Items tagged with rotate

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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)

 

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``

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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)

``

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``

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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, 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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

I uploaded this file AnimationTest.mw to the Maple Cloud. One a 3d animation and one just a 3d plot. When I open the file in the Maple Cloud from my browser,  I cannot rotate either plot with the mouse. Is there a way to change the worksheets so rotation from the browser will be possible?

I have created several animated 3-d figures using Maple.  Exporting an animation as a gif file I find that with, for example, Quicktime, I can run the animation. However I cannot rotate the 3-d figures using Quicktime.  Is there some other way to make such animations available to people not having Maple, so they can rotate the figure as well as run the animation? I would appreciate any ideas about this.

Construction of arabesques of melodic line BACH

Elena, Liya "Construction of arabesques of melodic line BACH", Kazan, Russia, school#57
       
> restart:
> with(plots):with(plottools):

      The setting and visualization of line BACH: B - note b-flat, A - note la, C - note do, H - note si.
> p0:=plot([[0,1],[2,0],[4,1.5],[6,1]],thickness=4,color=cyan,scaling=constrained);
>
>   p0 := PLOT(
>
>         CURVES([[0, 1.], [2., 0], [4., 1.500000000000000], [6., 1.]])
>
>         , SCALING(CONSTRAINED), THICKNESS(4), AXESLABELS( ,  ),
>
>         COLOUR(RGB, 0, 1.00000000, 1.00000000),
>
>         VIEW(DEFAULT, DEFAULT))
>
> plots[display](p0);
> r_i:=seq(rotate(p0,i*Pi/4),i=1..8):
> p1:=display(r_i,p0):plots[display](p1,scaling=constrained);

> c1:=circle([0,0],6,color=blue,thickness=2):
> plots[display](c1,p1,scaling=constrained);
> p_c:=plots[display](c1,p1,scaling=constrained):

> pt_i_2:=seq(translate(p1,0,2*6*i),i=0..4):
> plots[display](pt_i_2,scaling=constrained);
> pt_i_22:=seq(translate(p1,0,6*i),i=0..4):
> plots[display](pt_i_22,scaling=constrained);
> pt_i_222:=seq(translate(p1,0,1/2*6*i),i=0..4):
> plots[display](pt_i_222,scaling=constrained);

> pr:=rotate(p1,Pi/8):
> plots[display](pr,scaling=constrained);
> plots[display](p1,pr,scaling=constrained);
> pr_i:=seq(rotate(p1,Pi/16*i),i=0..8):
> plots[display](pr_i,scaling=constrained);


> pt_1:=translate(p1,0,2*6):
> pr_1_i:=seq(rotate(pt_1,Pi/3.5*i),i=0..6):
> plots[display](pr_1_i,scaling=constrained);
> pr_11_i:=seq(rotate(pt_1,Pi/5*i),i=0..10):
> plots[display](pr_11_i,scaling=constrained);
> pr_111_i:=seq(rotate(pt_1,Pi/6.5*i),i=0..12):
> plots[display](pr_111_i,scaling=constrained);


Elena, Liya "Designing of islamic arabesques", Kazan, Russia, school #57


> restart:
      At the theorem of cosines  c^2 = a^2+b^2-2*a*b*cos(phi);
      In our case  c=a0 ,  a=1 ,  a=b , phi; - acute angle of a rhombus (the tip of the kalam).
      s0 calculated at theorem of  Pythagoras.
     (а0 - horizontal diagonal of a  rhombus, s0 - vertical diagonal of a  rhombus)
> a:=1:phi:=Pi/4:
> a0:=sqrt(a^2+a^2-2*a^2*cos(phi));

                       a0 := sqrt(2 - sqrt(2))

> solve((s0^2)/4=a^2-(a0^2)/4,s0);

                sqrt(2 + sqrt(2)), -sqrt(2 + sqrt(2))


      The setting of initial parameters : the size of the tip of the pen-kalam and  depending on its - the main module size - point
       (а0 - horizontal diagonal of a  rhombus, s0 - vertical diagonal of a  rhombus)
> a0:=sqrt(2-sqrt(2)):
> s0:=sqrt(2+sqrt(2)):
      Connection the graphical libraries Maple
> with(plots):with(plottools):
      Construction of unit of measure (point) - rhombus - the tip of the kalam
> p0:=plot([[0,0],[a0/2,s0/2],[0,s0],[-a0/2,s0/2],[0,0]],scaling=constrained,color=gold,thickness=3):
> plots[display](p0);

The setting and construction of altitude of alif - the basis of the rules compilation of the proportions      Example, on style naskh altitude of alif amount five points
> p_i:=seq(plot([[0,0+s0*i],[a0/2,s0/2+s0*i],[0,s0+s0*i],[-a0/2,s0/2+s0*i],[0,0+s0*i]],scaling=constrained,color=black),i=0..4):
> pi:=display(p_i):
> plots[display](p_i);
The setting of appropriate circle of diameter, amount altitude of alifd0:=s0+s0*i:
> i:=4:
> d0:=d0:
> c0:=circle([0,d0/2],d0/2,color=blue):
> plots[display](p_i,c0);


Construction of flower by turning "point"r_i:=seq(rotate(p0,i*Pi/4),i=1..8):
> p1:=display(r_i,p0):plots[display](p1,scaling=constrained);

 The setting of circumscribed circlec1:=circle([0,0],s0,color=blue,thickness=2):
      Construction and the setting of flower inscribed in a circle
> plots[display](c1,p1,scaling=constrained);
> p_c:=plots[display](c1,p1,scaling=constrained):

The setting and construction of arabesque by horizontal parallel transport original flower with different stepspt_i_1:=seq(translate(p1,5*a0*i,0),i=0..4):
> plots[display](pt_i_1);
> pt_i_11:=seq(translate(p1,2*a0*i,0),i=0..4):
> plots[display](pt_i_11);
> pt_i_111:=seq(translate(p1,a0*7*i,0),i=0..4):
> plots[display](pt_i_111);

 The setting and construction of arabesque by vertical parallel transport original flower with different stepspt_i_2:=seq(translate(p1,0,2*s0*i),i=0..4):
> plots[display](pt_i_2);
> pt_i_22:=seq(translate(p1,0,s0*i),i=0..4):
> plots[display](pt_i_22);
> pt_i_222:=seq(translate(p1,0,1/2*s0*i),i=0..4):
> plots[display](pt_i_222);
 Getting arabesques by turning original flower on different anglespr:=rotate(p1,Pi/8):
> plots[display](pr);
> plots[display](p1,pr);

> pr_i:=seq(rotate(p1,Pi/16*i),i=0..8):
> plots[display](pr_i);


> pt_1:=translate(p1,0,2*s0):
> pr_1_i:=seq(rotate(pt_1,Pi/3.5*i),i=0..6):
> plots[display](pr_1_i);
> pr_11_i:=seq(rotate(pt_1,Pi/5*i),i=0..10):
> plots[display](pr_11_i);
> pr_111_i:=seq(rotate(pt_1,Pi/6.5*i),i=0..12):
> plots[display](pr_111_i);


I saw a presentation Calculus 1 -- I'm pretty sure it was Maple -- that showed how to set up a volume of solid of revolutionvisually rotated the region and looked at it from different points of view.

Is there someplace I could go to find out ho0w to do that.  I am new and in experienced in using Maple.

Thanks in advance.

Tim Wisecarver

Georgetown preparatory School

twisecarver@gprep.org

Hi,

  I would need to get access to the values of euler angles defining the orientation of a 3D plot.

I generate the 3D plot with a given orientation, then the user is allowed to rotate it with mouse orbit. How can I get the values of the new euler angles to use them in further computations?

In the plot/structure I cannot find any data concerned with orientation...

 

Thank you.

 

Marco

Hi, 

I have to plot in 2 different ways an ellipse that has been rotated in a plane. The equation of the ellipse is 

3x^2 - 3xy + 6y^2 -6x +7y =9

First of all I use the implicitplot which works great: 

restart;
f:=(x,y)->3*x^2-3*x*y+6*y^2-6*x+7*y-9;
with(plots):
implicitplot(f(x,y),x=-10..10,y=-10..10,numpoints=50000,scaling=constrained);

For the second method I really am not sure if what I'm doing is good. I tried with the plot3d, but it gave me some sort of weird shape, I really don't think it is what I am looking for. 

restart;
f:=(x,y)->3*x^2-3*x*y+6*y^2-6*x+7*y-9;
with(plots):
plot3d(f(x,y),x=-10..10,y=-10..10);

The I tried to reduce the equation to the form x^2/a^2 + y^2/b^2 = 1, but I could not, maybe because of the rotation. Still, I tried to take the ellipse function from Maple with some empirical numbers I just tried to create an ellipse looking like the first one. 

restart;
with(plottools):
with(plots):
a:=2.29:b:=1.38:x0:=0.8:y0:=-0.5:
elli:=ellipse([x0,y0],a,b,color=blue):
display(rotate(elli,0.4),scaling=constrained);
This time I get an ellipse similar to the first, but I don't really think it is legit to do it that way, in a sort of trial-and-error.

So I was wondering if there was another way like implicitplot to create the graph of that ellipse. 

Hello Primers

I am doing some homework with the software Maple 2015 where I am supposed to design a lamp through creating some line segments and a circle in a 2d coordinate system. But my question is, how do I add a third dimension and rotate all these line segments around the y-axis, so I can get an idea of how it looks like in 3d?

Here is a picture

Thanks in advance

Can we rotate 3d text in Maple like this shown here?

http://mathematica.stackexchange.com/questions/25065/rotating-3d-text

 

i have a work on Magic Squares , and i need to rotate or flip them to all 8 possible directions .
but i am confused to find such special commands in maple for doing my purpose !

may you guide me how can i do this programmaticaly ?

 

order4 := Array(1 .. 4, 1 .. 4, {(1, 1) = 8, (1, 2) = 11, (1, 3) = 14, (1, 4) = 1, (2, 1) = 13, (2, 2) = 2, (2, 3) = 7, (2, 4) = 12, (3, 1) = 3, (3, 2) = 16, (3, 3) = 9, (3, 4) = 6, (4, 1) = 10, (4, 2) = 5, (4, 3) = 4, (4, 4) = 15}, datatype = anything, storage = rectangular, order = Fortran_order)

order4 := Array(1..4, 1..4, {(1, 1) = 8, (1, 2) = 11, (1, 3) = 14, (1, 4) = 1, (2, 1) = 13, (2, 2) = 2, (2, 3) = 7, (2, 4) = 12, (3, 1) = 3, (3, 2) = 16, (3, 3) = 9, (3, 4) = 6, (4, 1) = 10, (4, 2) = 5, (4, 3) = 4, (4, 4) = 15})

(1)

``


Download magicsquare4.mw

Hello,

I am trying to make a three dimensional cube in maple by using matrices. I also have to make it rotate about the x,y,z axes, project it with three different origins, and translate it (I'm assuming this means translate it across an axis?). I have already made the cube, but when I try to rotate it across one of the axes by multiplying my matrix by one of the rotation matrices (this is what I put un maple: P1:= matrix([[1,0,0,0],[0,cos(theta),-sin(theta),0],[0,sin(theta),cos(theta),0...

I can't solve probably very easy problem. How to plot a filled semicircle which is rotated across one axis by an angle alpha? I came to the solution which I don't consider as the best one (since e.g. it will not work for alpha=Pi/2*(odd integer)) and I believe someone of you will show me a better approach. Thank you in advance.

My solution:

alpha := (1/6)*Pi:
plot3d([x, y, y*tan(alpha)], x = -1 .. 1, y = 0 .. sqrt(1-x^2)*cos(alpha), axes = normal, labels = ["x", "y", "z"...

Hello to everyone

Pls help,urgent....

I need to draw the deformation of one story building (for simplicity, 4 columns and 2 floors) whose columns and floors  under influence of external load acting to the left of the building at its intersection point undergo the deform shape like S . So means that when the building moves to the right its intersection point of column and floor has some small rotation.

I am new to Maple environment...

Suppose that you wish to animate the whole view of a plot. By whole view, I mean that it includes the axes and is not just a rotation of a plotted object such as a surface.

One simple way to do this is to call plots:-animate (or plots:-display on a list of plots supplied in a list, with its `insequence=true` option). The option `orientation` would contain the parameter that governs the animation (or generates the sequence).

But that entails recreating the same plot each time. The plot data might not even change. The key thing that changes is the ORIENTATION() descriptor within each 3d plot object in the reulting data structure. So this is inefficient in two key ways, in the worst case scenario.

1) It may even compute the plot's numeric results, as many times as there are frames in the resulting animation.

2) It stores as many instances of the grid of computed numeric data as there are frames.

We'd like to do better, if possible, reducing down to a single computation of the data, and a single instance of storage of a grid of data.

To keep this understandable, I'll consider the simple case of plotting a single 3d surface. More complicated cases can be handled with revisions to the techniques.

Avoiding problem 1) can be done in more than one way. Instead of plotting an expression, a procedure could be plotted, where that procedure has `option remember` so that it automatically stores computed results an immediately returns precomputed stored result when the arguments (x and y values) have been used already.

Another way to avoid problem 1) is to generate the unrotated plot once, and then to use plottools:-rotate to generate the other grids without necessitating recomputation of the surface. But this rotates only objects in the plot, and does alter the view of the axes.

But both 1) and 2) can be solved together by simply re-using the grid of computed data from an initial plot3d call, and then constructing each frame's plot data structure component "manually". The only thing that has to change, in each, is the ORIENTATION(...) subobject.

At 300 frames, the difference in the following example (Intel i7, Windows 7 Pro 64bit, Maple 15.01) is a 10-fold speedup and a seven-fold reduction is memory allocation, for the creation of the animation structure. I'm not inlining all the plots into this post, as they all look the same.

restart:
P:=1+x+1*x^2-1*y+1*y^2+1*x*y:

st,ba:=time(),kernelopts(bytesalloc):

plots:-animate(plot3d,[P,x=-5..5,y=-5..5,orientation=[A,45,45],
                       axes=normal,labels=[x,y,z]],
               A=0..360,frames=300);

time()-st,kernelopts(bytesalloc)-ba;

                                1.217, 25685408
restart:
P:=1+x+1*x^2-1*y+1*y^2+1*x*y:

st,ba:=time(),kernelopts(bytesalloc):

g:=plot3d(P,x=-5..5,y=-5..5,orientation=[-47,666,-47],
          axes=normal,labels=[x,y,z]):

plots:-display([seq(PLOT3D(GRID(op([1,1..2],g),op([1,3],g)),
                           remove(type,[op(g)],
                                  specfunc(anything,{GRID,ORIENTATION}))[],
                           ORIENTATION(A,45,45)),
                    A=0..360,360.0/300)],
               insequence=true);

time()-st,kernelopts(bytesalloc)-ba;

                                0.125, 3538296

By creating the entire animation data structure manually, we can get a further factor of 3 improvement in speed and a further factor of 3 reduction in memory allocation.

restart:
P:=1+x+1*x^2-1*y+1*y^2+1*x*y:

st,ba:=time(),kernelopts(bytesalloc):

g:=plot3d(P,x=-5..5,y=-5..5,orientation=[-47,666,-47],
          axes=normal,labels=[x,y,z]):

PLOT3D(ANIMATE(seq([GRID(op([1,1..2],g),op([1,3],g)),
                           remove(type,[op(g)],
                                  specfunc(anything,{GRID,ORIENTATION}))[],
                           ORIENTATION(A,45,45)],
                    A=0..360,360.0/300)));

time()-st,kernelopts(bytesalloc)-ba;

                                0.046, 1179432                            

Unfortunately, control over the orientation is missing from Plot Components, otherwise such an "animation" could be programmed into a Button. That might be a nice functionality improvement, although it wouldn't be very nice unless accompanied by a way to export all a Plot Component's views to GIF (or mpeg!).

The above example produces animations each of 300 frames. Here's a 60-frame version:

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