How to create 2D (3D) animation in Wolfram Mathematica with the camera following the object?

Question

I have a graphical object which is moving along a trajectory. How can I make the camera follow the object?

Answer 1

Since the question asks about 2D, here's how you can emulate a camera in 2D Graphics.

First, let's get the stackoverflow favicon.ico:

so = First@Import["http://sstatic.net/stackoverflow/img/favicon.ico"]

Well put this on top of some overlapping circles and make the "camera" follow the icon around by adjusting the PlotRange

Manipulate[Graphics[{
   Table[Circle[{j, 0}, i], {i, 0, 1, .1}, {j, {-.5, .5}}],
   Inset[so, pos, {0, 0}, .2]},
  PlotRange -> {{-.5, .5}, {-.5, .5}} + pos],
 {{pos, {0, 0}, ""}, {-1.4, -1}, {1.4, 1}, ControlPlacement -> Left}]

To show how it works (with out putting the above into Mathematica), we need to animate it. Originally I chose a variable step random walk drunk = Accumulate[RandomReal[{-.1, .1}, {200, 2}]] but it was a unpredictable! So instead, we'll make the icon follow the ABC logo

drunk = Table[{1.5 Sin[t], Cos[3 t]}, {t, 0, 2 Pi, .1}];
Animate[Graphics[{
   Table[Circle[{j, 0}, i], {i, 0, 1, .1}, {j, {-.5, .5}}],
   Inset[so, drunk[[pos]], {0, 0}, .2]},
  PlotRange -> {{-.5, .5}, {-.5, .5}} + drunk[[pos]]],
 {pos, 1, Length[drunk], 1}]

Answer 2

Let's draw a planet and its satellite, with the camera following the moon from a view directed toward the Earth. For example:

a = {-3.5, 3.5}; 
Animate[
 Show[
      Graphics3D[
           Sphere[3 {Cos@t, Sin@t, 0}, .5],  
                 ViewPoint -> 3.5 {Cos@t, Sin@t, 0},     
                 SphericalRegion -> True, 
                 PlotRange -> {a, a, a}, Axes -> False, Boxed -> False],
      myEarth], 
{t, 0, 2 Pi}]  

Where myEarth is another 3D Graphics (for reference).

Static vertical view:

a = {-3.5, 3.5}; 
Animate[
 Show[
      Graphics3D[
           Sphere[3 {Cos@t, Sin@t, 0}, .5],  
                 ViewPoint -> 3.5 {0,0,1},     
                 SphericalRegion -> True, 
                 PlotRange -> {a, a, a}, Axes -> False, Boxed -> False],
      myEarth], 
{t, 0, 2 Pi}]  

The trick is SphericalRegion -> True, without it the image perspective "moves" from frame to frame.

Edit

With two static objects: