A sphere is a ball, similar to a circle in three dimension, and all its surface’s points are equidistant from the centre.
However, the distance from the centre point to the surface is called the radius, and the equation of the sphere is : (x-a)² + (y-b)² + (z-c)² = r² .
(a,b,c) are the coordinates of the centre and r is the radius.
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#be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam.
#Author : Fouad Teniou
#Date : 06/05/10
#version :2.6
"""
Sphere class represents a geometric sphere and a completing_the_squares
function is used for the purpose, while an utility _checksign function
is used to check the sign of all the coefficients and return an empty string
for a positive number and a minus character for a negative number.
A string representation function for the three different outcome
possibilities is used to print the solution of the sphere equation.
"""
from math import sqrt
class Sphere(object):
"""
class that represents a geometric Sphere
"""
def __init__(self,coef_A = 0,coef_B = 0, coef_C = 0, coef_D= 0, coef_E = 0, coef_F = 0, coef_G = 0):
""" Sphere Construction takes coef_A,coef_B,coef_C,coef_D,coef_E,coef_F,coef_G constants """
self._A = coef_A
self._B = coef_B
self._C = coef_C
self._D = coef_D
self._E = coef_E
self._F = coef_F
self._G = coef_G
self._a = self._checkSign(self._D)
self._b = self._checkSign(self._E)
self._c = self._checkSign(self._F)
self._d = pow((self._D/2.0)/self._A,2)
self._e = pow((self._E/2.0)/self._B,2)
self._f = pow((self._F/2.0)/self._C,2)
self._g = chr(253)
self._h = (-self._G/self._A + self._d + self._e + self._f)
def _checkSign(self,value):
""" Utility method to check the values' sign
and return a sign string"""
if value >= 0:
return "+"
else :
return ""
def completing_the_squares(self):
"""
completing the squares function
"""
c_squares = "(x%s %s%sx + %s) + (y%s %s%sy + %s) + (z%s %s%sz + %s) = %s" % \
(self._g,self._a,self._D/self._A,self._d,
self._g,self._b,self._E/self._B,self._e,
self._g,self._c,self._F/self._C,self._f,self._h)
return c_squares
def __str__(self):
"""
String representation of a sphere
"""
print ("\n(x%s%s)%s + (y%s%s)%s + (z%s%s)%s = %s") % \
(self._a,(self._D/2.0)/self._A,self._g,self._b,(self._E/2.0)/self._B,
self._g,self._c,(self._F/2.0)/self._C,self._g,self._h)
if self._h > 0:
return "\n<The graph of this equation is a sphere with centre (%s,%s,%s) and radius %s\n" % \
(-1*self._D/2.0,-1*self._E/2.0,-1*self._F/2.0,"%2.3f" % (sqrt(self._h)))
elif self._h == 0:
return "\n<this sphere has radius = 0 and the graph is a single point(%s,%s,%s)\n " % \
(-1*self._D/2.0,-1*self._E/2.0,-1*self._F/2.0,float(m.sqrt(self._h)))
else :
return "\n<There is no graph for such equation "
if __name__ == "__main__":
sphere = Sphere(1,1,1,-2,-4,8,17)
print sphere.completing_the_squares()
print sphere
sphere1 = Sphere(1,1,1,10,4,2,-19)
print sphere1.completing_the_squares()
print sphere1
sphere2 = Sphere(2,2,2,-2,-3,5,-2)
print sphere2.completing_the_squares()
print sphere2
####C:\Windows\python "C:\Users\MyComputer\Documents\Pyt\Sphere7.py"
#(x² -2x + 1.0) + (y² -4y + 4.0) + (z² +8z + 16.0) = 4.0
#(x-1.0)² + (y-2.0)² + (z+4.0)² = 4.0
#<The graph of this equation is a sphere with centre (1.0,2.0,-4.0) #and radius 2.000
#(x² +10x + 25.0) + (y² +4y + 4.0) + (z² +2z + 1.0) = 49.0
#(x+5.0)² + (y+2.0)² + (z+1.0)² = 49.0
#<The graph of this equation is a sphere with centre (-5.0,-2.0,-1.0) #and radius 7.000
#(x² -1x + 0.25) + (y² -2y + 0.5625) + (z² +2z + 1.5625) = 3.375
#(x-0.5)² + (y-0.75)² + (z+1.25)² = 3.375
#<The graph of this equation is a sphere with centre (1.0,1.5,-2.5) #and radius 1.837
#################################################################
|
Tags: mathematics
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