On Mon, Sep 28, 2009 at 12:18 PM, Jeff Rush <j...@taupro.com> wrote: << trim >>
> My hobby in high school was (simple forms of) relativity and orbital > mechanics due to a strong SF interest, so the first program I ever wrote > was a time dilation graphing (using punctuation characters) program for > trips to nearby stars. I still have it somewhere on teletype paper and > punch tape. Along the way I lost interest in physics and found the > computer far more interesting because it could actually do stuff that > changed people's lives without a grant and committee approval. :-) > > -Jeff Speaking of orbital mechanics, this module depending on Visual Python and Python 2.x (x >= 5) uses various complex number techniques to move balls in circles, including a moon around a planet. The sun appears to get bigger and smaller as the default VPython view strives to adjust the frame automatically, which in this case causes some auto-zooming. There's a setting for this, part of the tweakable scaffolding. http://www.4dsolutions.net/ocn/python/orbits.py Of course this teaches about complex numbers, not about gravity wells so much. However, in the animation business, such short cuts are sometimes acceptable as its the special effect you're after, not trying to write a simulator or physics engine per se (don't that we don't have those too in some settings). Kirby """ By Kirby Urner, 4D Solutions, Portland, Oregon (copyleft) 2006 Last revised by the original author: 14 Nov 2006 (added Moon class) Complex numbers provide machinery for rotating in the XY plane, where the Y axis is "imaginary", the X axis "real". When two complex numbers multiply, their magnitudes are multiplied (think of vectors) while their angles get added. By keeping the magnitudes = 1, we focus on the angles. A scale factor applied afterwards can change the radius of the orbit. Or we may use the fact that e**(theta*complex(0,1)) takes us around in a circle. This 2nd technique shows up in a Planet class, easiest for having multiple balls, each with its own radius, color, increment, size of orbit. Since visual is expecting three floating points (x,y,z) for position, we use c.real and c.imag to break c into two floating point numbers for plotting purposes. """ import cmath import math from visual import * def orbit1(): """ multiply clock hand by a one degree incrementer """ m = complex(1,0) # vector pointing to 3 o'clock angle = math.radians(1.0) # normalized to unit radius (clock diameter = 2) onedegree = complex(cos(angle), sin(angle)) theball = sphere(pos = (m.real, m.imag), radius = 0.1, color = color.red ) while True: m = m * onedegree # multiplying causes rotation theball.pos = (m.real, m.imag) rate(100) def orbit2(): """ use e**(theta * i) to get coordinates of rotating ball cmath.exp handles a complex number """ onedegree = math.radians(1.0) i = complex(0,1) angle = 0 theball = sphere(pos = (1,0,0), radius = 0.1, color = color.green ) while True: angle += onedegree coords = cmath.exp(angle * i) theball.pos = (coords.real, coords.imag) rate(50) class Planet (object): # subclassing object gives a 'new style' class """ Orbit around (0,0,0) by increment (degrees) per each move invocation """ def __init__(self, distance=1.0, radius=0.1, increment=1, color = color.red): self.pos = (1.0, 0.0, 0.0) self.distance = distance self.radius = radius self.color = color self.theball = sphere(pos = self.pos, radius = self.radius, color = self.color) self.increment = math.radians(increment) self.angle = 0 def move(self): self.angle = self.angle + self.increment coords = cmath.exp(self.angle * complex(0,1)) self.coords = (coords.real * self.distance, coords.imag * self.distance) self.theball.pos = (self.coords[0], self.coords[1]) class Moon(Planet): """ Orbit around planet (1st argument) by increment (degrees) per each move invocation """ def __init__(self, planet, distance=1.0, radius=0.1, increment=1, color = color.red): super(Moon,self).__init__(distance, radius, increment, color) self.planet = planet def move(self): self.angle = self.angle + self.increment coords = cmath.exp(self.angle * complex(0,1)) self.coords = (coords.real * self.distance + self.planet.coords[0], coords.imag * self.distance + self.planet.coords[1]) self.theball.pos = (self.coords[0], self.coords[1]) def solarsystem(): sun = Planet(distance = 0, radius = 0.8, color = color.yellow) p1 = Planet(distance=6.0, radius=0.3, increment=0.5, color = color.green) p2 = Planet(distance=4.0, radius=0.1, increment=1.0, color = color.red) m1 = Moon(p1, distance = 1.0, radius = 0.1, increment = 3.0, color = color.cyan) while True: p1.move() p2.move() m1.move() rate(50) > _______________________________________________ > Edu-sig mailing list > Edu-sig@python.org > http://mail.python.org/mailman/listinfo/edu-sig > _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
