Re: How do I create a circular lamina?

*To*: mathgroup at smc.vnet.net*Subject*: [mg127528] Re: How do I create a circular lamina?*From*: Mark Green <drmoose94 at gmail.com>*Date*: Wed, 1 Aug 2012 04:58:11 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <24471452.12823.1343701025853.JavaMail.root@m06> <000101cd6ec6$4dd495d0$e97dc170$@comcast.net>

Hi, Thanks. I was aware of Presentations but the problem is that I need to be able to make the file into a CDF that I can share with others taking classes. As I understand it, if I used Presentations I would be unable to do this because I would have to include Presentations in the CDF file which I cannot do because it is commercial software. Mark On 31 Jul 2012, at 03:43, "djmpark" <djmpark at comcast.net> wrote: > The Presentations Application has the following routines that might be > useful in this regard: > > Circle3D[position, normal, radius, anglerange:{0,2\[Pi]}, plotoptions] will > draw a circle with the specified position and radius. The orientation of the > circle is given by the normal vector. > > Disk3D[position, normal, radius, anglerange:{0,2\[Pi]}, plotoptions] will > draw a disk with the specified position and radius. The orientation of the > disk is given by the normal vector. > > DrawArrow3DAxes[location, size, headsize:0.35, colors:{Blue,Green,Orange}] > will draw an orthogonal triad of 3D arrows at location, each arrow being of > length size. The arrows will point in the x, y and z directions. > > DrawLabeled3DAxes[{location, axessize, outlinedirective, fillcolor}, > xspecifications, yspecifications, zspecifications] will draw labeled 3D axes > centered at location. The xyz-specifications take the form {label, > labelsize, position, angle, alignment}. The labelsize is the vertical height > of the label expression, position is in terms of the axessize, angle is the > rotation of the reading direction from the x axis, and alignment is the rhs > of an Alignment option. > > AngleDisk3D[center, {vector1, vector2}, radius, opts] will draw a disk > segment of the given radius between vector1 and vector2. Options suitable > for Disk3D may be passed. > > AngleSquare3D[center, {vector1, vector2}, size, sidedirective:EdgeForm[]] > will draw an outlined square of the given size between vector1 and vector2, > which are assumed to be at right angles. > > EulerAngles[matrix, seqstring, opts] will return the Euler angles > corresponding to a sequence of axes rotations specified by seqstring. An > axes sequence of "XYZ" means rotation around the X axis by \[Psi], followed > by rotation about the Y axis by \[Theta], followed by rotation about the Z > axis by \[Phi]. Two sets of rotation angles {\[Psi],\[Theta],\[Phi]} are > returned. The first, canonical set, has -\[Pi]/2 <= \[Theta] <= \[Pi]/2 for > ABC sequences and 0 <= \[Theta] <= \[Pi] for ABA sequences. The second > solution corresponds to the other value of \[Theta] in the range -\[Pi] <= > \[Theta] <= \[Pi]. The answers are in terms of the standard alibi matrices, > unless alias is specified in the EAMode option. If the option EAMatrixTest > is set to True, the routine will check if the matrix is a proper rotation > matrix. If the matrix is degenerate for a given sequence, only \[Psi] > \[PlusMinus] \[Phi] can be determined. In this case, the \[Phi] = 0 solution > is returned, with the corresponding second solution. The option > EADegeneracyCriterion gives the criterion for determining degeneracy. > > RotationAngleAndAxis[rotationmatrix] will generate the axis of rotation and > the associated rotation angle in radians for a 3 x 3 rotation matrix. They > are returned as {angle, axis}. An equally valid answer is obtained by > reversing the signs of both the angle and the axis vector. > > > David Park > djmpark at comcast.net > http://home.comcast.net/~djmpark/index.html > > > > From: drmoose94 at gmail.com [mailto:drmoose94 at gmail.com] > > Hi, > > I want to be able to visualize Euler's Rotation Theorem (I don't think > there's an existing visualization/demonstration of that anywhere?), but in > order to do so I need to draw two intersecting great circles of spheres. > > I can't see any primitive that allows a circular lamina or disk to be drawn > in 3D. There's Disk[] and Circle[] in 2D, but Mathematica won't allow them > to be converted to 3D. I can make one via revolution plotting a constant > but that seems a really ugly hack. > > Is there a good way of getting a circular lamina in 3D/ > >

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