306.sagews

__main__:1: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...) __main__:53: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...) __main__:54: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...) __main__:57: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...) __main__:58: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...) __main__:59: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...) __main__:60: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)

#
# interact section
#   slider for parameter, 24 settings
#   checkboxes for various vector displays
#   computations at one value of parameter, t0
#

@interact
def _(
      pos_check = ("Position", True), 
      vel_check = ("Velocity", False),
      tan_check = ("Unit Tangent", False),
      nor_check = ("Unit Normal", False),
      bin_check = ("Unit Binormal", False),
      acc_check = ("Acceleration", False),
      tancomp_check = ("Tangential Component", False),
      norcomp_check = ("Normal Component", False),
      circle_check = ("Osculating Circle", False),
      t0 = slider(float(start), float(stop), float((stop-start)/24), float(start) , label = "Parameter"),
       ):
    #
    # location of interest
    #
    pos_tzero = position(t0)
    #
    # various scalar quantities at point
    #
    speed_component = speed(t0)
    tangent_component = speed_deriv(t0)
    normal_component = math.sqrt( acceleration(t0).norm()^2 - tangent_component^2 )
    curvature = normal_component/speed_component^2
    ## torsion = (1/speed_component)*(dB(t0)).dot_product(normal(t0))
 
    #
    # accumulate the graphic based on checkboxes
    #
    picture = path
    if pos_check:
        picture += arrow3d((0,0,0), pos_tzero, rgbcolor=(0,0,0))
    if vel_check:
        picture += arrow3d(pos_tzero, pos_tzero + velocity(t0), rgbcolor=(0,0.5,0))
    if tan_check:
        picture += arrow3d(pos_tzero, pos_tzero + tangent(t0), rgbcolor=(0,1,0) )
    if nor_check:
        picture += arrow3d(pos_tzero, pos_tzero + normal(t0), rgbcolor=(0.5,0,0))
    if bin_check:
        picture += arrow3d(pos_tzero, pos_tzero + binormal(t0), rgbcolor=(0,0,0.5))
    if acc_check:
        picture += arrow3d(pos_tzero, pos_tzero + acceleration(t0), rgbcolor=(1,0,1))
    if tancomp_check:
        picture += arrow3d(pos_tzero, pos_tzero + tangent_component*tangent(t0), rgbcolor=(1,0,1) )
    if norcomp_check:
        picture += arrow3d(pos_tzero, pos_tzero + normal_component*normal(t0), rgbcolor=(1,0,1))
    if circle_check:
        radius = 1.0/curvature
        m = identity_matrix(RDF,4)
        m[0:3,0] = -normal(t0)
        m[0:3,1] = tangent(t0)
        m[0:3,2] = binormal(t0)
        #m=matrix(zip(-normal(t0), tangent(t0), binormal(t0), pos_tzero+radius*normal(t0))).stack(matrix([0,0,0,1]))
        tx = sage.plot.plot3d.transform.Transformation(m=m)
        c = circle(center=(0,0), radius=radius, rgbcolor=(0.5,0,0)).plot3d()
        picture += c.transform(T=tx).translate(pos_tzero+radius*normal(t0))
    #
    # print textual info
    #
    print "Position vector: r(t)=", position(t)
    print "Speed is ", N(speed_component)
    print "Curvature is ", N(curvature)
    ## print "Torsion is ", N(torsion)

    #
    # show accumulated graphical info
    #
    show(picture, xmin=-3,xmax=3,ymin=-2,ymax=2,aspect_ratio=[1,1,1])