Okay... I'm not so good at maths (didn't even finish our version of high school) and is really tired right now, but I need to orbit four objects elliptically around the centroid and have been stuck for a while, but it's not like I haven't tried or come anywhere by myself. This is what I've come up with so far:
from math import cos,sin,pi,sqrt,atan2
def orbit(p, deg, pivot=(0.32563325, 0.123498),ellipse=(0.5, 0.743992)):
# p = current (x,y)-position of current object,
# Pivot = (x,y)-position of point to orbit around,
# retrieved by centroid((x1,y1),(x2,y2),(x3,y3),(x4,y4))
# Ellipse = (width,height) of ellipse to rotate around
# retrieved by ellipse((x1,y1),(x2,y2),(x3,y3),(x4,y4))
px,py = pivot
if ellipse == (0.0,0.0):
o = polar(p[0]-px,p[1]-py)[0]
xr,yr = 1.0,1.0
else:
ew,eh = ellipse
if ew < eh:
o = eh/2 # Distance to the point most far away from the middle of the ellipse (Outer radius)
xr = ew/eh # Horizontal ratio of ellipse so we can move it back properly into ellipse after performing circular orbit
yr = 1.0 # Verical movement will not be affected because it's on the large axis
else:
o = ew/2
xr = 1.0
yr = eh/ew
x,y = p[0]-px,p[1]-py # Subtract pivot's position (that's the the point I want to orbit around)
d,a = polar(x,y) # Get angle
x,y = rect(o,a+deg) # Move point as far away from middle as it will be as most and make circular orbit around pivot by deg degrees
x,y = x*xr,y*yr # Move points back to elliptic shape by multiplying positions with according ratio <--- I guess it's here something goes wrong
x,y = x+px,y+py # Move point back to original position by adding pivot's positions
return x,y
# Other functions
def centroid(*points):
x,y = izip(*points)
return (sum(x) / len(points), sum(y) / len(points))
def ellipse(*points):
x,y = izip(*points)
xd,yd = max(x)-min(x),max(y)-min(y)
return (xd,yd)
def polar(x,y):
d = sqrt(x**2 + y**2)
a = atan2(y,x) * (180.0/pi)
return d, a
def rect(d,a):
x = d * cos(a*pi/180.0)
y = d * sin(a*pi/180.0)
return x, y
If i use ellipse=(0.0,0.0) and orbit everything in an "ordinary" circle instead of an elliptic shape it works just fine, so I guess it's when I try to multiply the x/y-position with the ratio ew/eh or eh/ew I do something wrong but I can't figure out what at the moment.
I am a bit tired and will try and get some sleep now and see if I can solve it tomorrow but some helpt would really be appriciated here.
This encapsulates the math for each Ellipse, and shows sample usage; you will have to add code for whatever output you want.
from math import sin, cos, pi
class Ellipse(object):
@classmethod
def fromBox(cls, p1=(-1.,-1.), p2=(1.,1.), period=1., offs=0., clockwise=False):
"""
Construct an Ellipse from an axis-aligned bounding box
p1, p2 diagonally-opposed corners of the bounding box
period time for a complete orbit
offs offset into initial rotation
clockwise direction of rotation
"""
x1,y1 = p1
x2,y2 = p2
# find center point
cx, cy = (x1 + x2)*0.5, (y1 + y2)*0.5
# find major and minor semi-axes and corresponding theta
a,b = abs(x2 - x1)*0.5, abs(y2 - y1)*0.5
if a >= b:
theta = 0.0
else:
a,b = b,a
theta = pi/2
# return an Ellipse object
return cls(cx, cy, a, b, theta, period, offs, clockwise)
def __init__(self, x=0., y=0., a=1., b=1., theta=0., period=1., offs=0., clockwise=False):
"""
Create an ellipse
x,y center point
a semi-major axis
b semi-minor axis
theta major axis inclination (in radians)
period time for a complete orbit
offs offset into initial rotation
clockwise direction of rotation
"""
self.x = x
self.y = y
self.period = -period if clockwise else period
self._freq = self.period / (2. * pi)
self.offs = offs
s_th = sin(theta)
c_th = cos(theta)
self._ast = a * s_th
self._act = a * c_th
self._bst = b * s_th
self._bct = b * c_th
def at(self, t):
"""
Evaluate the ellipse at time t
"""
_t = (t - self.offs) * self._freq
st = sin(_t)
ct = cos(_t)
return self.x + self._act*ct - self._bst*st, self.y + self._act*st + self._bst*ct
def main():
a = Ellipse.fromBox((-0.67436675, -0.376502), (1.32563325, 0.623498))
b = Ellipse(0.32563325, 0.123498, 0.9, 0.6, pi/6)
c = Ellipse(0.32563325, 0.123498, 1.1, 0.5, pi/4)
d = Ellipse(0.32563325, 0.123498, 1.0, 0.5, pi/2)
t_step = 0.03
for t in xrange(200):
drawCircle(a.at(t*t_step), "red")
drawCircle(b.at(t*t_step), "blue")
drawCircle(c.at(t*t_step), "green")
drawCircle(d.at(t*t_step), "yellow")
if __name__=="__main__":
main()