Triangulations of our faces form the basis for morphing the triangles from one to the other over the course of the warping my face to my good friend Peter's.
Some people's faces are completely reshaped when morphing their face to the mean's geometry!
Above is my face caricatured to varying degrees of how a Dane would look. Notice my nose gets more pointed and my mouth begins to shrink and move down a bit.
We see above that morphing both appearance and shape together results in smoother more believable images. The appearnace and shape only morphs above look unrealistic whereas the transitions in the gif above and the midway face are smooth and believable.