http://www.ccl.net/cca/software/SOURCES/PYTHON/HINSEN/Vector.shtml
CCL Vector
```# This module defines 3d geometrical vectors with the standard
# operations on them.
#
# Last revision: 1996-1-26
#

"""This module defines three-dimensional geometrical vectors. Vectors support
the usual mathematical operations (v1, v2: vectors, s: scalar):
v1-v2           subtraction
v1*v2           scalar product
s*v1            multiplication with a scalar
v1/s            division by a scalar
v1.cross(v2)    cross product
v1.length()     length
v1.normal()     normal vector in direction of v1
v1.angle(v2)    angle between two vectors
v1.x(), v1[0]   first element
v1.y(), v1[1]   second element
v1.z(), v1[2]   third element

The module offers the following items for export:
Vector(x,y,z)   the constructor for vectors
isVector(x)     a type check function
ex, ey, ez      unit vectors along the x-, y-, and z-axes (predefined constants)

Note: vector elements can be any kind of numbers on which the operations
addition, subtraction, multiplication, division, comparison, sqrt, and acos
are defined. Integer elements are treated as floating point elements.
"""

import umath, types

class Vector:

isVector = 1

def __init__(self, x=0., y=0., z=0.):
self.data = [x,y,z]

def __repr__(self):
return 'Vector(%s,%s,%s)' % (`self.data[0]`,\
`self.data[1]`,`self.data[2]`)

def __str__(self):
return `self.data`

return Vector(self.data[0]+other.data[0],\
self.data[1]+other.data[1],self.data[2]+other.data[2])

def __neg__(self):
return Vector(-self.data[0], -self.data[1], -self.data[2])

def __sub__(self, other):
return Vector(self.data[0]-other.data[0],\
self.data[1]-other.data[1],self.data[2]-other.data[2])

def __rsub__(self, other):
return Vector(other.data[0]-self.data[0],\
other.data[1]-self.data[1],other.data[2]-self.data[2])

def __mul__(self, other):
if isVector(other):
return reduce(lambda a,b: a+b,
map(lambda a,b: a*b, self.data, other.data))
else:
return Vector(self.data[0]*other, self.data[1]*other,
self.data[2]*other)

def __rmul__(self, other):
if isVector(other):
return reduce(lambda a,b: a+b,
map(lambda a,b: a*b, self.data, other.data))
else:
return Vector(other*self.data[0], other*self.data[1],
other*self.data[2])

def __div__(self, other):
if isVector(other):
raise TypeError, "Can't divide by a vector"
else:
return Vector(_div(self.data[0],other), _div(self.data[1],other),
_div(self.data[2],other))

def __rdiv__(self, other):
raise TypeError, "Can't divide by a vector"

def __cmp__(self, other):
return cmp(self.data[0],other.data[0]) \
or cmp(self.data[1],other.data[1]) \
or cmp(self.data[2],other.data[2])

def __getitem__(self, index):
return self.data[index]

def x(self):
return self.data[0]
def y(self):
return self.data[1]
def z(self):
return self.data[2]

def length(self):
return umath.sqrt(self*self)

def normal(self):
len = self.length()
if len == 0:
raise ZeroDivisionError, "Can't normalize a zero-length vector"
return self/len

def cross(self, other):
if not isVector(other):
raise TypeError, "Cross product with non-vector"
return Vector(self.data[1]*other.data[2]-self.data[2]*other.data[1],
self.data[2]*other.data[0]-self.data[0]*other.data[2],
self.data[0]*other.data[1]-self.data[1]*other.data[0])

def angle(self, other):
if not isVector(other):
raise TypeError, "Angle between vector and non-vector"
cosa = (self*other)/(self.length()*other.length())
cosa = max(-1.,min(1.,cosa))
return umath.acos(cosa)

# Type check

def isVector(x):
return hasattr(x,'isVector')

# "Correct" division for arbitrary number types

def _div(a,b):
if type(a) == types.IntType and type(b) == types.IntType:
return float(a)/float(b)
else:
return a/b

# Some useful constants

ex = Vector(1.,0.,0.)
ey = Vector(0.,1.,0.)
ez = Vector(0.,0.,1.)
```
 Modified: Mon Jan 29 17:00:00 1996 GMT Page accessed 6396 times since Sat Apr 17 21:35:46 1999 GMT