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# This module defines 3d geometrical vectors with the standard
# operations on them.
#
# Written by: Konrad Hinsen
# 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 addition
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:
Vec3D(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 math, types
class Vec3:
isVec3 = 1
def __init__(self, x=0., y=0., z=0.):
self.data = [x,y,z]
def __repr__(self):
return 'Vec3(%s,%s,%s)' % (`self.data[0]`,\
`self.data[1]`,`self.data[2]`)
def __str__(self):
return `self.data`
def __add__(self, other):
return Vec3(self.data[0]+other.data[0],\
self.data[1]+other.data[1],self.data[2]+other.data[2])
__radd__ = __add__
def __neg__(self):
return Vec3(-self.data[0], -self.data[1], -self.data[2])
def __sub__(self, other):
return Vec3(self.data[0]-other.data[0],\
self.data[1]-other.data[1],self.data[2]-other.data[2])
def __rsub__(self, other):
return Vec3(other.data[0]-self.data[0],\
other.data[1]-self.data[1],other.data[2]-self.data[2])
def __mul__(self, other):
if isVec3(other):
return reduce(lambda a,b: a+b,
map(lambda a,b: a*b, self.data, other.data))
else:
return Vec3(self.data[0]*other, self.data[1]*other,
self.data[2]*other)
def __rmul__(self, other):
if isVec3(other):
return reduce(lambda a,b: a+b,
map(lambda a,b: a*b, self.data, other.data))
else:
return Vec3(other*self.data[0], other*self.data[1],
other*self.data[2])
def __div__(self, other):
if isVec3(other):
raise TypeError, "Can't divide by a vector"
else:
return Vec3(_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 math.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 isVec3(other):
raise TypeError, "Cross product with non-vector"
return Vec3(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 isVec3(other):
raise TypeError, "Angle between vector and non-vector"
cosa = (self*other)/(self.length()*other.length())
cosa = max(-1.,min(1.,cosa))
return math.acos(cosa)
class Vec2:
isVec2 = 1
def __init__(self, x=0., y=0.):
self.data = [x,y]
def __repr__(self):
return 'Vec2(%s,%s,%s)' % (`self.data[0]`,\
`self.data[1]`)
def __str__(self):
return `self.data`
def __add__(self, other):
return Vec2(self.data[0]+other.data[0],\
self.data[1]+other.data[1])
__radd__ = __add__
def __neg__(self):
return Vec2(-self.data[0], -self.data[1])
def __sub__(self, other):
return Vec2(self.data[0]-other.data[0],\
self.data[1]-other.data[1])
def __rsub__(self, other):
return Vec2(other.data[0]-self.data[0],\
other.data[1]-self.data[1])
def __mul__(self, other):
if isVec2(other):
return reduce(lambda a,b: a+b,
map(lambda a,b: a*b, self.data, other.data))
else:
return Vec2(self.data[0]*other, self.data[1]*other)
def __rmul__(self, other):
if isVec2(other):
return reduce(lambda a,b: a+b,
map(lambda a,b: a*b, self.data, other.data))
else:
return Vec2(other*self.data[0], other*self.data[1])
def __div__(self, other):
if isVec2(other):
raise TypeError, "Can't divide by a vector"
else:
return Vec2(_div(self.data[0],other), _div(self.data[1],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])
def __getitem__(self, index):
return self.data[index]
def x(self):
return self.data[0]
def y(self):
return self.data[1]
def length(self):
return math.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 isVec2(other):
# raise TypeError, "Cross product with non-vector"
# return Vec2(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 isVec2(other):
raise TypeError, "Angle between vector and non-vector"
cosa = (self*other)/(self.length()*other.length())
cosa = max(-1.,min(1.,cosa))
return math.acos(cosa)
# Type check
def isVec3(x):
return hasattr(x,'isVec3')
def isVec2(x):
return hasattr(x,'isVec2')
# "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 = Vec3(1.,0.,0.)
ey = Vec3(0.,1.,0.)
ez = Vec3(0.,0.,1.)
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