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Re: Re: A question about a sphere

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  • Subject: [mg107110] Re: [mg107097] Re: A question about a sphere
  • From: "David Park" <djmpark at>
  • Date: Wed, 3 Feb 2010 06:08:54 -0500 (EST)
  • References: <hk6cu2$m1a$> <25869435.1265112391516.JavaMail.root@n11>

Presentations does have a 3-dimensional circle, Circle3D in which one
specifies the origin, the normal, the radius and the angle range. Here is my
previous example using Circle3D and RotateOp to rotate about the z axis to
each position longitude position. (RotateOp is a postfix version of Rotate
which is convenient if one is rotating a large piece of graphics


sphere[r_, \[Phi]_, \[Theta]_] := 
 r {Cos[\[Phi]] Cos[\[Theta]], Cos[\[Phi]] Sin[\[Theta]], Sin[\[Phi]]} 
primeMeridian = 
  Circle3D[{0, 0, 0}, {0, 1, 0}, 1, {-\[Pi]/2, \[Pi]/2}]; 

 {(* Draw the sphere *)
  Opacity[.5], Orange,
  (* Draw 5 lines of latitude *)
  Opacity[1], Black,
  Table[Circle3D[{0, 0, Sin[lat]}, {0, 0, 1}, 
    Cos[lat]], {lat, {80 \[Degree], 40 \[Degree], 
     0, -40 \[Degree], -80 \[Degree]}}],
  (* Draw lines of longitude *)
  Table[primeMeridian // RotateOp[long, {0, 0, 1}], {long, 0, 
    288 \[Degree], 72 \[Degree]}]},
 NeutralLighting[0, .5, .1, 0 \[Degree], -30 \[Degree]],
 Boxed -> False,
 ImageSize -> 400] 

David Park
djmpark at  

From: dh [mailto:dh at] 

in mathematica there is no 3 dim circle. Therefore, we have to 
approximate the circles using small lines. Here is an example for what 
you asked for:
lat[phi_] :=
   Line[Table[{Cos[phi] Sin[th], Cos[phi] Cos[th], Sin[phi]}, {th, 0,
      2 Pi, Pi/20}]];
long[phi_] :=
   Line[Table[{Cos[th] Sin[phi], Cos[th] Cos[phi],
      Sin[th]}, {th, -Pi/2, Pi/2, Pi/20}]];
Graphics3D[{Sphere[{0, 0, 0}, 1]
   , Table[lat[th], {th, -Pi/2, Pi/2, Pi/6}]
   , Table[long[th], {th, -Pi, Pi, Pi/2.5}]
Note, as the circles are on the sphere it is not clear if they are 
visible or not. For certain positions the circles are not alsways drawn 
fully. To prevent this, you may either draw the circles a little bit 
larger than the spehre or use Opacity.

Marwa Abd El-Wahaab wrote:
> Dear Sir,
> I am a Mathematica 7 user.
> I have a question :
> I want to draw a sphere, then draw 5 circles on this sphere like
> *latitudes*and draw 5 lines on this sphere like
> *longitudes*.
> I need your help.
> Thanks in advance
> Marwa Ali

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