def line(pos=(0,0), np=2, rotate=0.0, scale=1.0, xscale=1.0, yscale=1.0,
thickness=None, start=(0,0), end=(0,1), path=False):
v = vis.vector((end[0]-start[0]), (end[1]-start[1]))
if thickness is None:
thickness = 0.01*vis.mag(v)
dv = thickness*vis.norm(vis.vector(0,0,1).cross(v))
dx = dv.x
dy = dv.y
cp = [] # outer line
cpi = [] # inner line
vline = (vis.vector(end)-vis.vector(start)).norm()
mline = vis.mag(vis.vector(end)-vis.vector(start))
for i in range(np):
x = start[0] + (vline*i)[0]/float(np-1)*mline
y = start[1] + (vline*i)[1]/float(np-1)*mline
cp.append( (x+pos[0],y+pos[1]) )
cpi.append( (x+pos[0]+dx,y+pos[1]+dy) )
if not path:
cpi.reverse()
for p in cpi:
cp.append(p)
cp.append(cp[0])
if rotate != 0.0: cp = rotatecp(cp, pos, rotate)
if scale != 1.0: xscale = yscale = scale
pp = Polygon(cp)
if xscale != 1.0 or yscale != 1.0: pp.scale(xscale,yscale)
if not path:
return pp
else:
return [cp]
def ship(s, v, a, dt, spaceship, predraw):
dst = vector(0, 0, 0) - s # computing spaceship - Sun distance vector
gravity_acc = (u / (mag2(dst))) * norm(dst) # computing gravity force
v += (gravity_acc + a) * dt # numerical integration of velocity
s += v * dt # numerical integration of position
spaceship.pos = s # assigning new position to the spaceship
spaceship.trail.append(pos=s, retain=2000) # appending spaceship trail with new position
# recovers the spaceship to the initial position in case of crashing into the Sun or going out of range:
if star_radius <= mag(s) or mag(s) <= sun_radius:
spaceship.pos = s0
spaceship.trail.pos = [] # clear the trail
s, v, a = vector(s0.astuple()), vector(v0.astuple()), vector(a0.astuple()) # assign initial values
predraw = False # redraw the orbital prediction
return s, v, a, predraw
def ship(s, v, a, dt, spaceship, predraw):
dst = vector(0, 0, 0) - s # computing spaceship - Sun distance vector
gravity_acc = (u / (mag2(dst))) * norm(dst) # computing gravity force
v += (gravity_acc + a) * dt # numerical integration of velocity
s += v * dt # numerical integration of position
spaceship.pos = s # assigning new position to the spaceship
spaceship.trail.append(
pos=s, retain=2000) # appending spaceship trail with new position
# recovers the spaceship to the initial position in case of crashing into the Sun or going out of range:
if star_radius <= mag(s) or mag(s) <= sun_radius:
spaceship.pos = s0
spaceship.trail.pos = [] # clear the trail
s, v, a = vector(s0.astuple()), vector(v0.astuple()), vector(
a0.astuple()) # assign initial values
predraw = False # redraw the orbital prediction
return s, v, a, predraw
def lbl_ship(popup, obj, s, v, a):
# get magnitudes of distance from the Sun, velocity and acceleration:
r0mag = mag(s)
v0mag = mag(v)
a0mag = mag(a) * 1e6 # converted from km/s^2 to m/s^2
eps = mag2(v) / 2 - u / r0mag # compute specific orbital energy
popup.pos = obj.pos # update label position to overlap with spaceship position
# update label text with new data:
popup.text = "Spaceship!" + \
"\nAcceleration: " + str(a) + \
"\nSpecific orbital energy: " + str(eps) + " MJ/kg" + \
"\nDistance from the Sun: " + str(int(round(r0mag))) + " km (" + str(
round(r0mag / 149598261, 2)) + " AU)" + \
"\nEngine Acceleration: " + str(round(a0mag, 2)) + " m/s^2" + \
"\nOrbital Velocity: " + str(round(v0mag, 2)) + " km/s"
popup.visible = True
return popup
def lbl_ship(popup, obj, s, v, a):
# get magnitudes of distance from the Sun, velocity and acceleration:
r0mag = mag(s)
v0mag = mag(v)
a0mag = mag(a) * 1e6 # converted from km/s^2 to m/s^2
eps = mag2(v) / 2 - u / r0mag # compute specific orbital energy
popup.pos = obj.pos # update label position to overlap with spaceship position
# update label text with new data:
popup.text = "Spaceship!" + \
"\nAcceleration: " + str(a) + \
"\nSpecific orbital energy: " + str(eps) + " MJ/kg" + \
"\nDistance from the Sun: " + str(int(round(r0mag))) + " km (" + str(
round(r0mag / 149598261, 2)) + " AU)" + \
"\nEngine Acceleration: " + str(round(a0mag, 2)) + " m/s^2" + \
"\nOrbital Velocity: " + str(round(v0mag, 2)) + " km/s"
popup.visible = True
return popup
def lbl(popup, obj, sw_lbl, dt):
# global variables for comparison between function calls
global obj_global, a_global, eps_global, name_global, radius_global
err = 1e20 # large number for error comparison in the for loop below
r0mag = mag(obj.pos) # computing the instantaneous distance from the Sun
if r0mag == 0: # turning off the planet label if the clicked object is centered at the origin (i.e. Sun, stars)
sw_lbl = not sw_lbl
return popup, sw_lbl
if obj_global != obj: # execute only if new object was chosen
# looking through the planet list searching for the closest value for semi major axis for the selected object:
for planet in planet_list:
if (abs(planet['a'] - r0mag)) < err:
err = (abs(planet['a'] - r0mag)) # assign new closest value
a_global = planet['a'] # assign semi-major axis
name_global = planet['name'] # assign planet name
radius_global = planet['radius'] # assign planet radius
eps_global = -u / (2 * a_global
) # compute specific orbital energy
obj_global = obj # assign new object as already labeled
v0mag = (2 * (eps_global + u / r0mag)
)**0.5 # velocity calculation using specific orbital energy
popup.pos = obj.pos # update label position to overlap with planet position
# update label text with new data:
popup.text = str(name_global) + \
"\nRadius: " + str(radius_global) + " km" + \
"\nDistance from the Sun: " + str(int(round(r0mag))) + " km (" + str(
round(r0mag / 149598261, 2)) + " AU)" + \
"\nOrbital Velocity: " + str(round(v0mag, 2)) + " km/s" + \
"\nTime scale: 1 s = " + str(round(f * dt * 365.25 * 86400 / (3600. * n), 3)) + "hrs"
popup.visible = True
return popup, sw_lbl
def lbl(popup, obj, sw_lbl, dt):
# global variables for comparison between function calls
global obj_global, a_global, eps_global, name_global, radius_global
err = 1e20 # large number for error comparison in the for loop below
r0mag = mag(obj.pos) # computing the instantaneous distance from the Sun
if r0mag == 0: # turning off the planet label if the clicked object is centered at the origin (i.e. Sun, stars)
sw_lbl = not sw_lbl
return popup, sw_lbl
if obj_global != obj: # execute only if new object was chosen
# looking through the planet list searching for the closest value for semi major axis for the selected object:
for planet in planet_list:
if (abs(planet['a'] - r0mag)) < err:
err = (abs(planet['a'] - r0mag)) # assign new closest value
a_global = planet['a'] # assign semi-major axis
name_global = planet['name'] # assign planet name
radius_global = planet['radius'] # assign planet radius
eps_global = -u / (2 * a_global) # compute specific orbital energy
obj_global = obj # assign new object as already labeled
v0mag = (2 * (eps_global + u / r0mag)) ** 0.5 # velocity calculation using specific orbital energy
popup.pos = obj.pos # update label position to overlap with planet position
# update label text with new data:
popup.text = str(name_global) + \
"\nRadius: " + str(radius_global) + " km" + \
"\nDistance from the Sun: " + str(int(round(r0mag))) + " km (" + str(
round(r0mag / 149598261, 2)) + " AU)" + \
"\nOrbital Velocity: " + str(round(v0mag, 2)) + " km/s" + \
"\nTime scale: 1 s = " + str(round(f * dt * 365.25 * 86400 / (3600. * n), 3)) + "hrs"
popup.visible = True
return popup, sw_lbl
def roundc(cp, roundness=0.1, nseg=8, invert=False):
vort = 0.0
cp.pop()
for i in range(len(cp)):
i1 = (i+1)%len(cp)
i2 = (i+2)%len(cp)
v1 = vis.vector(cp[i1]) - vis.vector(cp[i])
v2 = vis.vector(cp[(i2)%len(cp)]) - vis.vector(cp[i1])
dv = vis.dot(v1,v2)
vort += dv
if vort > 0: cp.reverse()
l = 999999
for i in range(len(cp)):
p1 = vis.vector(cp[i])
p2 = vis.vector(cp[(i+1)%len(cp)])
lm = vis.mag(p2-p1)
if lm < l: l = lm
r = l*roundness
ncp = []
lcp = len(cp)
for i in range(lcp):
i1 = (i+1)%lcp
i2 = (i+2)%lcp
w0 = vis.vector(cp[i])
w1 = vis.vector(cp[i1])
w2 = vis.vector(cp[i2])
wrt = vis.cross((w1-w0),(w2-w0))
v1 = w1-w0
v2 = w1-w2
rax = vis.norm(((vis.norm(v1)+vis.norm(v2))/2.0))
angle = acos(vis.dot(vis.norm(v2),vis.norm(v1)))
afl = 1.0
if wrt[2] > 0: afl = -1.0
angle2 = angle/2.0
cc = r/sin(angle2)
ccp = vis.vector(cp[i1]) - rax*cc
tt = r/tan(angle2)
t1 = vis.vector(cp[i1]) -vis.norm(v1)*tt
t2 = vis.vector(cp[i1]) -vis.norm(v2)*tt
ncp.append(tuple(t1)[0:2])
nc = []
a = 0
dseg = afl*(pi-angle)/nseg
if not invert:
for i in range(nseg):
nc.append(rotatep(t1, ccp, a))
ncp.append(tuple(nc[-1])[0:2])
a -= dseg
else:
dseg = afl*(angle)/nseg
for i in range(nseg):
nc.append(rotatep(t1, (cp[i1][0],cp[i1][1],0), a))
ncp.append(tuple(nc[-1])[0:2])
a += dseg
ncp.append(tuple(t2)[0:2])
ncp.append(ncp[0])
return ncp