3026-Solids of Revolution (x and y axis).sagews

#auto
# -*- coding: utf-8 -*-

var('u,v')
html("<h1>Solids of Revolution (x and y axis)</h1>")
html("<h2>Disk method</h2>")

@interact
def _(krivka=selector(["First Example (První příklad): 01a","Second Example (Druhý příklad): 01b","Third Example (Třetí příklad): 02c"], label="Curve (Křivka)", nrows=3, ncols=1, buttons=True),
      #a=slider(0, 3, step_size=1, default=0, label="Lower Limit (Dolní mez)"),
      #b=slider(4,10, step_size=1, default=4, label="Upper Limit (Horní mez)"),
      rotace=slider(0,360, step_size=1, default=220, label="Rotation in Degrees (Rotace ve stupních)"),
      #auto_update=False,
      ):
  #tachyon=("Raytrace", False)
  pet=krivka[0:1]
  if pet == "F":
      f(x)=sqrt(3+x)
      popisek="\sqrt{3+x}"
      a=-1
      b=3
  elif pet == "S":
      f(x)=sqrt((x-2)/(2*x+1))
      popisek="\sqrt{(x-2)/(2x+1)}"
      a=2
      b=3
  elif pet == "T":
      f(x)=sqrt((2-x)/(3+2*x))
      popisek="\sqrt{(2-x)/(3+2x)}"
      a=1
      b=2
  horniv=rotace/360*2*pi
  # neviditelné
  
  html("$y=f(x)=%s,\quad x\in<%s,%s>$"%(popisek,a,b))
  """
  f(x)=sqrt(x)
  a=1
  b=4
  
  f(x)=x
  a=0
  b=2
  """
  
  #F(x,y)=y-f(x)
  Fx=f(x) # F(x,y)
  #Fy=y^2
  V=integral(pi*Fx^2,x,a,b)
  derx=diff(Fx,x)
  S=integral(2*pi*Fx*sqrt(1+derx^2),x,a,b)
  
  print "\nFor full rotation...\n"
  print "Vx =",V,"[units^3]"
  print "Vx = %4.4f" % (V),"[units^3]\n"
  print "Sx =",S,"[units^2]"
  print "Sx = %4.4f" % (S),"[units^2]\n"

  #print "y=f(x)=%s" % (f(x))
  #print "a=%s" % (a)
  #print "b=%s" % (b)
  
  mycurve = plot(f(x),a,b,color="orange")
  show(mycurve,aspect_ratio=1,figsize=3)
    
  #Sx=integral(2*pi*F
  #return
  #
  mypc=parametric_plot3d([u*cos(0),u*sin(0),f(u)],(u,a,b),color="orange",thickness=8)
  mypb=parametric_plot3d([u*cos(v),u*sin(v),f(u)],(u,a,b),(v,0,2*pi),color="blue", opacity=0.05)
  mysb=parametric_plot3d([u,sin(v)*f(u),cos(v)*f(u)],(u,a,b),(v,0,2*pi),color="green", opacity=0.05)
  #
  myp=parametric_plot3d([u*cos(v),u*sin(v),f(u)],(u,a,b),(v,0,horniv),color="blue")
  mys=parametric_plot3d([u,sin(v)*f(u),cos(v)*f(u)],(u,a,b),(v,0,horniv),color="green")
  #
  #myr=parametric_plot3d([u,sin(v)*g(u),cos(v)*g(u)],(u,5,6),(v,0,2*pi),color="yellow")
  show(mypb+mysb+myp+mys+mypc,aspect_ratio=1,figsize=5, viewer="jmol")
  #(mypb+mysb+myp+mys+mypc).save("moje.png",aspect_ratio=1,figsize=6,viewer="jmol")

Solids of Revolution (x and y axis)

Disk method

Curve (Křivka)  Rotation in Degrees (Rotace ve stupních)  [removed] [removed] [removed] [removed]