import math
radius = 4.000
diameter = radius *2
# sphere r=4 R=8
# this spere is y=sqrt(16-x*x)
# per cylinder volume is PI*r*r*dtx
def sphere_function(xpos,dtx):return math.sqrt(16.00-xpos*xpos) * math.sqrt(16.00-xpos*xpos)*dtx# @n is the is this sphere that will split to n piece along xpos
# if sphere r=4, slice is 8, dtx= R/8 = 1
def calculateVolume(n):v = 0dtx = diameter/nfor j in range(0,n,1):xp = j*(diameter/n) - radius   #if sphere radius is 4,left plot is -4 ,right plot is 4v += sphere_function(xp,dtx)return v# sphere volume use base function : 3/4 * PI * (R*R*R)
def ruleCacluateVolume(r):return 4/3.000 * r*r*rif __name__ == "__main__":#split a sphere to 20 cylinderprint "use 4   slice :"  ,calculateVolume(4)print "use 8   slice :"  ,calculateVolume(8)print "use 20  slice :"  ,calculateVolume(20)print "use 120 slice :"  ,calculateVolume(120)print "use 200 slice :"  ,calculateVolume(200)

import math#
# curve function is y=sqrt(x)
# x range->0-5
#

maxRange = 5.0def clinder_volume(xpos,dtx):return math.sqrt(xpos*xpos) * dtxdef curve_volume(n):v = 0.0dtx = maxRange/nfor x in range(0,n,1):xpos = x*(maxRange/n)v += clinder_volume(xpos,dtx)return vif __name__ == "__main__":print curve_volume(15)

# Trapezoidal
# S = 1/2(y0+ 2y1 + 2y2 + 2y3+...+ 2yn-1 + yn)def Trapezoidal(down,up,n,func):if up==down:return 0.0h = float(up-down) / float(n)start = func(down)end = func(up)process = 0.0for dt in xrange(0,n+1,1):if dt == 0 or dt == n:continueprocess += 2 * func(down + dt * h)sum =  (start + end + process) * (h/2.0)return sum# Simpson
# S = h/3(y0 + 4y1 + 2y2 + 4y3 + 2y4 + ... + 2yn-1 + yn)
# func is f(x)
def Simpson(down,up,n,func):if up==down:return 0.0h = float(up-down) / float(n)start = func(down)end = func(up)process = 0.0for dt in xrange(0,n+1,1):if dt == 0 or dt == n:continue# select the 1 3 5 7 9... indexif dt%2 == 1:process += 4 * func(down + dt * h)# select the 2 4 6 8 10... indexif dt%2 == 0:process += 2 * func(down + dt * h)sum =  (start + end + process) * (h/3.0)return sumif __name__ == "__main__":# part1# fx = 5x^4 [0,2]  n=4func = lambda x:5*x*x*x*xT = Simpson(0,2,4,func)print T# part2# fx = x [1,2] n=4func2 = lambda x:xT2 = Simpson(1,2,4,func2)print T2# part3# fx = x*xfunc3 = lambda x:x*xT3 = Trapezoidal(1,2,4,func3)print T3func4 = lambda x:x*x + 1T_T4 = Trapezoidal(-1,1,4,func4)S_T4 = Simpson(-1,1,4,func4)print T_T4,S_T4

float ptsx[];
float ptsy[];
float ptsz[];
int npt = npoints(0);
resize(ptsx,npt);
resize(ptsy,npt);
resize(ptsz,npt);for(int i=0;i<npt;i++)
{vector pos = point(0,"P",i);ptsx[i] = pos.x;ptsy[i] = pos.y;ptsz[i] = pos.z;
}float maxy = max(ptsy);
float miny = min(ptsy);printf("%f,%f\n",miny,maxy);float dttop = pow(maxy,3)  /  3.0;
float dtbottom = pow(miny,3) / 3.0;float volume = dttop - dtbottom; adddetailattrib(geoself(),"cvolume",volume);