In talking with other internal art practitioners, a few have asked about Xingyi (Hsing-i). Questions center around whether it is an internal style in the way Bagua and Tai Chi Chuan are practiced. Some styles practice the form in an extremely hard and fast pattern, and you can see the dominating power Xingyi is known for. Here's one example, but some are even "harder":
The style I am learning is much softer and smoother. The master of our lineage was Li Gui Chang. He practiced his Xingyi in a very smooth way that more resembles Tai Chi Chuan, but the fa jin (explosive power) is still evident. In this way, the mind remains calm, all the elements of internal martial arts are present yet meditative like Tai Chi Chuan.
Here is an example of Pi Chuan (Splitting Fist) in Song-style Xingyi:
And here's a guy doing first the Tuo (Water-skimmer or Alligator form), followed by the Five Elements:
Note the similarities; a solid "root" is hit between transitional movement. But here is the difference from Tai Chi Chuan - Tai Chi sets the root before the technique (punch, elbow, shoulder, etc.) is executed. Xingyi is (as Tim Cartmell described) "mass in motion". It has been described as "controlled falling" into a technique. Done correctly, all of your body mass is added to the technique rather than, for instance, arm strength alone.
I always feel that Tai Chi Chuan balances my Yin and Yang energy the best, Bagua has the most Yoga and spiral energy.
But even performed softly, Xingyi raises more Yang energy and you can see why the Chinese chose it for military and battlefield use.