I think the code below is short enough and didactic / general purpose enough to archive / share here on edu-sig, (c) MIT License, versus say Github.
It runs with only visual (Visual Python) as a dependency, which makes it a great demo and provides assets out of the box (simple Vector and Edge classes) to use with that excellent package. Then I'm going to post another demo which in turns depends on this module, and on this one: https://mail.python.org/pipermail/edu-sig/2013-August/010872.html This demo will further show how to use stickworks.py (below) as a resource. NOTE: some code may have word-wrapped during transport. Perform standard maintenance before first use. Kirby """ Some infrastructure for working with Vectors and Edges, including an xyplotter generator and axes maker. (c) By Kirby Urner, Sept 13, 2006, 2013, MIT License # no warranty, "as is" (feel free to bring up to your own # standards before using it to build bridges). Originally # for learning purposes. Updated Sept 29, 2006: make Edge color a class-level attribute add funky derivative demo refactor a bit Updated Sept 27, 2013: made Python 3.2 compatible Original Code: http://www.4dsolutions.net/ocn/python/stickworks.py Video: http://youtu.be/4iMSGKXJ_Ds Some relevant discussion: http://mail.python.org/pipermail/edu-sig/2006-September/007145.html http://mail.python.org/pipermail/edu-sig/2006-September/007149.html http://mail.python.org/pipermail/edu-sig/2006-September/007150.html http://mail.python.org/pipermail/edu-sig/2006-September/007312.html """ from visual import vector, cylinder, cross, dot, diff_angle import visual class Vector (object): """ A wrapper for visual.vector that expresses a cylinder via draw(), always pegged to the origin """ radius = 0.03 def __init__(self, xyz, color=(0,0,1)): self.v = vector(*xyz) self.xyz = xyz self.color = color self.cyl = None def draw(self): """define and render the cylinder""" self.cyl = cylinder(pos = (0,0,0), axis = self.v, radius = self.radius, color = self.color) def erase(self): """toss the cylinder""" if self.cyl: self.cyl.visible = 0 self.cyl = None def __repr__(self): return 'Vector @ (%s,%s,%s)' % self.xyz # some vector ops, including scalar multiplication def diff_angle(self, other): return self.v.diff_angle(other.v) def cross(self, other): temp = cross(self.v, other.v) return Vector((temp.x, temp.y, temp.z)) def dot(self, other): return dot(self.v, other.v) def __sub__(self, other): temp = self.v - other.v return Vector((temp.x, temp.y, temp.z)) def __add__(self, other): temp = self.v + other.v return Vector((temp.x, temp.y, temp.z)) def __mul__(self, scalar): temp = self.v * scalar return Vector((temp.x, temp.y, temp.z)) __rmul__ = __mul__ def __neg__(self): return Vector((-self.v.x, -self.v.y, -self.v.z)) def _length(self): return pow(self.v.x ** 2 + self.v.y ** 2 + self.v.z ** 2, 0.5) length = property(_length) class Edge (object): """ Edges are defined by two Vectors (above) and express as cylinder via draw(). """ radius = 0.03 color = (1,0,0) def __init__(self, v0, v1, color=None): if not isinstance(v0, Vector) or not isinstance(v1, Vector): raise TypeError("Wrong input types") if not color==None: self.color = color self.v0 = v0 self.v1 = v1 self.cyl = None def draw(self): """define and render the cylinder""" temp = (self.v1 - self.v0).xyz self.cyl = cylinder(pos = self.v0.xyz, axis = vector(*temp), radius = self.radius, color = self.color) def erase(self): """toss the cylinder""" if self.cyl: self.cyl.visible = 0 self.cyl = None def _length(self): return (self.v1 - self.v0).length length = property(_length) def __repr__(self): return 'Edge from %s to %s' % (self.v0, self.v1) def xyplotter(domain, f): """ domain should be an initialized generator, ready for next() triggering. f is any function of x. Consecutive Vectors trace connected edges. """ x0 = next(domain) y0 = f(x0) while True: x1 = next(domain) y1 = f(x1) e = Edge( Vector((x0, y0, 0)), Vector((x1, y1, 0)) ) e.draw() yield None x0, y0 = x1, y1 def axes(x=0,y=0,z=0): """ Draw some axes on the VPython canvas """ v0 = Vector((x,0,0)) v0.draw() v0 = Vector((-x,0,0)) v0.draw() v0 = Vector((0,y,0)) v0.draw() v0 = Vector((0,-y,0)) v0.draw() v0 = Vector((0,0,z)) v0.draw() v0 = Vector((0,0,-z)) v0.draw() def dgen(start, step): """ generic domain generator """ while True: yield start start += step def testme(): """ >>> from stickworks import testme Visual 2005-01-08 >>> testme() See: http://www.4dsolutions.net/ocn/graphics/cosines.png """ from math import cos def f(x): return cos(x) d = dgen(-5, 0.1) axes(-5,1,0) graph = xyplotter(d, f) for i in xrange(100): graph.next() def testmemore(): """ See: http://www.4dsolutions.net/ocn/graphics/pycalculus.png """ def snakeywakey(x): """ Polynomial with x-axis crossings at 3,2,-3,-7, with scaler to keep y-values under control (from a plotting point of view) """ return 0.01 * (x-3)*(x-2)*(x+3)*(x+7) def deriv(f, h=1e-5): """ Generic df(x)/dx approximator (discrete h) """ def funk(x): return (f(x+h)-f(x))/h return funk d1 = dgen(-8, 0.1) d2 = dgen(-8, 0.1) d3 = dgen(-8, 0.1) axes(-8,5,3) deriv_snakeywakey = deriv(snakeywakey) second_deriv = deriv(deriv_snakeywakey) graph1 = xyplotter(d1, snakeywakey) graph2 = xyplotter(d2, deriv_snakeywakey) graph3 = xyplotter(d3, second_deriv) Edge.color = (1,0,0) # make snakeywakey red for i in range(130): next(graph1) Edge.color = (0,1,0) # make derivative green for i in range(130): next(graph2) Edge.color = (0,1,1) # make 2nd derivative cyan for i in range(130): next(graph3) if __name__ == '__main__': testmemore()
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