Items tagged with transform

Feed

I take the Inverse Laplace Transform on a specific function and the shown result is still an integral.

Would you like to explain it to me?

Thanks.

 

 

I can't take the inverse laplace transform of one kind of functions.

Would you like to help me?

Thanks.


My last series of questions have been to do with animations. Have had some really good help. I am using a rotation type matrix so I can't readilly use the rotate command. That means painfully breaking up the body into its individual components to apply the matrix to. The matrix is derived from some very nolinear functions. I have just included a general Euler rotation matrix here. Have looked inside the rotate command but don't  have enough experience to develop my own. Now I know this sort of command would not be limited to rotating the body as a general 3x3 matrix would transform the body. That would not be a problem, could be useful for other things.

In Mathematica there is a command "GeometricTransformation" that does this.

restart

with(plots):

with(plottools):

NULL

Cylinder := proc (a::list, b::list, dia := .1, colr := "Blue") plots:-arrow(a, b, width = dia, shape = cylindrical_arrow, head_length = 0., head_width = 0.1e-1, colour = colr) end proc

proc (a::list, b::list, dia := .1, colr := "Blue") plots:-arrow(a, b, width = dia, shape = cylindrical_arrow, head_length = 0., head_width = 0.1e-1, colour = colr) end proc

(1)


Body2 := display([point([1, -.2, 0], colour = red, symbolsize = 50, symbol = solidsphere), point([-1, -.2, 0], colour = red, symbolsize = 50, symbol = solidsphere), point([0, 1, 0], colour = purple, symbolsize = 50, symbol = solidsphere), Cylinder([0, 0, 0], [1, -.2, 0], 0.75e-1, "Red"), Cylinder([0, 0, 0], [1, -.2, -0.1e-1], 0.75e-1, "Nautical GrayViolet"), Cylinder([0, 0, 0], [-1, -.2, 0], 0.75e-1, "Red"), Cylinder([0, 0, 0], [-1, -.2, -0.1e-1], 0.75e-1, "Nautical GrayViolet"), Cylinder([0, 0, 0], [0, 1, 0], 0.65e-1, "Green"), Cylinder([0, 0, 0], [0, 1, -0.1e-1], 0.65e-1, "Nautical GrayViolet"), line([0, 0, 0], [.5, 0, 0], colour = red, thickness = 4), line([0, 0, 0], [0, .5, 0], colour = yellow, thickness = 4), line([0, 0, 0], [0, 0, .5], colour = blue, thickness = 4), plots:-textplot3d([.5, 0.5e-1, 0, "X"]), plots:-textplot3d([.1, .5, 0, "Y"]), plots:-textplot3d([0.5e-1, 0, .5, "Z"])], scaling = constrained)

 

NULL

NULL

``

NULL

Rot1 := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(w1*t), (2, 3) = -sin(w1*t), (3, 1) = 0, (3, 2) = sin(w1*t), (3, 3) = cos(w1*t)})

Rot2 := Matrix(3, 3, {(1, 1) = cos(w2*t), (1, 2) = 0, (1, 3) = sin(w2*t), (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = -sin(w2*t), (3, 2) = 0, (3, 3) = cos(w2*t)})

Rot3 := Matrix(3, 3, {(1, 1) = cos(w3*t), (1, 2) = -sin(w3*t), (1, 3) = 0, (2, 1) = sin(w3*t), (2, 2) = cos(w3*t), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

Rot := Rot3.Rot2.Rot1

Matrix(%id = 18446744074366030062)

(2)

NULL

w1 := .35; 1; w2 := .45; 1; w3 := .15

.15

(3)

`~`[evalf](Rot)

Matrix(%id = 18446744074366015718)

(4)

``

NULL

``

NULL

NULL

plots:-animate(plottools:-rotate, [Body2, -w1*t, -w2*t, -w3*t], t = 0 .. 8*Pi, frames = 100);

 

rotate, [Body2, -w1*t, -w2*t, -w3*t]

plottools:-rotate, [INTERFACE_PLOT3D(POINTS(Matrix(1, 3, {(1, 1) = 1.0, (1, 2) = -.2, (1, 3) = .0}, datatype = float[8]), COLOUR(RGB, 1.00000000, 0., 0.), SYMBOL(_SOLIDSPHERE, 50)), POINTS(Matrix(1, 3, {(1, 1) = -1.0, (1, 2) = -.2, (1, 3) = .0}, datatype = float[8]), COLOUR(RGB, 1.00000000, 0., 0.), SYMBOL(_SOLIDSPHERE, 50)), POINTS(Matrix(1, 3, {(1, 1) = .0, (1, 2) = 1.0, (1, 3) = .0}, datatype = float[8]), COLOUR(RGB, .47058824, 0., .44705882), SYMBOL(_SOLIDSPHERE, 50)), POLYGONS([[-0.735435508125000e-2, -0.367717753350000e-1, 0.], [.992645645102007, -.236771775759177, -0.209165228258335e-9], [.993005592857848, -.234972036971338, -0.115881374996887e-1], [-0.699440732540857e-2, -0.349720365471609e-1, -0.115881372905235e-1]], [[-0.699440732540857e-2, -0.349720365471609e-1, -0.115881372905235e-1], [.993005592857848, -.234972036971338, -0.115881374996887e-1], [.994050201935779, -.229748991580870, -0.220419471726219e-1], [-0.594979824747744e-2, -0.297489911566927e-1, -0.220419469634567e-1]], [[-0.594979824747744e-2, -0.297489911566927e-1, -0.220419469634567e-1], [.994050201935779, -.229748991580870, -0.220419471726219e-1], [.995677218721006, -.221613907661821, -0.303381375009383e-1], [-0.432278146225039e-2, -0.216139072376438e-1, -0.303381372917731e-1]], [[-0.432278146225039e-2, -0.216139072376438e-1, -0.303381372917731e-1], [.995677218721006, -.221613907661821, -0.303381375009383e-1], [.997727379477255, -.211363103894868, -0.356646195767702e-1], [-0.227262070600146e-2, -0.113631034706908e-1, -0.356646193676049e-1]], [[-0.227262070600146e-2, -0.113631034706908e-1, -0.356646193676049e-1], [.997727379477255, -.211363103894868, -0.356646195767702e-1], [1.00000000017722, -.200000000415126, -0.375000002091652e-1], [-0.603361199706648e-11, 0.905042028455399e-11, -0.375000000000000e-1]], [[-0.603361199706648e-11, 0.905042028455399e-11, -0.375000000000000e-1], [1.00000000017722, -.200000000415126, -0.375000002091652e-1], [1.00227262087778, -.188636896936271, -0.356646195720166e-1], [0.227262069452484e-2, 0.113631034879057e-1, -0.356646193628514e-1]], [[0.227262069452484e-2, 0.113631034879057e-1, -0.356646193628514e-1], [1.00227262087778, -.188636896936271, -0.356646195720166e-1], [1.00432278163693, -.178386093165939, -0.303381374874881e-1], [0.432278145367776e-2, 0.216139072582375e-1, -0.303381372783229e-1]], [[0.432278145367776e-2, 0.216139072582375e-1, -0.303381372783229e-1], [1.00432278163693, -.178386093165939, -0.303381374874881e-1], [1.00594979842278, -.170251009261168, -0.220419471662447e-1], [0.594979823951994e-2, 0.297489911630093e-1, -0.220419469570794e-1]], [[0.594979823951994e-2, 0.297489911630093e-1, -0.220419469570794e-1], [1.00594979842278, -.170251009261168, -0.220419471662447e-1], [1.00699440750585, -.165027963866877, -0.115881374707930e-1], [0.699440732258864e-2, 0.349720365572996e-1, -0.115881372616278e-1]], [[0.699440732258864e-2, 0.349720365572996e-1, -0.115881372616278e-1], [1.00699440750585, -.165027963866877, -0.115881374707930e-1], [1.00735435526451, -.163228225089177, -0.193782471119685e-9], [0.735435508125000e-2, 0.367717753350000e-1, 0.153827571386498e-10]], [[0.735435508125000e-2, 0.367717753350000e-1, 0.153827571386498e-10], [1.00735435526451, -.163228225089177, -0.193782471119685e-9], [1.00699440750864, -.165027963877132, 0.115881370817223e-1], [0.699440732538538e-2, 0.349720365470449e-1, 0.115881372908875e-1]], [[0.699440732538538e-2, 0.349720365470449e-1, 0.115881372908875e-1], [1.00699440750864, -.165027963877132, 0.115881370817223e-1], [1.00594979842810, -.170251009280673, 0.220419467728040e-1], [0.594979824483964e-2, 0.297489911435037e-1, 0.220419469819693e-1]], [[0.594979824483964e-2, 0.297489911435037e-1, 0.220419469819693e-1], [1.00594979842810, -.170251009280673, 0.220419467728040e-1], [1.00432278164426, -.178386093192786, 0.303381370872412e-1], [0.432278146099970e-2, 0.216139072313904e-1, 0.303381372964064e-1]], [[0.432278146099970e-2, 0.216139072313904e-1, 0.303381372964064e-1], [1.00432278164426, -.178386093192786, 0.303381370872412e-1], [1.00227262088639, -.188636896967832, 0.356646191631932e-1], [0.227262070313230e-2, 0.113631034563450e-1, 0.356646193723585e-1]], [[0.227262070313230e-2, 0.113631034563450e-1, 0.356646193723585e-1], [1.00227262088639, -.188636896967832, 0.356646191631932e-1], [1.00000000018627, -.200000000448311, 0.374999997908348e-1], [0.301680511369943e-11, -0.241344546721620e-10, 0.375000000000000e-1]], [[0.301680511369943e-11, -0.241344546721620e-10, 0.375000000000000e-1], [1.00000000018627, -.200000000448311, 0.374999997908348e-1], [.997727379485863, -.211363103926428, 0.356646191489326e-1], [-0.227262069739400e-2, -0.113631035022515e-1, 0.356646193580979e-1]], [[-0.227262069739400e-2, -0.113631035022515e-1, 0.356646193580979e-1], [.997727379485863, -.211363103926428, 0.356646191489326e-1], [.995677218727138, -.221613907694618, 0.303381370601159e-1], [-0.432278145611840e-2, -0.216139072704407e-1, 0.303381372692812e-1]], [[-0.432278145611840e-2, -0.216139072704407e-1, 0.303381372692812e-1], [.995677218727138, -.221613907694618, 0.303381370601159e-1], [.994050201941964, -.229748991596052, 0.220419467354693e-1], [-0.594979824129318e-2, -0.297489911718755e-1, 0.220419469446345e-1]], [[-0.594979824129318e-2, -0.297489911718755e-1, 0.220419469446345e-1], [.994050201941964, -.229748991596052, 0.220419467354693e-1], [.993005592859736, -.234972036986138, 0.115881370378327e-1], [-0.699440732352089e-2, -0.349720365619608e-1, 0.115881372469979e-1]], [[-0.699440732352089e-2, -0.349720365619608e-1, 0.115881372469979e-1], [.993005592859736, -.234972036986138, 0.115881370378327e-1], [.992645645102007, -.236771775759177, -0.209164985926649e-9], [-0.735435508125000e-2, -0.367717753350000e-1, 0.242331686164888e-15]], COLOR(RGB, 1.00000000, 0., 0.), STYLE(PATCHNOGRID)), MESH([[[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [.999019419505757, -.204902903802177, -0.209165228258335e-9]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [.999072550071272, -.204637250973416, -0.162349755518864e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [.999226184247292, -.203869080093290, -0.307106377261356e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [.999463673386966, -.202681634396058, -0.418583260047787e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [.999759281856985, -.201203592048134, -0.484700153886188e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [1.00008097589279, -.199595121872107, -0.498292267419858e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [1.00039389495399, -.198030526569535, -0.457886684244053e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [1.00066412940488, -.196679354318648, -0.367861976253090e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [1.00086239514958, -.195688025598428, -0.237973717435060e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [1.00096720701824, -.195163966257762, -0.822973160568944e-3]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [1.00096720701857, -.195163966257828, 0.822972742238406e-3]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [1.00086239515054, -.195688025598620, 0.237973675602012e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [1.00066412940636, -.196679354318944, 0.367861934420039e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [1.00039389495583, -.198030526569903, 0.457886642411004e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [1.00008097589479, -.199595121872508, 0.498292225586812e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [.999759281858935, -.201203592048524, 0.484700112053144e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [.999463673388649, -.202681634396394, 0.418583218214745e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [.999226184248528, -.203869080093537, 0.307106335428315e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [.999072550071925, -.204637250973547, 0.162349713685823e-2]], [[1.00000000018326, -.200000000424177, -0.209165228258335e-9], [.999019419505757, -.204902903802177, -0.209165195947444e-9]]], COLOR(RGB, 1.00000000, 0., 0.), STYLE(PATCHNOGRID)), POLYGONS([[.9926456449, -.2367717757, -0.2091652283e-9], [.9930055927, -.2349720370, -0.1158813750e-1], [.9940502018, -.2297489916, -0.2204194718e-1], [.9956772185, -.2216139076, -0.3033813750e-1], [.9977273793, -.2113631039, -0.3566461958e-1], [1.000000000, -.2000000004, -0.3750000021e-1], [1.002272621, -.1886368969, -0.3566461957e-1], [1.004322781, -.1783860931, -0.3033813749e-1], [1.005949798, -.1702510092, -0.2204194717e-1], [1.006994407, -.1650279638, -0.1158813751e-1], [1.007354355, -.1632282251, -0.1937824747e-9], [1.006994407, -.1650279639, 0.1158813712e-1], [1.005949798, -.1702510092, 0.2204194677e-1], [1.004322781, -.1783860932, 0.3033813709e-1], [1.002272621, -.1886368970, 0.3566461916e-1], [1.000000000, -.2000000004, 0.3749999979e-1], [.9977273793, -.2113631039, 0.3566461916e-1], [.9956772186, -.2216139076, 0.3033813710e-1], [.9940502018, -.2297489915, 0.2204194680e-1], [.9930055927, -.2349720370, 0.1158813697e-1], [.9926456449, -.2367717757, -0.3149307354e-9]], COLOUR(RGB, 1.00000000, 0., 0.), STYLE(PATCHNOGRID)), POLYGONS([[-0.7354355081e-2, -0.3677177534e-1, 0.], [-0.6994407325e-2, -0.3497203655e-1, -0.1158813729e-1], [-0.5949798246e-2, -0.2974899115e-1, -0.2204194697e-1], [-0.4322781463e-2, -0.2161390724e-1, -0.3033813729e-1], [-0.2272620706e-2, -0.1136310347e-1, -0.3566461937e-1], [-0.6033612348e-11, 0.9050418530e-11, -0.375e-1], [0.2272620694e-2, 0.1136310348e-1, -0.3566461936e-1], [0.4322781455e-2, 0.2161390726e-1, -0.3033813728e-1], [0.5949798240e-2, 0.2974899116e-1, -0.2204194696e-1], [0.6994407321e-2, 0.3497203655e-1, -0.1158813730e-1], [0.7354355081e-2, 0.3677177534e-1, 0.1538275356e-10], [0.6994407323e-2, 0.3497203654e-1, 0.1158813733e-1], [0.5949798246e-2, 0.2974899115e-1, 0.2204194698e-1], [0.4322781461e-2, 0.2161390723e-1, 0.3033813730e-1], [0.2272620702e-2, 0.1136310345e-1, 0.3566461937e-1], [0.3016806167e-11, -0.2413444941e-10, 0.375e-1], [-0.2272620690e-2, -0.1136310346e-1, 0.3566461937e-1], [-0.4322781445e-2, -0.2161390721e-1, 0.3033813731e-1], [-0.5949798234e-2, -0.2974899113e-1, 0.2204194701e-1], [-0.6994407329e-2, -0.3497203659e-1, 0.1158813718e-1], [-0.7354355081e-2, -0.3677177534e-1, -0.1057655071e-9]], COLOUR(RGB, 1.00000000, 0., 0.), STYLE(PATCHNOGRID)), POLYGONS([[-0.735435508125000e-2, -0.367717753350000e-1, 0.], [.992645645246188, -.236771775767635, -0.999999971771556e-2], [.992894173967097, -.234949753172760, -0.215875799259210e-1], [-0.710582636034092e-2, -0.349497527401258e-1, -0.115875802082055e-1]], [[-0.710582636034092e-2, -0.349497527401258e-1, -0.115875802082055e-1], [.992894173967097, -.234949753172760, -0.215875799259210e-1], [.993838270481540, -.229706605269551, -0.320408870476349e-1], [-0.616172984589807e-2, -0.297066048369160e-1, -0.220408873299194e-1]], [[-0.616172984589807e-2, -0.297066048369160e-1, -0.220408873299194e-1], [.993838270481540, -.229706605269551, -0.320408870476349e-1], [.995385520044752, -.221555567906064, -0.403366785490455e-1], [-0.461448028268624e-2, -0.215555674734292e-1, -0.303366788313300e-1]], [[-0.461448028268624e-2, -0.215555674734292e-1, -0.303366788313300e-1], [.995385520044752, -.221555567906064, -0.403366785490455e-1], [.997384467091878, -.211294521397264, -0.456629045622413e-1], [-0.261553323556026e-2, -0.112945209646293e-1, -0.356629048445258e-1]], [[-0.261553323556026e-2, -0.112945209646293e-1, -0.356629048445258e-1], [.997384467091878, -.211294521397264, -0.456629045622413e-1], [.999639440750421, -.199927888509230, -0.474981969614656e-1], [-0.360559577016597e-3, 0.721119234045172e-4, -0.374981972437500e-1]], [[-0.360559577016597e-3, 0.721119234045172e-4, -0.374981972437500e-1], [.999639440750421, -.199927888509230, -0.474981969614656e-1], [1.00192970849245, -.188568314438677, -0.456629045574880e-1], [0.192970816501175e-2, 0.114316859939582e-1, -0.356629048397724e-1]], [[0.192970816501175e-2, 0.114316859939582e-1, -0.356629048397724e-1], [1.00192970849245, -.188568314438677, -0.456629045574880e-1], [1.00403108296081, -.178327753410208, -0.403366785355960e-1], [0.403108263337123e-2, 0.216722470224262e-1, -0.303366788178805e-1]], [[0.403108263337123e-2, 0.216722470224262e-1, -0.303366788178805e-1], [1.00403108296081, -.178327753410208, -0.403366785355960e-1], [1.00573786696860, -.170208622949861, -0.320408870412580e-1], [0.573786664116063e-2, 0.297913774827737e-1, -0.220408873235424e-1]], [[0.573786664116063e-2, 0.297913774827737e-1, -0.220408873235424e-1], [1.00573786696860, -.170208622949861, -0.320408870412580e-1], [1.00688298861537, -.165005680068356, -0.215875798970267e-1], [0.688298828793412e-2, 0.349943203642792e-1, -0.115875801793112e-1]], [[0.688298828793412e-2, 0.349943203642792e-1, -0.115875801793112e-1], [1.00688298861537, -.165005680068356, -0.215875798970267e-1], [1.00735435540884, -.163228225097664, -0.999999970233354e-2], [0.735435508139790e-2, 0.367717753349704e-1, 0.153820176356745e-10]], [[0.735435508139790e-2, 0.367717753349704e-1, 0.153820176356745e-10], [1.00735435540884, -.163228225097664, -0.999999970233354e-2], [1.00710582668776, -.165050247692626, 0.158758049085392e-2], [0.710582636032123e-2, 0.349497527400091e-1, 0.115875802085695e-1]], [[0.710582636032123e-2, 0.349497527400091e-1, 0.115875802085695e-1], [1.00710582668776, -.165050247692626, 0.158758049085392e-2], [1.00616173017088, -.170293395608943, 0.120408876307155e-1], [0.616172984343827e-2, 0.297066048236914e-1, 0.220408873484310e-1]], [[0.616172984343827e-2, 0.297066048236914e-1, 0.220408873484310e-1], [1.00616173017088, -.170293395608943, 0.120408876307155e-1], [1.00461448060892, -.178444432965468, 0.203366791182475e-1], [0.461448028148011e-2, 0.215555674671669e-1, 0.303366788359631e-1]], [[0.461448028148011e-2, 0.215555674671669e-1, 0.303366788359631e-1], [1.00461448060892, -.178444432965468, 0.203366791182475e-1], [1.00261553356017, -.188705479482360, 0.256629051315635e-1], [0.261553323273681e-2, 0.112945209502744e-1, 0.356629048492791e-1]], [[0.261553323273681e-2, 0.112945209502744e-1, 0.356629048492791e-1], [1.00261553356017, -.188705479482360, 0.256629051315635e-1], [1.00036055990144, -.200072112371123, 0.274981975260344e-1], [0.360559573999790e-3, -0.721119384885516e-4, 0.374981972437500e-1]], [[0.360559573999790e-3, -0.721119384885516e-4, 0.374981972437500e-1], [1.00036055990144, -.200072112371123, 0.274981975260344e-1], [.998070292159511, -.211431686440929, 0.256629051173036e-1], [-0.192970816792660e-2, -0.114316860082948e-1, 0.356629048350191e-1]], [[-0.192970816792660e-2, -0.114316860082948e-1, 0.356629048350191e-1], [.998070292159511, -.211431686440929, 0.256629051173036e-1], [.995968917691539, -.221672247467247, 0.203366790911236e-1], [-0.403108263589881e-2, -0.216722470346121e-1, 0.303366788088391e-1]], [[-0.403108263589881e-2, -0.216722470346121e-1, 0.303366788088391e-1], [.995968917691539, -.221672247467247, 0.203366790911236e-1], [.994262133684385, -.229791377924251, 0.120408875933825e-1], [-0.573786664305352e-2, -0.297913774916160e-1, 0.220408873110981e-1]], [[-0.573786664305352e-2, -0.297913774916160e-1, 0.220408873110981e-1], [.994262133684385, -.229791377924251, 0.120408875933825e-1], [.993117012038431, -.234994320801547, 0.158758044696644e-2], [-0.688298828900703e-2, -0.349943203689123e-1, 0.115875801646820e-1]], [[-0.688298828900703e-2, -0.349943203689123e-1, 0.115875801646820e-1], [.993117012038431, -.234994320801547, 0.158758044696644e-2], [.992645645246188, -.236771775767635, -0.999999971771532e-2], [-0.735435508125000e-2, -0.367717753350000e-1, 0.242320036432573e-15]], COLOR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), MESH([[[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [.999019419649938, -.204902903810635, -0.999999971771556e-2]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [.999056940415278, -.204634129021832, -0.116234190165393e-1]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [.999196656355183, -.203863174494476, -0.130709156443897e-1]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [.999423427079648, -.202673585114198, -0.141856308814147e-1]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [.999712678461967, -.201194271348732, -0.148467680350938e-1]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [1.00003306562667, -.199585539798484, -0.149826826362258e-1]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [1.00034986965314, -.198021721488966, -0.145786462288458e-1]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [1.00062875990938, -.196672280399154, -0.136784424269641e-1]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [1.00083951430872, -.195683449409867, -0.123796222806159e-1]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [1.00095929434178, -.195162383702087, -0.108229331059291e-1]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [1.00097511998340, -.195165548830419, -0.917706632950211e-2]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [1.00088527627976, -.195692601804097, -0.762037715481521e-2]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [1.00069949919022, -.196686428255353, -0.632155700846704e-2]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [1.00043792054505, -.198039331667387, -0.542135320658539e-2]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [1.00012888644927, -.199604703963047, -0.501731679920534e-2]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [.999805885542316, -.201212912764842, -0.515323140033731e-2]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [.999503919984330, -.202689683695170, -0.581436855401634e-2]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [.999255712429000, -.203874985709265, -0.692908379104140e-2]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [.999088160016282, -.204640372942047, -0.837658041889176e-2]], [[1.00000000032744, -.200000000432635, -0.999999971771556e-2], [.999019419649938, -.204902903810635, -0.999999971771553e-2]]], COLOR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), POLYGONS([[.9926456449, -.2367717757, -0.9999999718e-2], [.9928941736, -.2349497531, -0.2158757993e-1], [.9938382702, -.2297066052, -0.3204088706e-1], [.9953855197, -.2215555679, -0.4033667855e-1], [.9973844668, -.2112945214, -0.4566290457e-1], [.9996394404, -.1999278885, -0.4749819696e-1], [1.001929708, -.1885683144, -0.4566290456e-1], [1.004031083, -.1783277534, -0.4033667854e-1], [1.005737867, -.1702086229, -0.3204088705e-1], [1.006882988, -.1650056800, -0.2158757994e-1], [1.007354355, -.1632282251, -0.9999999703e-2], [1.007105826, -.1650502477, 0.1587580532e-2], [1.006161730, -.1702933956, 0.1204088763e-1], [1.004614480, -.1784444329, 0.2033667912e-1], [1.002615533, -.1887054795, 0.2566290513e-1], [1.000360560, -.2000721123, 0.2749819752e-1], [.9980702918, -.2114316864, 0.2566290513e-1], [.9959689174, -.2216722474, 0.2033667913e-1], [.9942621334, -.2297913778, 0.1204088766e-1], [.9931170117, -.2349943208, 0.1587580382e-2], [.9926456449, -.2367717757, -0.9999999824e-2]], COLOUR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), POLYGONS([[-0.7354355081e-2, -0.3677177534e-1, 0.], [-0.7105826360e-2, -0.3494975274e-1, -0.1158758021e-1], [-0.6161729845e-2, -0.2970660483e-1, -0.2204088734e-1], [-0.4614480284e-2, -0.2155556747e-1, -0.3033667883e-1], [-0.2615533236e-2, -0.1129452096e-1, -0.3566290485e-1], [-0.3605595770e-3, 0.7211192340e-4, -0.3749819724e-1], [0.1929708164e-2, 0.1143168599e-1, -0.3566290484e-1], [0.4031082635e-2, 0.2167224703e-1, -0.3033667882e-1], [0.5737866641e-2, 0.2979137748e-1, -0.2204088733e-1], [0.6882988286e-2, 0.3499432036e-1, -0.1158758022e-1], [0.7354355081e-2, 0.3677177534e-1, 0.1538201406e-10], [0.7105826359e-2, 0.3494975273e-1, 0.1158758025e-1], [0.6161729845e-2, 0.2970660483e-1, 0.2204088735e-1], [0.4614480282e-2, 0.2155556746e-1, 0.3033667884e-1], [0.2615533232e-2, 0.1129452094e-1, 0.3566290485e-1], [0.3605595740e-3, -0.7211193849e-4, 0.3749819724e-1], [-0.1929708160e-2, -0.1143168597e-1, 0.3566290485e-1], [-0.4031082624e-2, -0.2167224698e-1, 0.3033667885e-1], [-0.5737866635e-2, -0.2979137745e-1, 0.2204088738e-1], [-0.6882988295e-2, -0.3499432040e-1, 0.1158758010e-1], [-0.7354355082e-2, -0.3677177534e-1, -0.1057604226e-9]], COLOUR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), POLYGONS([[-0.735435508125000e-2, 0.367717753350000e-1, 0.], [-1.00735435526451, -.163228225089177, -0.209165228258335e-9], [-1.00699440750400, -.165027963876084, -0.115881374996887e-1], [-0.699440732074735e-2, 0.349720365480931e-1, -0.115881372905235e-1]], [[-0.699440732074735e-2, 0.349720365480931e-1, -0.115881372905235e-1], [-1.00699440750400, -.165027963876084, -0.115881374996887e-1], [-1.00594979842187, -.170251009265711, -0.220419471726219e-1], [-0.594979823861126e-2, 0.297489911584659e-1, -0.220419469634567e-1]], [[-0.594979823861126e-2, 0.297489911584659e-1, -0.220419469634567e-1], [-1.00594979842187, -.170251009265711, -0.220419471726219e-1], [-1.00432278163330, -.178386093184092, -0.303381375009383e-1], [-0.432278145004715e-2, 0.216139072400845e-1, -0.303381372917731e-1]], [[-0.432278145004715e-2, 0.216139072400845e-1, -0.303381372917731e-1], [-1.00432278163330, -.178386093184092, -0.303381375009383e-1], [-1.00227262087491, -.188636896950617, -0.356646195767702e-1], [-0.227262069165569e-2, 0.113631034735600e-1, -0.356646193676049e-1]], [[-0.227262069165569e-2, 0.113631034735600e-1, -0.356646193676049e-1], [-1.00227262087491, -.188636896950617, -0.356646195767702e-1], [-1.00000000017421, -.200000000430210, -0.375000002091652e-1], [0.905041888043352e-11, -0.603361410305399e-11, -0.375000000000000e-1]], [[0.905041888043352e-11, -0.603361410305399e-11, -0.375000000000000e-1], [-1.00000000017421, -.200000000430210, -0.375000002091652e-1], [-.997727379474386, -.211363103909213, -0.356646195720166e-1], [0.227262070887061e-2, -0.113631034850366e-1, -0.356646193628514e-1]], [[0.227262070887061e-2, -0.113631034850366e-1, -0.356646193628514e-1], [-.997727379474386, -.211363103909213, -0.356646195720166e-1], [-.995677218717376, -.221613907679974, -0.303381374874881e-1], [0.432278146588100e-2, -0.216139072557969e-1, -0.303381372783229e-1]], [[0.432278146588100e-2, -0.216139072557969e-1, -0.303381372783229e-1], [-.995677218717376, -.221613907679974, -0.303381374874881e-1], [-.994050201934871, -.229748991585413, -0.220419471662447e-1], [0.594979824838611e-2, -0.297489911612361e-1, -0.220419469570794e-1]], [[0.594979824838611e-2, -0.297489911612361e-1, -0.220419469570794e-1], [-.994050201934871, -.229748991585413, -0.220419471662447e-1], [-.993005592856007, -.234972036980544, -0.115881374707930e-1], [0.699440732724986e-2, -0.349720365563674e-1, -0.115881372616278e-1]], [[0.699440732724986e-2, -0.349720365563674e-1, -0.115881372616278e-1], [-.993005592856007, -.234972036980544, -0.115881374707930e-1], [-.992645645102007, -.236771775759177, -0.193782471119685e-9], [0.735435508125000e-2, -0.367717753350000e-1, 0.153827571386498e-10]], [[0.735435508125000e-2, -0.367717753350000e-1, 0.153827571386498e-10], [-.992645645102007, -.236771775759177, -0.193782471119685e-9], [-.993005592862533, -.234972036972154, 0.115881370817223e-1], [0.699440732072415e-2, -0.349720365479772e-1, 0.115881372908875e-1]], [[0.699440732072415e-2, -0.349720365479772e-1, 0.115881372908875e-1], [-.993005592862533, -.234972036972154, 0.115881370817223e-1], [-.994050201947283, -.229748991569454, 0.220419467728040e-1], [0.594979823597347e-2, -0.297489911452769e-1, 0.220419469819693e-1]], [[0.594979823597347e-2, -0.297489911452769e-1, 0.220419469819693e-1], [-.994050201947283, -.229748991569454, 0.220419467728040e-1], [-.995677218734460, -.221613907658008, 0.303381370872412e-1], [0.432278144879647e-2, -0.216139072338310e-1, 0.303381372964064e-1]], [[0.432278144879647e-2, -0.216139072338310e-1, 0.303381372964064e-1], [-.995677218734460, -.221613907658008, 0.303381370872412e-1], [-.997727379494470, -.211363103883391, 0.356646191631932e-1], [0.227262068878653e-2, -0.113631034592142e-1, 0.356646193723585e-1]], [[0.227262068878653e-2, -0.113631034592142e-1, 0.356646193723585e-1], [-.997727379494470, -.211363103883391, 0.356646191631932e-1], [-1.00000000019532, -.200000000403059, 0.374999997908348e-1], [-0.120672257638006e-10, 0.211176484906620e-10, 0.375000000000000e-1]], [[-0.120672257638006e-10, 0.211176484906620e-10, 0.375000000000000e-1], [-1.00000000019532, -.200000000403059, 0.374999997908348e-1], [-1.00227262089500, -.188636896924794, 0.356646191489326e-1], [-0.227262071173976e-2, 0.113631034993824e-1, 0.356646193580979e-1]], [[-0.227262071173976e-2, 0.113631034993824e-1, 0.356646193580979e-1], [-1.00227262089500, -.188636896924794, 0.356646191489326e-1], [-1.00432278165158, -.178386093156177, 0.303381370601159e-1], [-0.432278146832164e-2, 0.216139072680001e-1, 0.303381372692812e-1]], [[-0.432278146832164e-2, 0.216139072680001e-1, 0.303381372692812e-1], [-1.00432278165158, -.178386093156177, 0.303381370601159e-1], [-1.00594979843342, -.170251009254075, 0.220419467354693e-1], [-0.594979825015935e-2, 0.297489911701022e-1, 0.220419469446345e-1]], [[-0.594979825015935e-2, 0.297489911701022e-1, 0.220419469446345e-1], [-1.00594979843342, -.170251009254075, 0.220419467354693e-1], [-1.00699440751144, -.165027963863148, 0.115881370378327e-1], [-0.699440732818211e-2, 0.349720365610286e-1, 0.115881372469979e-1]], [[-0.699440732818211e-2, 0.349720365610286e-1, 0.115881372469979e-1], [-1.00699440751144, -.165027963863148, 0.115881370378327e-1], [-1.00735435526451, -.163228225089177, -0.209164985926649e-9], [-0.735435508125000e-2, 0.367717753350000e-1, 0.242331686164888e-15]], COLOR(RGB, 1.00000000, 0., 0.), STYLE(PATCHNOGRID)), MESH([[[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-1.00098058086076, -.195097097046177, -0.209165228258335e-9]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-1.00092745029459, -.195362749874807, -0.162349755518864e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-1.00077381611799, -.196130920754817, -0.307106377261356e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-1.00053632697786, -.197318366451959, -0.418583260047787e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-1.00024071850758, -.198796408799829, -0.484700153886188e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-.999919024471724, -.200404878975846, -0.498292267419858e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-.999606105410681, -.201969474278451, -0.457886684244053e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-.999335870960154, -.203320646529410, -0.367861976253090e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-.999137605215977, -.204311975249734, -0.237973717435060e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-.999032793347941, -.204836034590525, -0.822973160568944e-3]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-.999032793348272, -.204836034590592, 0.822972742238406e-3]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-.999137605216934, -.204311975249925, 0.237973675602012e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-.999335870961634, -.203320646529706, 0.367861934420039e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-.999606105412523, -.201969474278819, 0.457886642411004e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-.999919024473728, -.200404878976247, 0.498292225586812e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-1.00024071850953, -.198796408800219, 0.484700112053144e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-1.00053632697955, -.197318366452296, 0.418583218214745e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-1.00077381611922, -.196130920755064, 0.307106335428315e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-1.00092745029524, -.195362749874937, 0.162349713685823e-2]], [[-1.00000000018326, -.200000000424177, -0.209165228258335e-9], [-1.00098058086076, -.195097097046177, -0.209165195947444e-9]]], COLOR(RGB, 1.00000000, 0., 0.), STYLE(PATCHNOGRID)), POLYGONS([[-1.007354355, -.1632282251, -0.2091652283e-9], [-1.006994407, -.1650279638, -0.1158813750e-1], [-1.005949798, -.1702510092, -0.2204194718e-1], [-1.004322781, -.1783860932, -0.3033813750e-1], [-1.002272621, -.1886368969, -0.3566461958e-1], [-1.000000000, -.2000000004, -0.3750000021e-1], [-.9977273793, -.2113631039, -0.3566461957e-1], [-.9956772185, -.2216139077, -0.3033813749e-1], [-.9940502018, -.2297489916, -0.2204194717e-1], [-.9930055927, -.2349720370, -0.1158813751e-1], [-.9926456449, -.2367717757, -0.1937824747e-9], [-.9930055927, -.2349720369, 0.1158813712e-1], [-.9940502018, -.2297489916, 0.2204194677e-1], [-.9956772186, -.2216139076, 0.3033813709e-1], [-.9977273793, -.2113631038, 0.3566461916e-1], [-1.000000000, -.2000000004, 0.3749999979e-1], [-1.002272621, -.1886368969, 0.3566461916e-1], [-1.004322781, -.1783860932, 0.3033813710e-1], [-1.005949798, -.1702510093, 0.2204194680e-1], [-1.006994407, -.1650279638, 0.1158813697e-1], [-1.007354355, -.1632282251, -0.3149307354e-9]], COLOUR(RGB, 1.00000000, 0., 0.), STYLE(PATCHNOGRID)), POLYGONS([[-0.7354355081e-2, 0.3677177534e-1, 0.], [-0.6994407321e-2, 0.3497203655e-1, -0.1158813729e-1], [-0.5949798238e-2, 0.2974899115e-1, -0.2204194697e-1], [-0.4322781451e-2, 0.2161390724e-1, -0.3033813729e-1], [-0.2272620692e-2, 0.1136310347e-1, -0.3566461937e-1], [0.9050418530e-11, -0.6033612348e-11, -0.375e-1], [0.2272620708e-2, -0.1136310348e-1, -0.3566461936e-1], [0.4322781467e-2, -0.2161390726e-1, -0.3033813728e-1], [0.5949798248e-2, -0.2974899116e-1, -0.2204194696e-1], [0.6994407325e-2, -0.3497203655e-1, -0.1158813730e-1], [0.7354355081e-2, -0.3677177534e-1, 0.1538275356e-10], [0.6994407319e-2, -0.3497203654e-1, 0.1158813733e-1], [0.5949798238e-2, -0.2974899115e-1, 0.2204194698e-1], [0.4322781449e-2, -0.2161390723e-1, 0.3033813730e-1], [0.2272620688e-2, -0.1136310345e-1, 0.3566461937e-1], [-0.1206722471e-10, 0.2111764323e-10, 0.375e-1], [-0.2272620704e-2, 0.1136310346e-1, 0.3566461937e-1], [-0.4322781457e-2, 0.2161390721e-1, 0.3033813731e-1], [-0.5949798242e-2, 0.2974899113e-1, 0.2204194701e-1], [-0.6994407333e-2, 0.3497203659e-1, 0.1158813718e-1], [-0.7354355081e-2, 0.3677177534e-1, -0.1057655071e-9]], COLOUR(RGB, 1.00000000, 0., 0.), STYLE(PATCHNOGRID)), POLYGONS([[-0.735435508125000e-2, 0.367717753350000e-1, 0.], [-1.00735435540869, -.163228225097635, -0.999999971771556e-2], [-1.00688298861325, -.165005680077506, -0.215875799259210e-1], [-0.688298828581500e-2, 0.349943203551283e-1, -0.115875802082055e-1]], [[-0.688298828581500e-2, 0.349943203551283e-1, -0.115875802082055e-1], [-1.00688298861325, -.165005680077506, -0.215875799259210e-1], [-1.00573786696763, -.170208622954392, -0.320408870476349e-1], [-0.573786664019063e-2, 0.297913774782426e-1, -0.220408873299194e-1]], [[-0.573786664019063e-2, 0.297913774782426e-1, -0.220408873299194e-1], [-1.00573786696763, -.170208622954392, -0.320408870476349e-1], [-1.00403108295705, -.178327753428336, -0.403366785490455e-1], [-0.403108262961129e-2, 0.216722470042991e-1, -0.303366788313300e-1]], [[-0.403108262961129e-2, 0.216722470042991e-1, -0.303366788313300e-1], [-1.00403108295705, -.178327753428336, -0.403366785490455e-1], [-1.00192970848953, -.188568314453013, -0.456629045622413e-1], [-0.192970816209689e-2, 0.114316859796215e-1, -0.356629048445258e-1]], [[-0.192970816209689e-2, 0.114316859796215e-1, -0.356629048445258e-1], [-1.00192970848953, -.188568314453013, -0.456629045622413e-1], [-.999639440747405, -.199927888524314, -0.474981969614656e-1], [0.360559580033403e-3, 0.721119083204828e-4, -0.374981972437500e-1]], [[0.360559580033403e-3, 0.721119083204828e-4, -0.374981972437500e-1], [-.999639440747405, -.199927888524314, -0.474981969614656e-1], [-.997384467089054, -.211294521411619, -0.456629045574880e-1], [0.261553323838371e-2, -0.112945209789842e-1, -0.356629048397724e-1]], [[0.261553323838371e-2, -0.112945209789842e-1, -0.356629048397724e-1], [-.997384467089054, -.211294521411619, -0.456629045574880e-1], [-.995385520041251, -.221555567924243, -0.403366785355960e-1], [0.461448028618753e-2, -0.215555674916081e-1, -0.303366788178805e-1]], [[0.461448028618753e-2, -0.215555674916081e-1, -0.303366788178805e-1], [-.995385520041251, -.221555567924243, -0.403366785355960e-1], [-.993838270480693, -.229706605274106, -0.320408870412580e-1], [0.616172984674543e-2, -0.297066048414716e-1, -0.220408873235424e-1]], [[0.616172984674543e-2, -0.297066048414716e-1, -0.220408873235424e-1], [-.993838270480693, -.229706605274106, -0.320408870412580e-1], [-.992894173965534, -.234949753182022, -0.215875798970267e-1], [0.710582636190438e-2, -0.349497527493878e-1, -0.115875801793112e-1]], [[0.710582636190438e-2, -0.349497527493878e-1, -0.115875801793112e-1], [-.992894173965534, -.234949753182022, -0.215875798970267e-1], [-.992645645246336, -.236771775767664, -0.999999970233354e-2], [0.735435508110210e-2, -0.367717753350296e-1, 0.153820176356745e-10]], [[0.735435508110210e-2, -0.367717753350296e-1, 0.153820176356745e-10], [-.992645645246336, -.236771775767664, -0.999999970233354e-2], [-.993117012041650, -.234994320787648, 0.158758049085392e-2], [0.688298828578831e-2, -0.349943203550130e-1, 0.115875802085695e-1]], [[0.688298828578831e-2, -0.349943203550130e-1, 0.115875802085695e-1], [-.993117012041650, -.234994320787648, 0.158758049085392e-2], [-.994262133690063, -.229791377897724, 0.120408876307155e-1], [0.573786663737485e-2, -0.297913774650892e-1, 0.220408873484310e-1]], [[0.573786663737485e-2, -0.297913774650892e-1, 0.220408873484310e-1], [-.994262133690063, -.229791377897724, 0.120408876307155e-1], [-.995968917699122, -.221672247430689, 0.203366791182475e-1], [0.403108262831606e-2, -0.216722469980545e-1, 0.303366788359631e-1]], [[0.403108262831606e-2, -0.216722469980545e-1, 0.303366788359631e-1], [-.995968917699122, -.221672247430689, 0.203366791182475e-1], [-.998070292168256, -.211431686397920, 0.256629051315635e-1], [0.192970815918203e-2, -0.114316859652849e-1, 0.356629048492791e-1]], [[0.192970815918203e-2, -0.114316859652849e-1, 0.356629048492791e-1], [-.998070292168256, -.211431686397920, 0.256629051315635e-1], [-1.00036055991049, -.200072112325871, 0.274981975260344e-1], [-0.360559583050210e-3, -0.721118932364484e-4, 0.374981972437500e-1]], [[-0.360559583050210e-3, -0.721118932364484e-4, 0.374981972437500e-1], [-1.00036055991049, -.200072112325871, 0.274981975260344e-1], [-1.00261553356865, -.188705479439296, 0.256629051173036e-1], [-0.261553324120715e-2, 0.112945209933391e-1, 0.356629048350191e-1]], [[-0.261553324120715e-2, 0.112945209933391e-1, 0.356629048350191e-1], [-1.00261553356865, -.188705479439296, 0.256629051173036e-1], [-1.00461448061598, -.178444432928806, 0.203366790911236e-1], [-0.461448028854124e-2, 0.215555675038288e-1, 0.303366788088391e-1]], [[-0.461448028854124e-2, 0.215555675038288e-1, 0.303366788088391e-1], [-1.00461448061598, -.178444432928806, 0.203366790911236e-1], [-1.00616173017584, -.170293395582273, 0.120408875933825e-1], [-0.616172984839901e-2, 0.297066048503617e-1, 0.220408873110981e-1]], [[-0.616172984839901e-2, 0.297066048503617e-1, 0.220408873110981e-1], [-1.00616173017584, -.170293395582273, 0.120408875933825e-1], [-1.00710582669013, -.165050247678558, 0.158758044696644e-2], [-0.710582636269596e-2, 0.349497527540771e-1, 0.115875801646820e-1]], [[-0.710582636269596e-2, 0.349497527540771e-1, 0.115875801646820e-1], [-1.00710582669013, -.165050247678558, 0.158758044696644e-2], [-1.00735435540869, -.163228225097635, -0.999999971771532e-2], [-0.735435508125000e-2, 0.367717753350000e-1, 0.242320036432573e-15]], COLOR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), MESH([[[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-1.00098058100494, -.195097097054635, -0.999999971771556e-2]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-1.00091184063859, -.195359627923223, -0.116234190165393e-1]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-1.00074428822588, -.196125015156004, -0.130709156443897e-1]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-1.00049608067055, -.197310317170100, -0.141856308814147e-1]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-1.00019411511256, -.198787088100427, -0.148467680350938e-1]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-.999871114205606, -.200395296902223, -0.149826826362258e-1]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-.999562080109826, -.201960669197882, -0.145786462288458e-1]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-.999300501464656, -.203313572609916, -0.136784424269641e-1]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-.999114724375112, -.204307399061172, -0.123796222806159e-1]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-.999024880671474, -.204834452034850, -0.108229331059291e-1]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-.999040706313101, -.204837617163182, -0.917706632950211e-2]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-.999160486346161, -.204316551455402, -0.762037715481521e-2]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-.999371240745494, -.203327720466115, -0.632155700846704e-2]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-.999650131001741, -.201978279376304, -0.542135320658539e-2]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-.999966935028209, -.200414461066785, -0.501731679920534e-2]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-1.00028732219291, -.198805729516537, -0.515323140033731e-2]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-1.00057657357523, -.197326415751071, -0.581436855401634e-2]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-1.00080334429969, -.196136826370793, -0.692908379104140e-2]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-1.00094306023960, -.195365871843437, -0.837658041889176e-2]], [[-1.00000000032744, -.200000000432635, -0.999999971771556e-2], [-1.00098058100494, -.195097097054635, -0.999999971771553e-2]]], COLOR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), POLYGONS([[-1.007354355, -.1632282251, -0.9999999718e-2], [-1.006882988, -.1650056800, -0.2158757993e-1], [-1.005737867, -.1702086229, -0.3204088706e-1], [-1.004031083, -.1783277534, -0.4033667855e-1], [-1.001929708, -.1885683144, -0.4566290457e-1], [-.9996394404, -.1999278885, -0.4749819696e-1], [-.9973844668, -.2112945214, -0.4566290456e-1], [-.9953855197, -.2215555679, -0.4033667854e-1], [-.9938382702, -.2297066052, -0.3204088705e-1], [-.9928941736, -.2349497531, -0.2158757994e-1], [-.9926456449, -.2367717757, -0.9999999703e-2], [-.9931170117, -.2349943208, 0.1587580532e-2], [-.9942621334, -.2297913779, 0.1204088763e-1], [-.9959689174, -.2216722474, 0.2033667912e-1], [-.9980702918, -.2114316864, 0.2566290513e-1], [-1.000360560, -.2000721123, 0.2749819752e-1], [-1.002615533, -.1887054794, 0.2566290513e-1], [-1.004614480, -.1784444330, 0.2033667913e-1], [-1.006161730, -.1702933956, 0.1204088766e-1], [-1.007105826, -.1650502476, 0.1587580382e-2], [-1.007354355, -.1632282251, -0.9999999824e-2]], COLOUR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), POLYGONS([[-0.7354355081e-2, 0.3677177534e-1, 0.], [-0.6882988286e-2, 0.3499432036e-1, -0.1158758021e-1], [-0.5737866639e-2, 0.2979137747e-1, -0.2204088734e-1], [-0.4031082630e-2, 0.2167224701e-1, -0.3033667883e-1], [-0.1929708162e-2, 0.1143168598e-1, -0.3566290485e-1], [0.3605595800e-3, 0.7211190832e-4, -0.3749819724e-1], [0.2615533238e-2, -0.1129452097e-1, -0.3566290484e-1], [0.4614480287e-2, -0.2155556749e-1, -0.3033667882e-1], [0.6161729847e-2, -0.2970660484e-1, -0.2204088733e-1], [0.7105826360e-2, -0.3494975274e-1, -0.1158758022e-1], [0.7354355081e-2, -0.3677177534e-1, 0.1538201406e-10], [0.6882988283e-2, -0.3499432035e-1, 0.1158758025e-1], [0.5737866639e-2, -0.2979137747e-1, 0.2204088735e-1], [0.4031082628e-2, -0.2167224700e-1, 0.3033667884e-1], [0.1929708158e-2, -0.1143168596e-1, 0.3566290485e-1], [-0.3605595830e-3, -0.7211189323e-4, 0.3749819724e-1], [-0.2615533234e-2, 0.1129452095e-1, 0.3566290485e-1], [-0.4614480278e-2, 0.2155556744e-1, 0.3033667885e-1], [-0.6161729841e-2, 0.2970660481e-1, 0.2204088738e-1], [-0.7105826367e-2, 0.3494975278e-1, 0.1158758010e-1], [-0.7354355080e-2, 0.3677177534e-1, -0.1057604226e-9]], COLOUR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), POLYGONS([[0.325000000000000e-1, 0., 0.], [0.325000000000000e-1, 1., -0.205103380800000e-9], [0.309093367791805e-1, .999999999997940, -0.100430525235571e-1], [0.309093367791805e-1, -0.205986398406613e-11, -0.100430523184537e-1]], [[0.309093367791805e-1, -0.205986398406613e-11, -0.100430523184537e-1], [0.309093367791805e-1, .999999999997940, -0.100430525235571e-1], [0.262930523156186e-1, .999999999996082, -0.191030209067659e-1], [0.262930523156186e-1, -0.391809412940337e-11, -0.191030207016625e-1]], [[0.262930523156186e-1, -0.391809412940337e-11, -0.191030207016625e-1], [0.262930523156186e-1, .999999999996082, -0.191030209067659e-1], [0.191030206962697e-1, .999999999994607, -0.262930525246400e-1], [0.191030206962697e-1, -0.539279392228825e-11, -0.262930523195366e-1]], [[0.191030206962697e-1, -0.539279392228825e-11, -0.262930523195366e-1], [0.191030206962697e-1, .999999999994607, -0.262930525246400e-1], [0.100430522997504e-1, .999999999993660, -0.309093369903610e-1], [0.100430522997504e-1, -0.633960947294214e-11, -0.309093367852576e-1]], [[0.100430522997504e-1, -0.633960947294214e-11, -0.309093367852576e-1], [0.100430522997504e-1, .999999999993660, -0.309093369903610e-1], [-0.666586142674826e-11, .999999999993334, -0.325000002051034e-1], [-0.666586142674826e-11, -0.666585987600000e-11, -0.325000000000000e-1]], [[-0.666586142674826e-11, -0.666585987600000e-11, -0.325000000000000e-1], [-0.666586142674826e-11, .999999999993334, -0.325000002051034e-1], [-0.100430523124296e-1, .999999999993660, -0.309093369862413e-1], [-0.100430523124296e-1, -0.633960947209717e-11, -0.309093367811379e-1]], [[-0.100430523124296e-1, -0.633960947209717e-11, -0.309093367811379e-1], [-0.100430523124296e-1, .999999999993660, -0.309093369862413e-1], [-0.191030207123139e-1, .999999999994607, -0.262930525129832e-1], [-0.191030207123139e-1, -0.539279391989740e-11, -0.262930523078799e-1]], [[-0.191030207123139e-1, -0.539279391989740e-11, -0.262930523078799e-1], [-0.191030207123139e-1, .999999999994607, -0.262930525129832e-1], [-0.262930523196341e-1, .999999999996082, -0.191030209012389e-1], [-0.262930523196341e-1, -0.391809412826976e-11, -0.191030206961355e-1]], [[-0.262930523196341e-1, -0.391809412826976e-11, -0.191030206961355e-1], [-0.262930523196341e-1, .999999999996082, -0.191030209012389e-1], [-0.309093367873175e-1, .999999999997940, -0.100430524985141e-1], [-0.309093367873175e-1, -0.205986397892974e-11, -0.100430522934108e-1]], [[-0.309093367873175e-1, -0.205986397892974e-11, -0.100430522934108e-1], [-0.309093367873175e-1, .999999999997940, -0.100430524985141e-1], [-0.325000000000000e-1, 1., -0.191771657946503e-9], [-0.325000000000000e-1, 0.273438142914076e-20, 0.133317228534965e-10]], [[-0.325000000000000e-1, 0.273438142914076e-20, 0.133317228534965e-10], [-0.325000000000000e-1, 1., -0.191771657946503e-9], [-0.309093367790780e-1, 1.00000000000206, 0.100430521136658e-1], [-0.309093367790780e-1, 0.205986398413084e-11, 0.100430523187692e-1]], [[-0.309093367790780e-1, 0.205986398413084e-11, 0.100430523187692e-1], [-0.309093367790780e-1, 1.00000000000206, 0.100430521136658e-1], [-0.262930523039618e-1, 1.00000000000392, 0.191030205126033e-1], [-0.262930523039618e-1, 0.391809413269409e-11, 0.191030207177067e-1]], [[-0.262930523039618e-1, 0.391809413269409e-11, 0.191030207177067e-1], [-0.262930523039618e-1, 1.00000000000392, 0.191030205126033e-1], [-0.191030206907427e-1, 1.00000000000539, 0.262930521184488e-1], [-0.191030206907427e-1, 0.539279392311186e-11, 0.262930523235522e-1]], [[-0.191030206907427e-1, 0.539279392311186e-11, 0.262930523235522e-1], [-0.191030206907427e-1, 1.00000000000539, 0.262930521184488e-1], [-0.100430522870711e-1, 1.00000000000634, 0.309093365842740e-1], [-0.100430522870711e-1, 0.633960947378711e-11, 0.309093367893773e-1]], [[-0.100430522870711e-1, 0.633960947378711e-11, 0.309093367893773e-1], [-0.100430522870711e-1, 1.00000000000634, 0.309093365842740e-1], [0.199975842802448e-10, 1.00000000000667, 0.324999997948966e-1], [0.199975842802448e-10, 0.666585987600000e-11, 0.325000000000000e-1]], [[0.199975842802448e-10, 0.666585987600000e-11, 0.325000000000000e-1], [0.199975842802448e-10, 1.00000000000667, 0.324999997948966e-1], [0.100430523251088e-1, 1.00000000000634, 0.309093365719148e-1], [0.100430523251088e-1, 0.633960947125220e-11, 0.309093367770182e-1]], [[0.100430523251088e-1, 0.633960947125220e-11, 0.309093367770182e-1], [0.100430523251088e-1, 1.00000000000634, 0.309093365719148e-1], [0.191030207230995e-1, 1.00000000000539, 0.262930520949403e-1], [0.191030207230995e-1, 0.539279391829017e-11, 0.262930523000437e-1]], [[0.191030207230995e-1, 0.539279391829017e-11, 0.262930523000437e-1], [0.191030207230995e-1, 1.00000000000539, 0.262930520949403e-1], [0.262930523274703e-1, 1.00000000000392, 0.191030204802465e-1], [0.262930523274703e-1, 0.391809412605760e-11, 0.191030206853499e-1]], [[0.262930523274703e-1, 0.391809412605760e-11, 0.191030206853499e-1], [0.262930523274703e-1, 1.00000000000392, 0.191030204802465e-1], [0.309093367914372e-1, 1.00000000000206, 0.100430520756282e-1], [0.309093367914372e-1, 0.205986397632919e-11, 0.100430522807316e-1]], [[0.309093367914372e-1, 0.205986397632919e-11, 0.100430522807316e-1], [0.309093367914372e-1, 1.00000000000206, 0.100430520756282e-1], [0.325000000000000e-1, 1., -0.205103170779205e-9], [0.325000000000000e-1, 0.430759750263987e-25, 0.210020794676236e-15]], COLOR(RGB, 0., .50196078, 0.), STYLE(PATCHNOGRID)), MESH([[[0., 1., -0.205103380800000e-9], [0.500000000000000e-2, 1., -0.205103380800000e-9]], [[0., 1., -0.205103380800000e-9], [0.472908620850317e-2, .999999999999667, -0.162349755112680e-2]], [[0., 1., -0.205103380800000e-9], [0.394570254698197e-2, .999999999999370, -0.307106376855171e-2]], [[0., 1., -0.205103380800000e-9], [0.273474079061214e-2, .999999999999141, -0.418583259641602e-2]], [[0., 1., -0.205103380800000e-9], [0.122742743570400e-2, .999999999999006, -0.484700153480003e-2]], [[0., 1., -0.205103380800000e-9], [-0.412896727361669e-3, .999999999998978, -0.498292267013673e-2]], [[0., 1., -0.205103380800000e-9], [-0.200847712326482e-2, .999999999999061, -0.457886683837868e-2]], [[0., 1., -0.205103380800000e-9], [-0.338640785812869e-2, .999999999999245, -0.367861975846905e-2]], [[0., 1., -0.205103380800000e-9], [-0.439736875603244e-2, .999999999999512, -0.237973717028876e-2]], [[0., 1., -0.205103380800000e-9], [-0.493180651701360e-2, .999999999999831, -0.822973156507097e-3]], [[0., 1., -0.205103380800000e-9], [-0.493180651701362e-2, 1.00000000000017, 0.822972746300253e-3]], [[0., 1., -0.205103380800000e-9], [-0.439736875603246e-2, 1.00000000000049, 0.237973676008197e-2]], [[0., 1., -0.205103380800000e-9], [-0.338640785812875e-2, 1.00000000000075, 0.367861934826223e-2]], [[0., 1., -0.205103380800000e-9], [-0.200847712326489e-2, 1.00000000000094, 0.457886642817189e-2]], [[0., 1., -0.205103380800000e-9], [-0.412896727361699e-3, 1.00000000000102, 0.498292225992997e-2]], [[0., 1., -0.205103380800000e-9], [0.122742743570392e-2, 1.00000000000099, 0.484700112459329e-2]], [[0., 1., -0.205103380800000e-9], [0.273474079061208e-2, 1.00000000000086, 0.418583218620930e-2]], [[0., 1., -0.205103380800000e-9], [0.394570254698193e-2, 1.00000000000063, 0.307106335834500e-2]], [[0., 1., -0.205103380800000e-9], [0.472908620850316e-2, 1.00000000000033, 0.162349714092008e-2]], [[0., 1., -0.205103380800000e-9], [0.500000000000000e-2, 1., -0.205103348489109e-9]]], COLOR(RGB, 0., .50196078, 0.), STYLE(PATCHNOGRID)), POLYGONS([[0.3250e-1, 1., -0.2051033808e-9], [0.3090933678e-1, 1., -0.1004305253e-1], [0.2629305231e-1, 1., -0.1910302092e-1], [0.1910302070e-1, 1., -0.2629305252e-1], [0.1004305230e-1, 1., -0.3090933700e-1], [-0.6665859876e-11, 1., -0.3250000021e-1], [-0.1004305231e-1, 1., -0.3090933699e-1], [-0.1910302071e-1, 1., -0.2629305252e-1], [-0.2629305232e-1, 1., -0.1910302091e-1], [-0.3090933678e-1, 1., -0.1004305253e-1], [-0.3250e-1, 1., -0.1917716610e-9], [-0.3090933677e-1, 1., 0.1004305214e-1], [-0.2629305230e-1, 1., 0.1910302051e-1], [-0.1910302069e-1, 1., 0.2629305211e-1], [-0.1004305229e-1, 1., 0.3090933658e-1], [0.1999757963e-10, 1., 0.3249999979e-1], [0.1004305230e-1, 1., 0.3090933658e-1], [0.1910302067e-1, 1., 0.2629305213e-1], [0.2629305229e-1, 1., 0.1910302053e-1], [0.3090933681e-1, 1., 0.1004305201e-1], [0.3250e-1, 1., -0.2967668203e-9]], COLOUR(RGB, 0., .50196078, 0.), STYLE(PATCHNOGRID)), POLYGONS([[0.325e-1, 0., 0.], [0.3090933678e-1, -0.2059863984e-11, -0.1004305232e-1], [0.2629305231e-1, -0.3918094131e-11, -0.1910302071e-1], [0.1910302070e-1, -0.5392793920e-11, -0.2629305231e-1], [0.1004305230e-1, -0.6339609474e-11, -0.3090933679e-1], [-0.6665859876e-11, -0.6665859876e-11, -0.325e-1], [-0.1004305231e-1, -0.6339609472e-11, -0.3090933678e-1], [-0.1910302071e-1, -0.5392793920e-11, -0.2629305231e-1], [-0.2629305232e-1, -0.3918094129e-11, -0.1910302070e-1], [-0.3090933678e-1, -0.2059863984e-11, -0.1004305232e-1], [-0.325e-1, 0.2734380793e-20, 0.1333171975e-10], [-0.3090933677e-1, 0.2059863991e-11, 0.1004305235e-1], [-0.2629305230e-1, 0.3918094133e-11, 0.1910302072e-1], [-0.1910302069e-1, 0.5392793922e-11, 0.2629305232e-1], [-0.1004305229e-1, 0.6339609474e-11, 0.3090933679e-1], [0.1999757963e-10, 0.6665859876e-11, 0.325e-1], [0.1004305230e-1, 0.6339609474e-11, 0.3090933679e-1], [0.1910302067e-1, 0.5392793926e-11, 0.2629305234e-1], [0.2629305229e-1, 0.3918094137e-11, 0.1910302074e-1], [0.3090933681e-1, 0.2059863964e-11, 0.1004305222e-1], [0.325e-1, -0.1880048134e-19, -0.9166343950e-10]], COLOUR(RGB, 0., .50196078, 0.), STYLE(PATCHNOGRID)), POLYGONS([[0.325000000000000e-1, 0., 0.], [0.325000000000000e-1, 1.00000000030024, -0.999999952097830e-2], [0.309093367791805e-1, .999899574803041, -0.200425497249797e-1], [0.309093367791805e-1, -0.100425497199263e-3, -0.100425502040014e-1]], [[0.309093367791805e-1, -0.100425497199263e-3, -0.100425502040014e-1], [0.309093367791805e-1, .999899574803041, -0.200425497249797e-1], [0.262930523156186e-1, .999808979653215, -0.291020651441972e-1], [0.262930523156186e-1, -0.191020647024533e-3, -0.191020656232189e-1]], [[0.262930523156186e-1, -0.191020647024533e-3, -0.191020656232189e-1], [0.262930523156186e-1, .999808979653215, -0.291020651441972e-1], [0.191030206962697e-1, .999737082935245, -0.362917372878126e-1], [0.191030206962697e-1, -0.262917364995091e-3, -0.262917377668343e-1]], [[0.191030206962697e-1, -0.262917364995091e-3, -0.262917377668343e-1], [0.191030206962697e-1, .999737082935245, -0.362917372878126e-1], [0.100430522997504e-1, .999690922400780, -0.409077909568521e-1], [0.100430522997504e-1, -0.309077899460438e-3, -0.309077914358738e-1]], [[0.100430522997504e-1, -0.309077899460438e-3, -0.309077914358738e-1], [0.100430522997504e-1, .999690922400780, -0.409077909568521e-1], [-0.666586142674826e-11, .999675016564670, -0.424983746444783e-1], [-0.666586142674826e-11, -0.324983735570000e-3, -0.324983751235000e-1]], [[-0.666586142674826e-11, -0.324983735570000e-3, -0.324983751235000e-1], [-0.666586142674826e-11, .999675016564670, -0.424983746444783e-1], [-0.100430523124296e-1, .999690922400821, -0.409077909527326e-1], [-0.100430523124296e-1, -0.309077899419243e-3, -0.309077914317543e-1]], [[-0.100430523124296e-1, -0.309077899419243e-3, -0.309077914317543e-1], [-0.100430523124296e-1, .999690922400821, -0.409077909527326e-1], [-0.191030207123139e-1, .999737082935362, -0.362917372761564e-1], [-0.191030207123139e-1, -0.262917364878529e-3, -0.262917377551781e-1]], [[-0.191030207123139e-1, -0.262917364878529e-3, -0.262917377551781e-1], [-0.191030207123139e-1, .999737082935362, -0.362917372761564e-1], [-0.262930523196341e-1, .999808979653271, -0.291020651386705e-1], [-0.262930523196341e-1, -0.191020646969266e-3, -0.191020656176922e-1]], [[-0.262930523196341e-1, -0.191020646969266e-3, -0.191020656176922e-1], [-0.262930523196341e-1, .999808979653271, -0.291020651386705e-1], [-0.309093367873175e-1, .999899574803291, -0.200425496999380e-1], [-0.309093367873175e-1, -0.100425496948846e-3, -0.100425501789597e-1]], [[-0.309093367873175e-1, -0.100425496948846e-3, -0.100425501789597e-1], [-0.309093367873175e-1, .999899574803291, -0.200425496999380e-1], [-0.325000000000000e-1, 1.00000000030037, -0.999999950764724e-2], [-0.325000000000000e-1, 0.133310556754254e-12, 0.133310563180144e-10]], [[-0.325000000000000e-1, 0.133310556754254e-12, 0.133310563180144e-10], [-0.325000000000000e-1, 1.00000000030037, -0.999999950764724e-2], [-0.309093367790780e-1, 1.00010042579744, 0.425506833385547e-4], [-0.309093367790780e-1, 0.100425497202417e-3, 0.100425502043169e-1]], [[-0.309093367790780e-1, 0.100425497202417e-3, 0.100425502043169e-1], [-0.309093367790780e-1, 1.00010042579744, 0.425506833385547e-4], [-0.262930523039618e-1, 1.00019102094742, 0.910206611828399e-2], [-0.262930523039618e-1, 0.191020647184967e-3, 0.191020656392623e-1]], [[-0.262930523039618e-1, 0.191020647184967e-3, 0.191020656392623e-1], [-0.262930523039618e-1, 1.00019102094742, 0.910206611828399e-2], [-0.191030206907427e-1, 1.00026291766528, 0.162917382498713e-1], [-0.191030206907427e-1, 0.262917365035245e-3, 0.262917377708496e-1]], [[-0.191030206907427e-1, 0.262917365035245e-3, 0.262917377708496e-1], [-0.191030206907427e-1, 1.00026291766528, 0.162917382498713e-1], [-0.100430522870711e-1, 1.00030907819974, 0.209077919190150e-1], [-0.100430522870711e-1, 0.309077899501633e-3, 0.309077914399933e-1]], [[-0.100430522870711e-1, 0.309077899501633e-3, 0.309077914399933e-1], [-0.100430522870711e-1, 1.00030907819974, 0.209077919190150e-1], [0.199975842802448e-10, 1.00032498403581, 0.224983756025217e-1], [0.199975842802448e-10, 0.324983735570000e-3, 0.324983751235000e-1]], [[0.199975842802448e-10, 0.324983735570000e-3, 0.324983751235000e-1], [0.199975842802448e-10, 1.00032498403581, 0.224983756025217e-1], [0.100430523251088e-1, 1.00030907819962, 0.209077919066565e-1], [0.100430523251088e-1, 0.309077899378047e-3, 0.309077914276348e-1]], [[0.100430523251088e-1, 0.309077899378047e-3, 0.309077914276348e-1], [0.100430523251088e-1, 1.00030907819962, 0.209077919066565e-1], [0.191030207230995e-1, 1.00026291766504, 0.162917382263640e-1], [0.191030207230995e-1, 0.262917364800171e-3, 0.262917377473423e-1]], [[0.191030207230995e-1, 0.262917364800171e-3, 0.262917377473423e-1], [0.191030207230995e-1, 1.00026291766504, 0.162917382263640e-1], [0.262930523274703e-1, 1.00019102094710, 0.910206608592882e-2], [0.262930523274703e-1, 0.191020646861415e-3, 0.191020656069071e-1]], [[0.262930523274703e-1, 0.191020646861415e-3, 0.191020656069071e-1], [0.262930523274703e-1, 1.00019102094710, 0.910206608592882e-2], [0.309093367914372e-1, 1.00010042579706, 0.425506453028170e-4], [0.309093367914372e-1, 0.100425496822060e-3, 0.100425501662811e-1]], [[0.309093367914372e-1, 0.100425496822060e-3, 0.100425501662811e-1], [0.309093367914372e-1, 1.00010042579706, 0.425506453028170e-4], [0.325000000000000e-1, 1.00000000030024, -0.999999952097809e-2], [0.325000000000000e-1, 0.210010284311579e-17, 0.210010294434581e-15]], COLOR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), MESH([[[0., 1.00000000030024, -0.999999952097830e-2], [0.500000000000000e-2, 1.00000000030024, -0.999999952097830e-2]], [[0., 1.00000000030024, -0.999999952097830e-2], [0.472908620850317e-2, .999983766139249, -0.116234156983037e-1]], [[0., 1.00000000030024, -0.999999952097830e-2], [0.394570254698197e-2, .999969291201501, -0.130709095429185e-1]], [[0., 1.00000000030024, -0.999999952097830e-2], [0.273474079061214e-2, .999958144071102, -0.141856226365775e-1]], [[0., 1.00000000030024, -0.999999952097830e-2], [0.122742743570400e-2, .999951532712596, -0.148467585190271e-1]], [[0., 1.00000000030024, -0.999999952097830e-2], [-0.412896727361669e-3, .999950173569263, -0.149826728588235e-1]], [[0., 1.00000000030024, -0.999999952097830e-2], [-0.200847712326482e-2, .999954213925374, -0.145786372283216e-1]], [[0., 1.00000000030024, -0.999999952097830e-2], [-0.338640785812869e-2, .999963215945650, -0.136784351573451e-1]], [[0., 1.00000000030024, -0.999999952097830e-2], [-0.439736875603244e-2, .999976204121513, -0.123796175083584e-1]], [[0., 1.00000000030024, -0.999999952097830e-2], [-0.493180651701360e-2, .999991770982578, -0.108229313268617e-1]], [[0., 1.00000000030024, -0.999999952097830e-2], [-0.493180651701362e-2, 1.00000822961790, -0.917706771509494e-2]], [[0., 1.00000000030024, -0.999999952097830e-2], [-0.439736875603246e-2, 1.00002379647897, -0.762038153359821e-2]], [[0., 1.00000000030024, -0.999999952097830e-2], [-0.338640785812875e-2, 1.00003678465483, -0.632156388461160e-2]], [[0., 1.00000000030024, -0.999999952097830e-2], [-0.200847712326489e-2, 1.00004578667511, -0.542136181363501e-2]], [[0., 1.00000000030024, -0.999999952097830e-2], [-0.412896727361699e-3, 1.00004982703122, -0.501732618313310e-2]], [[0., 1.00000000030024, -0.999999952097830e-2], [0.122742743570392e-2, 1.00004846788788, -0.515324052292951e-2]], [[0., 1.00000000030024, -0.999999952097830e-2], [0.273474079061208e-2, 1.00004185652938, -0.581437640537902e-2]], [[0., 1.00000000030024, -0.999999952097830e-2], [0.394570254698193e-2, 1.00003070939898, -0.692908949903805e-2]], [[0., 1.00000000030024, -0.999999952097830e-2], [0.472908620850316e-2, 1.00001623446123, -0.837658334365285e-2]], [[0., 1.00000000030024, -0.999999952097830e-2], [0.500000000000000e-2, 1.00000000030024, -0.999999952097827e-2]]], COLOR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), POLYGONS([[0.3250e-1, 1.000000000, -0.9999999521e-2], [0.3090933678e-1, .9998995745, -0.2004254973e-1], [0.2629305231e-1, .9998089794, -0.2910206515e-1], [0.1910302070e-1, .9997370826, -0.3629173728e-1], [0.1004305230e-1, .9996909221, -0.4090779096e-1], [-0.6665859876e-11, .9996750163, -0.4249837464e-1], [-0.1004305231e-1, .9996909221, -0.4090779095e-1], [-0.1910302071e-1, .9997370826, -0.3629173728e-1], [-0.2629305232e-1, .9998089794, -0.2910206514e-1], [-0.3090933678e-1, .9998995745, -0.2004254973e-1], [-0.3250e-1, 1.000000000, -0.9999999508e-2], [-0.3090933677e-1, 1.000100425, 0.42550719e-4], [-0.2629305230e-1, 1.000191021, 0.9102066119e-2], [-0.1910302069e-1, 1.000262917, 0.1629173825e-1], [-0.1004305229e-1, 1.000309078, 0.2090779192e-1], [0.1999757963e-10, 1.000324984, 0.2249837560e-1], [0.1004305230e-1, 1.000309078, 0.2090779192e-1], [0.1910302067e-1, 1.000262917, 0.1629173827e-1], [0.2629305229e-1, 1.000191021, 0.9102066139e-2], [0.3090933681e-1, 1.000100425, 0.42550589e-4], [0.3250e-1, 1.000000000, -0.9999999613e-2]], COLOUR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), POLYGONS([[0.325e-1, 0., 0.], [0.3090933678e-1, -0.1004254972e-3, -0.1004255021e-1], [0.2629305231e-1, -0.1910206471e-3, -0.1910206563e-1], [0.1910302070e-1, -0.2629173649e-3, -0.2629173776e-1], [0.1004305230e-1, -0.3090778995e-3, -0.3090779144e-1], [-0.6665859876e-11, -0.3249837356e-3, -0.3249837512e-1], [-0.1004305231e-1, -0.3090778994e-3, -0.3090779143e-1], [-0.1910302071e-1, -0.2629173649e-3, -0.2629173776e-1], [-0.2629305232e-1, -0.1910206470e-3, -0.1910206562e-1], [-0.3090933678e-1, -0.1004254972e-3, -0.1004255021e-1], [-0.325e-1, 0.1333105257e-12, 0.1333105321e-10], [-0.3090933677e-1, 0.1004254975e-3, 0.1004255024e-1], [-0.2629305230e-1, 0.1910206472e-3, 0.1910206564e-1], [-0.1910302069e-1, 0.2629173650e-3, 0.2629173777e-1], [-0.1004305229e-1, 0.3090778995e-3, 0.3090779144e-1], [0.1999757963e-10, 0.3249837356e-3, 0.3249837512e-1], [0.1004305230e-1, 0.3090778995e-3, 0.3090779144e-1], [0.1910302067e-1, 0.2629173652e-3, 0.2629173779e-1], [0.2629305229e-1, 0.1910206474e-3, 0.1910206566e-1], [0.3090933681e-1, 0.1004254962e-3, 0.1004255011e-1], [0.325e-1, -0.9165885226e-12, -0.9165885668e-10]], COLOUR(RGB, .30980392, .30980392, .44313725), STYLE(PATCHNOGRID)), CURVES([[0., 0., 0.], [.5, 0., 0.]], COLOUR(RGB, 1.00000000, 0., 0.), THICKNESS(4)), CURVES([[0., 0., 0.], [0., .5, 0.]], COLOUR(RGB, 1.00000000, 1.00000000, 0.), THICKNESS(4)), CURVES([[0., 0., 0.], [0., 0., .5]], COLOUR(RGB, 0., 0., 1.00000000), THICKNESS(4)), TEXT([.5, 0.5e-1, 0.], "X"), TEXT([.1, .5, 0.], "Y"), TEXT([0.5e-1, 0., .5], "Z"), SCALING(CONSTRAINED)), -.35*t, -.45*t, -.15*t]

(5)

plottools:-rotate, [cyl1, -5*w1, -7*w2, -11*w3]

plottools:-rotate, [INTERFACE_PLOT3D(POLYGONS([[.540427485050000, 5.19695964945000, 6.], [-2.45957251817905, -1.80304035106433, .200000001926034], [-2.40020333012780, -1.72663599020061, 0.770796414867743e-1], [.599796673101250, 5.27336401031372, 5.87707963956074]], [[.599796673101250, 5.27336401031372, 5.87707963956074], [-2.40020333012780, -1.72663599020061, 0.770796414867743e-1], [-2.30165945204901, -1.67699040331239, -0.338084176330629e-1], [.698340551180034, 5.32300959720195, 5.76619158044090]], [[.698340551180034, 5.32300959720195, 5.76619158044090], [-2.30165945204901, -1.67699040331239, -0.338084176330629e-1], [-2.17358704532711, -1.65896324634667, -.121809679601480], [.826412957901933, 5.34103675416766, 5.67819031847249]], [[.826412957901933, 5.34103675416766, 5.67819031847249], [-2.17358704532711, -1.65896324634667, -.121809679601480], [-2.02852272927863, -1.67431914307083, -.178309967803099], [.971477273950412, 5.32568085744350, 5.62169003027087]], [[.971477273950412, 5.32568085744350, 5.62169003027087], [-2.02852272927863, -1.67431914307083, -.178309967803099], [-1.88066641043479, -1.72155495120473, -.197778640223966], [1.11933359279426, 5.27844504930960, 5.60222135785000]], [[1.11933359279426, 5.27844504930960, 5.60222135785000], [-1.88066641043479, -1.72155495120473, -.197778640223966], [-1.74449129507320, -1.79604690074401, -.178309967752677], [1.25550870815585, 5.20395309977032, 5.62169003032129]], [[1.25550870815585, 5.20395309977032, 5.62169003032129], [-1.74449129507320, -1.79604690074401, -.178309967752677], [-1.63332715194140, -1.89050320099137, -.121809679458808], [1.36667285128764, 5.10949679952296, 5.67819031861516]], [[1.36667285128764, 5.10949679952296, 5.67819031861516], [-1.63332715194140, -1.89050320099137, -.121809679458808], [-1.55805550257248, -1.99567781058744, -0.338084175654165e-1], [1.44194450065657, 5.00432218992689, 5.76619158050855]], [[1.44194450065657, 5.00432218992689, 5.76619158050855], [-1.55805550257248, -1.99567781058744, -0.338084175654165e-1], [-1.52604446000964, -2.10127550657275, 0.770796417932837e-1], [1.47395554321941, 4.89872449394158, 5.87707963986725]], [[1.47395554321941, 4.89872449394158, 5.87707963986725], [-1.52604446000964, -2.10127550657275, 0.770796417932837e-1], [-1.54042748832800, -2.19695965007855, .200000002089205], [1.45957251490105, 4.80304035043578, 6.00000000016317]], [[1.45957251490105, 4.80304035043578, 6.00000000016317], [-1.54042748832800, -2.19695965007855, .200000002089205], [-1.59979667633290, -2.27336401083013, .322920362369154], [1.40020332689614, 4.72663598968420, 6.12292036044312]], [[1.40020332689614, 4.72663598968420, 6.12292036044312], [-1.59979667633290, -2.27336401083013, .322920362369154], [-1.69834055463283, -2.32300959778309, .433808421681501], [1.30165944859622, 4.67699040273124, 6.23380841975547]], [[1.30165944859622, 4.67699040273124, 6.23380841975547], [-1.69834055463283, -2.32300959778309, .433808421681501], [-1.82641296122388, -2.34103675468290, .521809683502696], [1.17358704200517, 4.65896324583143, 6.32180968157666]], [[1.17358704200517, 4.65896324583143, 6.32180968157666], [-1.82641296122388, -2.34103675468290, .521809683502696], [-1.97147727737388, -2.32568085791628, .578309971705590], [1.02852272585517, 4.67431914259805, 6.37830996977956]], [[1.02852272585517, 4.67431914259805, 6.37830996977956], [-1.97147727737388, -2.32568085791628, .578309971705590], [-2.11933359621183, -2.27844504974314, .597778644076033], [.880666407017220, 4.72155495077119, 6.39777864215000]], [[.880666407017220, 4.72155495077119, 6.39777864215000], [-2.11933359621183, -2.27844504974314, .597778644076033], [-2.25550871154906, -2.20395310017252, .578309971554321], [.744491291679984, 4.79604690034181, 6.37830996962829]], [[.744491291679984, 4.79604690034181, 6.37830996962829], [-2.25550871154906, -2.20395310017252, .578309971554321], [-2.36667285464043, -2.10949679990479, .521809683214967], [.633327148588615, 4.89050320060954, 6.32180968128893]], [[.633327148588615, 4.89050320060954, 6.32180968128893], [-2.36667285464043, -2.10949679990479, .521809683214967], [-2.44194450395682, -2.00432219030132, .433808421285475], [.558055499272224, 4.99567781021301, 6.23380841935944]], [[.558055499272224, 4.99567781021301, 6.23380841935944], [-2.44194450395682, -2.00432219030132, .433808421285475], [-2.47395554646015, -1.89872449432231, .322920361903599], [.526044456768893, 5.10127550619202, 6.12292035997756]], [[.526044456768893, 5.10127550619202, 6.12292035997756], [-2.47395554646015, -1.89872449432231, .322920361903599], [-2.45957251817905, -1.80304035106433, .200000001926036], [.540427485049999, 5.19695964945000, 6.00000000000000]], COLOR(RGB, 1.00000000, 1.00000000, 0.), STYLE(PATCHNOGRID)), MESH([[[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00459572837855, -1.99803040401983, .200000001926034]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00395924377148, -1.99723301259337, .198708416786364]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00289371401770, -1.99673546724239, .197556794937584]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00151460579941, -1.99659168472588, .196669932476266]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99997136689115, -1.99681724611051, .196143934711182]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99843123117443, -1.99738770832032, .196035801661874]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99706109625184, -1.99824125292325, .196357251222094]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99600943750207, -1.99928538511744, .197073449344185]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99539021846883, -2.00040695697829, .198106784848663]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99527054114253, -2.00148442879169, .199345279799763]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99566337441848, -2.00240103976796, .200654724052304]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99652614871577, -2.00305746088513, .201893219003405]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99776536905199, -2.00338255872975, .202926554507882]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99924674667521, -2.00334110390592, .203642752629974]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00080975133403, -2.00293758868706, .203964202190194]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00228500722112, -2.00221574020830, .203856069140886]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00351264747019, -2.00125378195296, .203330071375802]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00435963821144, -2.00015595702432, .202443208914484]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00473419485564, -1.99904123178791, .201291587065705]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00459572837855, -1.99803040401983, .200000001926034]]], COLOR(RGB, 1.00000000, 1.00000000, 0.), STYLE(PATCHNOGRID)), POLYGONS([[-2.459572518, -1.803040352, .200000002], [-2.400203330, -1.726635991, 0.77079642e-1], [-2.301659452, -1.676990404, -0.33808418e-1], [-2.173587045, -1.658963247, -.121809680], [-2.028522729, -1.674319144, -.178309968], [-1.880666410, -1.721554952, -.197778640], [-1.744491295, -1.796046901, -.178309968], [-1.633327152, -1.890503202, -.121809679], [-1.558055502, -1.995677811, -0.33808418e-1], [-1.526044460, -2.101275507, 0.77079642e-1], [-1.540427488, -2.196959650, .200000002], [-1.599796676, -2.273364012, .322920363], [-1.698340554, -2.323009598, .433808422], [-1.826412961, -2.341036755, .521809684], [-1.971477277, -2.325680858, .578309972], [-2.119333596, -2.278445050, .597778644], [-2.255508711, -2.203953101, .578309972], [-2.366672854, -2.109496801, .521809684], [-2.441944503, -2.004322191, .433808422], [-2.473955546, -1.898724494, .322920361], [-2.459572518, -1.803040351, .200000001]], COLOUR(RGB, 1.00000000, 1.00000000, 0.), STYLE(PATCHNOGRID)), POLYGONS([[.5404274850, 5.196959649, 6.], [.5997966730, 5.273364010, 5.877079640], [.6983405512, 5.323009597, 5.766191580], [.8264129578, 5.341036754, 5.678190318], [.9714772740, 5.325680857, 5.621690030], [1.119333593, 5.278445049, 5.602221358], [1.255508708, 5.203953100, 5.621690030], [1.366672851, 5.109496800, 5.678190319], [1.441944501, 5.004322190, 5.766191580], [1.473955543, 4.898724494, 5.877079640], [1.459572515, 4.803040350, 6.000000000], [1.400203327, 4.726635990, 6.122920361], [1.301659449, 4.676990403, 6.233808420], [1.173587042, 4.658963246, 6.321809682], [1.028522726, 4.674319143, 6.378309970], [.8806664070, 4.721554951, 6.397778642], [.7444912921, 4.796046900, 6.378309970], [.6333271492, 4.890503200, 6.321809682], [.5580554996, 4.995677810, 6.233808420], [.5260444567, 5.101275507, 6.122920359], [.5404274853, 5.196959650, 5.999999999]], COLOUR(RGB, 1.00000000, 1.00000000, 0.), STYLE(PATCHNOGRID)), SCALING(CONSTRAINED)), -1.75, -3.15, -1.65]

(6)

NULL

``


 

Download Anim_How-3.mw

The piecewise plot below displays a sphere truncated by the plane z = 2 - y.

f := proc (x, y, z) options operator, arrow; piecewise(z <= 2-y, x^2+y^2+z^2-16, z-2+y) end proc; implicitplot3d(f, -4 .. 4, -4 .. 4, -4 .. 4, style = surface, numpoints = 50000);

The 3 transforms below when executed in display(T(sphere([0, 0, 0], 4, numpoints = 50000)), scaling = constrained) display the truncated sphere differently:

1) the truncating plane only partly conforms to the boundary of the truncated sphere

2) the truncated sphere is correct provided that the else condition coordinate is in the truncating plane and truncated sphere

3) the truncated sphere is correct but hollow

 

1) T := transform(proc (x, y, z) options operator, arrow; `if`(z <= 2-y, [x, y, z], [x, y, 2-y]) end proc)

2) T := transform(proc (x, y, z) options operator, arrow; `if`(z <= 2-y, [x, y, z], [0, 0, 2]) end proc)

3) T := transform(proc (x, y, z) options operator, arrow; `if`(z <= 2-y, [x, y, z], [`&+-`(sqrt(16-y^2-z^2)), y, 2-y]) end proc)

Please explain the different behavior of the three transforms.           

Hello, 

 

I am not sure how to find the Heaviside Laplace transform 

 

H(t-1)e^(3t-3)

 

 

 

 

Thank you:)

Dear Community,

Would someone have a good and easy to understand/implement description of the Den Iseger algorithm for the numerical inversion of Laplace transform? Even better if someone would have a Maple script to do it, that would be superb.

Tx in advance,

best regards

Andras

Hello,

To summarize, I have a variable ε = order(1),  which maple has assumed is a funtion ε(x,y,z) and so when I differentiate epsilon with respect to x (or y or z) I do not get 0. I get ε(or εy, εz). How do I ensure maple does not assume this?

More detail of my process:

I declare functions,

I have the function I want to transform,

Now I transform the variables to the new co-ordinate system. i.e. from (x,n,q) to (s,Y,z)

                   

Good! - Everything correct so far. 

Now I want to linearise so i introduce x=x0+ε*x1; and the same for (Y,z), 

               

As you can see, epsilon has derivatives, which it should not. 

How I can avoid this? 

Thanks in advance - im well and truely stumped over this.

P.s. if the images do not show, the script can be found here: 

https://www.dropbox.com/sh/34gepa60xf4droq/AAAJlUcQ_Jwkc96topPvcxtXa?dl=0 

Hello,

I have this list :
T:=[alpha(t),beta(t)]

I would like to create this list automatically:

Tmod:=[alpha_,beta_]

In other words, how can I remove the 3 characters "(t)" and replace it by "_"

Do you have ideas to do so ?

Thanks a lot for your help

f=x^2.  It's easy to compute the fouier transform. F(y)=fourier(f,x,y).

However, I want to do more. replace the variable y with a new formula g(z)=z^2.

I tried  "subs(y=g,F)". But failed. Need your help.

with(MTM):

f := x^2

x^2

(1)

F := fourier(f, x, y)

-2*Pi*Dirac(2, y)

(2)

g := z^2

z^2

(3)

subs(y = g, F)

-2*Pi*Dirac(2, y) = z^2

(4)

NULL

``

 

Download code.mw

Hi,

 

I was wondering how to go about plotting a Fourier Tranform in Maple.

My assignment is to plot a simple harmonic equation as a Fourier transform, depicting amplitude against fequency.

I've been given: x'' + w^2 x = 0

And want to obtain both the f(x) = a0 sin(wt) + b0cos(wt) form, and a graph of the the amplitude (c^2 =a0^2 + b0^2) against frequency.

I know how to do this on paper but not in Maple, so any help with line commands and layout would be very much appreciated.

 

Thanks

How evaluate system of two integral equation by laplace transform ?

 

with(inttrans):

L := laplace((1/2)*x^2+(1/2)*x^3+(1/12)*x^4 = int(u(t)*(-1+x-t)+v(t)*(1+x-t), t = 0 .. x), x, s);

(s^2+3*s+2)/s^5 = laplace(int(u(t)*(-1+x-t)+v(t)*(1+x-t), t = 0 .. x), x, s)

 

(3*s^2-s+2)/s^5 = laplace(int((1+x-t)*u(t)+(-1+x-t)*v(t), t = 0 .. x), x, s)

(1)

``

 

Download Qu_2_mapel.mwQu_2_mapel.mw

In Maple 15 it seems that plottools:-transform only accepts this form of conditional statement:  

`if`(conditional expression, true expression, false expression).

Is there any way to have plottools:-transform process more than one condition? Do later versions of Maple permit this?

Hi everyone,

 

Consider this maple 18 doc: Euler18.mw

 

The code is regular code for Julia sets of the exponential.

 

To see how the Julia set behaves at infinity, I apply the transform mu(z)=1/z.

 

The plot3d command correctly plots the Julia set at an appropriate neighborhood of infinity, but:

1) Axes are not transformed

2) Saving as .eps produces an empty plot, sans the axes (plot is saved correctly, when not applying mu(z))

 

Is there any trick to force the axes to also show correctly with the transformed ranges?

Seems that this misalignment is bothering the .eps renderer, which probably plots the graph in twilight zone, given the false ranges of the untransformed axes.

 

Any ideas on how to force the saveas .eps to work in this case?

 

Many thanks,

Yiannis

Hallo everybody,

I just started to use maple and I think I need some help from more experienced users.
I would like to transform the stationary Navier Stokes equations to toroidal coordinates.


The definition of my coordinate system is as follows:
x = -r * cos(sigma)
y = cos(Theta) * ( R + r * sin(sigma) )
z = sin(Theta) * ( R + r * sin(sigma) )


I tried to define the coordinate system and transform each term of the equation:

div( rho * CC) = -grad(p) + div(Tau)

I can transform the pressure gradient. However, I get an error for the divergence of the tensors.
Could someone please give me a hint on how to get the divergences?

Thanks!
Uwe



My code is printed below:

restart: with(plots): with(LinearAlgebra): with(VectorCalculus): with(linalg):

#torus defintion
x := -r*cos(sigma);
y := cos(Theta)*(R+r*sin(sigma));
z := sin(Theta)*(R+r*sin(sigma));
R := .35;
AddCoordinates(torus1[r, sigma, Theta], [cos(Theta)*(R+r*sin(sigma)), sin(Theta)*(R+r*sin(sigma)), -r*cos(sigma)]);
SetCoordinates(torus1[r, sigma, Theta]);

#pressure gradient
PressureGradient := Gradient(p(r, sigma, Theta, t));

#left hand side
c := vector(3, ([Cr, Ctheta, Cx])(r, sigma, Theta, t));
rhoCC := rho*multiply(c, transpose(c));
LHS := Divergence(rhoCC)

Hi all, 

I'm trying to implement the smithChart on Maple, but this error "Error, (in unknown) invalid transform: output is not 2 or 3 element" keeps popping up for some reason. I have no idea how to fix it. Can anyone help me with this? Here is the smithChart:




smithChart.mw

 

smithChart := proc(r)
  local i, a, b, c;
   a := PLOT(seq(plottools[arc]([-i*r/4, 0], i*r/4, 0..Pi),
                 i = 1..4),

  plottools[arc]([0, r/2], r/2,
            Pi-arcsin(3/5)..3*Pi/2),
  plottools[arc]([0,r], r, Pi..Pi+arcsin(15/17)),
  plottools[arc]([0, 2*r], 2*r,
            Pi+arcsin(3/5)..Pi+arcsin(63/65)),
  plottools[arc]([0,4*r], 4*r,
            Pi+arcsin(15/17)..Pi+arcsin(63/65)));

  b := plottools[transform]((x, y) -> [x-y])(a);
  c := plottools[line]([0,0], [-2*r, 0]):
  plots[display](a, b, c, axes = none, scaling = constrained, args[2..nargs]);
  end proc:

smithChart(1);
Error, (in unknown) invalid transform: output is not 2 or 3 elements

1 2 3 Page 1 of 3