=1 * unit_mm, y=-rs2 * sin(theta_c), h_align=-1, v_align=-1, gap=0.7 * unit_mm,
rotation=0)
context.text(text="VERSA", x=rs2 * cos(theta_b), y=unit_mm, h_align=1, v_align=-1, gap=0.7 * unit_mm,
rotation=-pi / 2)
context.text(text="ORIENS", x=-r_12 * 0.95, y=0, h_align=-1, v_align=-1, gap=0.8 * unit_mm, rotation=0)
context.text(text="OCCIDENS", x=r_12 * 0.95, y=0, h_align=1, v_align=-1, gap=0.8 * unit_mm, rotation=0)
r_label = (rs1 + rs2) / 2
offset = 5 * unit_deg
# Divisions of scale
q = 90 * unit_deg
for i in range(1, 12):
rs = rs2 if (i % 4 == 0) else rs1
theta = -atan(i / 12)
context.begin_path()
context.move_to(x=rs * cos(theta_b), y=-rs * cos(theta_b) * tan(theta))
context.line_to(x=r_12 * cos(theta_b), y=-r_12 * cos(theta_b) * tan(theta))
context.stroke()
if i % 4 == 0:
context.text(text="{:d}".format(i),
x=r_label * cos(theta_b), y=-r_label * cos(theta_b) * tan(theta - offset),
h_align=0, v_align=0, gap=0, rotation=-q - theta)
theta = -atan(12 / i)
context.begin_path()
context.move_to(x=rs * sin(theta_b) / tan(theta), y=-rs * sin(theta_b))
context.line_to(x=r_12 * sin(theta_b) / tan(theta), y=-r_12 * sin(theta_b))
context.stroke()
if i % 4 == 0:
context.text(text="{:d}".format(i),
x=r_label * sin(theta_b) / tan(theta - offset), y=-r_label * sin(theta_b),
h_align=0, v_align=0, gap=0, rotation=-q - theta)
theta = -2 * q - theta
context.begin_path()
context.move_to(x=rs * sin(theta_b) / tan(theta), y=-rs * sin(theta_b))
context.line_to(x=r_12 * sin(theta_b) / tan(theta), y=-r_12 * sin(theta_b))
context.stroke()
if i % 4 == 0:
context.text(text="{:d}".format(i),
x=r_label * sin(theta_b) / tan(theta + offset), y=-r_label * sin(theta_b),
h_align=0, v_align=0, gap=0, rotation=-q - theta)
theta = -2 * q + atan(i / 12)
context.begin_path()
context.move_to(x=rs * cos(theta_c), y=-rs * cos(theta_c) * tan(theta))
context.line_to(x=r_12 * cos(theta_c), y=-r_12 * cos(theta_c) * tan(theta))
context.stroke()
if i % 4 == 0:
context.text(text="{:d}".format(i),
x=r_label * cos(theta_c), y=-r_label * cos(theta_c) * tan(theta + offset),
h_align=0, v_align=0, gap=0, rotation=-q - theta)
theta = - 45 * unit_deg
context.text(text="12", x=r_label * sin(theta_b) / tan(theta - offset), y=-r_label * sin(theta_b), h_align=0,
v_align=0, gap=0, rotation=-pi / 4)
theta = -135 * unit_deg
context.text(text="12", x=r_label * sin(theta_b) / tan(theta + offset), y=-r_label * sin(theta_b), h_align=0,
v_align=0, gap=0, rotation=pi / 4)
# Unequal hours scale
context.begin_path()
context.circle(centre_x=0, centre_y=-r_12 / 2, radius=r_12 / 2)
context.stroke()
for theta in arange(15 * unit_deg, 75.1 * unit_deg, 15 * unit_deg):
y_centre = r_12 * cos(theta) / 2 + r_12 * sin(theta) / 2 * tan(theta)
arc_end = atan2(r_12 * sin(theta), r_12 * cos(theta) / 2 - r_12 * sin(theta) / 2 * tan(theta))
context.begin_path()
context.arc(centre_x=0, centre_y=-y_centre, radius=y_centre,
arc_from=arc_end - pi / 2, arc_to=-arc_end - pi / 2)
context.stroke()
# Finish up
context.set_color(color=theme['text'])
context.circular_text(text=text[language]['copyright'], centre_x=0, centre_y=0, radius=r_12 - 2 * unit_mm,
azimuth=270, spacing=1, size=0.7)
def do_rendering(self, settings, context):
"""
This method is required to actually render this item.
:param settings:
A dictionary of settings required by the renderer.
:param context:
A GraphicsContext object to use for drawing
:return:
None
"""
is_southern = settings['latitude'] < 0
language = settings['language']
latitude = abs(settings['latitude'])
theme = themes[settings['theme']]
context.set_font_size(1.2)
r_2 = r_1 - r_gap
r_3 = r_1 * 0.1 + r_2 * 0.9
r_4 = r_1 * 0.2 + r_2 * 0.8
r_5 = r_1
r_6 = r_1 * 0.4 + r_2 * 0.6
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_1) # Outer edge of planisphere
context.fill(color=theme['background'])
context.begin_sub_path()
context.circle(centre_x=0, centre_y=0, radius=central_hole_size) # White out central hole
context.stroke(color=theme['edge'])
context.clip()
for dec in arange(-80, 85, 15):
r = radius(dec=dec, latitude=latitude)
if r > r_2:
continue
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r)
context.stroke(color=theme['grid'])
# Draw constellation stick figures
for line in open("raw_data/constellation_stick_figures.dat", "rt"):
line = line.strip()
# Ignore blank lines and comment lines
if (len(line) == 0) or (line[0] == '#'):
continue
# Split line into words
[name, ra1, dec1, ra2, dec2] = line.split()
if is_southern:
ra1 = -float(ra1)
ra2 = -float(ra2)
dec1 = -float(dec1)
dec2 = -float(dec2)
r_point_1 = radius(dec=float(dec1), latitude=latitude)
if r_point_1 > r_2:
continue
r_point_2 = radius(dec=float(dec2), latitude=latitude)
if r_point_2 > r_2:
continue
p1 = (-r_point_1 * cos(float(ra1) * unit_deg), -r_point_1 * sin(float(ra1) * unit_deg))
p2 = (-r_point_2 * cos(float(ra2) * unit_deg), -r_point_2 * sin(float(ra2) * unit_deg))
# Impose a maximum length of 4 cm on constellation stick figures; they get quite distored at the edge
if hypot(p2[0] - p1[0], p2[1] - p1[1]) > 4 * unit_cm:
continue
context.begin_path()
context.move_to(x=p1[0], y=p1[1])
context.line_to(x=p2[0], y=p2[1])
context.stroke(color=theme['stick'], line_width=1, dotted=True)
# Draw stars from Yale Bright Star Catalogue
for star_descriptor in fetch_bright_star_list()['stars'].values():
[ra, dec, mag] = star_descriptor[:3]
# Discard stars fainter than mag 4
if mag == "-" or float(mag) > 4.0:
continue
ra = float(ra)
dec = float(dec)
if is_southern:
ra *= -1
dec *= -1
r = radius(dec=dec, latitude=latitude)
if r > r_2:
continue
context.begin_path()
context.circle(centre_x=-r * cos(ra * unit_deg), centre_y=-r * sin(ra * unit_deg),
radius=0.18 * unit_mm * (5 - mag))
context.fill(color=theme['star'])
# Write constellation names
context.set_font_size(0.7)
context.set_color(theme['constellation'])
for line in open("raw_data/constellation_names.dat"):
line = line.strip()
# Ignore blank lines and comment lines
if (len(line) == 0) or (line[0] == '#'):
continue
# Split line into words
[name, ra, dec] = line.split()[:3]
# Translate constellation name, if required
if name in text[language]['constellation_translations']:
name = text[language]['constellation_translations'][name]
ra = float(ra) * 360. / 24
dec = float(dec)
if is_southern:
ra = -ra
dec = -dec
name2 = re.sub("_", " ", name)
r = radius(dec=dec, latitude=latitude)
if r > r_2:
continue
p = (-r * cos(ra * unit_deg), -r * sin(ra * unit_deg))
a = atan2(p[0], p[1])
context.text(text=name2, x=p[0], y=p[1], h_align=0, v_align=0, gap=0, rotation=unit_rev / 2 - a)
# Calendar ring counts clockwise in northern hemisphere; anticlockwise in southern hemisphere
s = -1 if not is_southern else 1
def theta2014(d):
"""
Convert Julian Day into a rotation angle of the sky about the NCP at midnight, relative to spring equinox.
:param d:
Julian day
:return:
Rotation angle, radians
"""
return (d - calendar.julian_day(year=2014, month=3, day=20, hour=16, minute=55, sec=0)) / 365.25 * unit_rev
# Write month names
context.set_font_size(1.8)
context.set_color(theme['date'])
for mn, (mlen, name) in enumerate(text[language]['months']):
theta = s * theta2014(calendar.julian_day(year=2014, month=mn+1, day=mlen // 2, hour=12, minute=0, sec=0))
# We supply circular_text with a negative radius here, as a fudge to orientate the text with bottom-inwards
context.circular_text(text=name, centre_x=0, centre_y=0, radius=-(r_1 * 0.65 + r_2 * 0.35),
azimuth=theta / unit_deg + 180,
spacing=1, size=1)
# Write day ticks
for mn, (mlen, name) in enumerate(text[language]['months']):
# Tick marks
for d in range(1, mlen + 1):
theta = s * theta2014(calendar.julian_day(year=2014, month=mn+1, day=d, hour=0, minute=0, sec=0))
R = r_3 if (d % 5) else r_4 # Multiples of 5 get longer ticks
if d == mlen:
R = r_5
context.begin_path()
context.move_to(x=r_2 * cos(theta), y=-r_2 * sin(theta))
context.line_to(x=R * cos(theta), y=-R * sin(theta))
context.stroke(line_width=1, dotted=False)
# Numeric labels
for d in [10, 20, mlen]:
theta = s * theta2014(calendar.julian_day(year=2014, month=mn+1, day=d, hour=0, minute=0, sec=0))
context.set_font_size(1.0)
theta2 = theta + 0.15 * unit_deg
context.text(text="%d" % (d / 10), x=r_6 * cos(theta2), y=-r_6 * sin(theta2),
h_align=1, v_align=0,
gap=0,
rotation=-theta + pi/2)
theta2 = theta - 0.15 * unit_deg
context.text(text="%d" % (d % 10), x=r_6 * cos(theta2), y=-r_6 * sin(theta2),
h_align=-1, v_align=0,
gap=0,
rotation=-theta + pi/2)
context.begin_path()
context.circle(centre_x=0, centre_y=0, radius=r_2)
context.stroke(color=theme['date'], line_width=1, dotted=False)