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 convert(pos=(0, 0, 0), up=(0, 1, 0), points=None, closed=True):
pos = vector(pos)
up = norm(vector(up))
up0 = vector(0, 1, 0)
angle = acos(up.dot(up0))
reorient = (angle > 0.0)
axis = up0.cross(up)
pts = []
for pt in points:
newpt = vector(pt[0], 0, -pt[1])
if reorient: newpt = newpt.rotate(angle=angle, axis=axis)
pts.append(pos + newpt)
if closed and (pts[-1] != pts[0]): pts.append(pts[0])
return pts
def convert(pos=(0,0,0), up=(0,1,0), points=None, closed=True):
pos = vector(pos)
up = norm(vector(up))
up0 = vector(0,1,0)
angle = acos(up.dot(up0))
reorient = (angle > 0.0)
axis = up0.cross(up)
pts = []
for pt in points:
newpt = vector(pt[0],0,-pt[1])
if reorient: newpt = newpt.rotate(angle=angle, axis=axis)
pts.append(pos+newpt)
if closed and (pts[-1] != pts[0]): pts.append(pts[0])
return pts
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 key_check(ship_mode, s, v, a, dt, sw_lbl, lbl_off, predraw, earthpos, t, ship):
if scene.kb.keys: # check if there are any keys pressed in the queue
key = scene.kb.getkey() # retrieve the pressed key
# change simulation speed: (steps are small on purpose; user has to press and hold for smooth transition)
if key == 'q' and 1 <= dt < 125:
dt += 2
elif key == 'q' and dt <= 0.95:
dt += 0.05
elif key == 'a' and dt > 1:
dt -= 2
elif key == 'a' and 0.2 < dt <= 1:
dt -= 0.05
elif key == 'esc':
Exit() # exit the program
elif key == 'p':
lbl.visible = True # show pause label
lbl.pos = scene.center # center the label on the screen
scene.kb.getkey() # wait for key input
lbl.visible = False # hide pause label
elif key == 'x':
if scene.stereo == 'nostereo':
scene.stereo = 'redcyan' # turn on 3D rendering mode (red-cyan)
elif scene.stereo == 'redcyan':
scene.stereo = 'crosseyed' # turn on 3D rendering mode (cross-eyed)
else:
scene.stereo = 'nostereo' # turn off 3D rendering mode
elif key == 'l':
sw_lbl = not sw_lbl # planet/spaceship label switch
lbl_off = not lbl_off
elif key == 's':
#if ship_mode:
# music.fadeout(2500) # fade out music when quitting spaceship mode
# else:
# music.play(-1) # turn on music when entering spaceship mode
ship_mode = not ship_mode # spaceship mode switch
a = vector(0, 0, 0) # reset acceleration
sw_lbl = True # turn on spaceship label
# spaceship thrusters control:
elif key == 'up':
#a += vector(0, 0, am) # old cartesian steering
a += am*norm(v) # accelerate into the direction of motion
elif key == 'down':
a -= am*norm(v) # accelerate against the direction of motion
elif key == 'left':
a -= am*cross(norm(v),cross(norm(v),norm(s))) # accelerate to the left of the velocity
elif key == 'right':
a += am*cross(norm(v),cross(norm(v),norm(s))) # accelerate to the right of the velocity
elif key == 'd':
a += am*cross(norm(v),norm(s)) # accelerate to the 'top' of the velocity
elif key == 'c':
a -= am*cross(norm(v),norm(s)) # accelerate to the 'bottom' of the velocity
elif key == '0':
a = vector(0, 0, 0) # reset acceleration
# pre-programmed spaceship positions/scenarios:
elif key == '1': # Earth-Sun Lagrange point 3 (L3 - 'counter-Earth')
s = -earthpos
v0 = (planets[2][1][:, (int(-t + 1)) % n] - planets[2][1][:, (int(-t)) % n]) / (365.25 * 86400 / n)
v = vector(v0[0], v0[1], v0[2])
a = vector(0, 0, 0)
predraw = False
ship.trail.append(pos=s, retain=1)
elif key == '2': # polar orbit around the Sun
s = vector(3e+07, -2e+06, 2e+08)
v = vector(0, 24, 0)
a = vector(0, 0, 0)
predraw = False
ship.trail.append(pos=s, retain=1)
elif key == '3': # orbit of the probe Helios 2 (fastest man-made object to date - 0.02% speed of light)
s = vector(43e6, 0, 0) # perihelion
v = vector(0, 0, 70.22)
a = vector(0, 0, 0)
predraw = False
ship.trail.append(pos=s, retain=1)
elif key == '4': # Halley's comet (derived using specific orbital energy, 162.3 deg inclination)
s = vector(87813952, 0, 0) # perihelion
v = vector(0, 16.7, 52)
a = vector(0, 0, 0)
predraw = False
ship.trail.append(pos=s, retain=1)
return ship_mode, s, v, a, dt, sw_lbl, lbl_off, predraw, ship
def key_check(ship_mode, s, v, a, dt, sw_lbl, lbl_off, predraw, earthpos, t,
ship):
if scene.kb.keys: # check if there are any keys pressed in the queue
key = scene.kb.getkey() # retrieve the pressed key
# change simulation speed: (steps are small on purpose; user has to press and hold for smooth transition)
if key == 'q' and 1 <= dt < 125:
dt += 2
elif key == 'q' and dt <= 0.95:
dt += 0.05
elif key == 'a' and dt > 1:
dt -= 2
elif key == 'a' and 0.2 < dt <= 1:
dt -= 0.05
elif key == 'esc':
Exit() # exit the program
elif key == 'p':
lbl.visible = True # show pause label
lbl.pos = scene.center # center the label on the screen
scene.kb.getkey() # wait for key input
lbl.visible = False # hide pause label
elif key == 'x':
if scene.stereo == 'nostereo':
scene.stereo = 'redcyan' # turn on 3D rendering mode (red-cyan)
elif scene.stereo == 'redcyan':
scene.stereo = 'crosseyed' # turn on 3D rendering mode (cross-eyed)
else:
scene.stereo = 'nostereo' # turn off 3D rendering mode
elif key == 'l':
sw_lbl = not sw_lbl # planet/spaceship label switch
lbl_off = not lbl_off
elif key == 's':
#if ship_mode:
# music.fadeout(2500) # fade out music when quitting spaceship mode
# else:
# music.play(-1) # turn on music when entering spaceship mode
ship_mode = not ship_mode # spaceship mode switch
a = vector(0, 0, 0) # reset acceleration
sw_lbl = True # turn on spaceship label
# spaceship thrusters control:
elif key == 'up':
#a += vector(0, 0, am) # old cartesian steering
a += am * norm(v) # accelerate into the direction of motion
elif key == 'down':
a -= am * norm(v) # accelerate against the direction of motion
elif key == 'left':
a -= am * cross(norm(v), cross(
norm(v), norm(s))) # accelerate to the left of the velocity
elif key == 'right':
a += am * cross(norm(v), cross(
norm(v), norm(s))) # accelerate to the right of the velocity
elif key == 'd':
a += am * cross(norm(v),
norm(s)) # accelerate to the 'top' of the velocity
elif key == 'c':
a -= am * cross(
norm(v), norm(s)) # accelerate to the 'bottom' of the velocity
elif key == '0':
a = vector(0, 0, 0) # reset acceleration
# pre-programmed spaceship positions/scenarios:
elif key == '1': # Earth-Sun Lagrange point 3 (L3 - 'counter-Earth')
s = -earthpos
v0 = (planets[2][1][:, (int(-t + 1)) % n] -
planets[2][1][:, (int(-t)) % n]) / (365.25 * 86400 / n)
v = vector(v0[0], v0[1], v0[2])
a = vector(0, 0, 0)
predraw = False
ship.trail.append(pos=s, retain=1)
elif key == '2': # polar orbit around the Sun
s = vector(3e+07, -2e+06, 2e+08)
v = vector(0, 24, 0)
a = vector(0, 0, 0)
predraw = False
ship.trail.append(pos=s, retain=1)
elif key == '3': # orbit of the probe Helios 2 (fastest man-made object to date - 0.02% speed of light)
s = vector(43e6, 0, 0) # perihelion
v = vector(0, 0, 70.22)
a = vector(0, 0, 0)
predraw = False
ship.trail.append(pos=s, retain=1)
elif key == '4': # Halley's comet (derived using specific orbital energy, 162.3 deg inclination)
s = vector(87813952, 0, 0) # perihelion
v = vector(0, 16.7, 52)
a = vector(0, 0, 0)
predraw = False
ship.trail.append(pos=s, retain=1)
return ship_mode, s, v, a, dt, sw_lbl, lbl_off, predraw, ship
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
