At this point, it is best to learn by example. Let us focus our effort on studying the three dimensional structure of an exploding star: the supernova remnant Cassiopeia A.
What is so special about Cassiopeia A?
Well, Cassiopeia A (Cas-A for short) is the youngest known supernova remnant in our galaxy. Before that, though, Cas-A was a very massive star that underwent a stellar explosion of epic proportion. This event, known as a supernova, marks the death of a massive star and left behind a corpse (neutron star or a black hole) surrounded by material that was ejected from the star when it exploded.
Cas-A was thought to explode in the 1600s, which may seem like a long time ago, but 400 years is a very short time by astronomy standards (for comparison, the Earth is about 4.54 billion years old!). In addition to being very young, Cas-A is also very close: it is a mere 10000 light years away (again a number that seems large but really isn’t by astronomy standards).
Look at the image of Cassiopeia at the top of this page. The color in the image corresponds to different frequencies of light. Blue and green are taken in the X-rays (green corresponding to a spectral line of iron), while orange and red correspond to the spectral line of silicon and argon respectively. All these elements are material that were ejected from the star when it exploded 400 years ago.
Now, let us focus on argon. What happens when we use our Doppler frequency-to-velocity technique from last page on Cas-A? The following picture shows the velocities of argon in different regions of Cas-A.
Although we are still stuck with a two dimensional picture, we can already see some three dimensional structures. We can see that in some regions the argon is moving away from us, and in other regions they are moving towards us. Further, we know much more than the direction of their motion. We can see that Cas-A is composed of multiple regions: some of which are faster or slower than the other.