Title: Processing Geometry: Graphics as a Mathematical Discipline

References: 

http://www-grail.usc.edu/pubs/Des02.pdf

Additional references:

http://www-grail.usc.edu/pubs.html
http://www.multires.caltech.edu/pubs/pubs.htm

Three questions (Pick one and answer it as a one-page essay):

1) Describe some of the potential applications of Digital Geometry in our everyday life.
2) What makes Geometry Processing more challenging than Signal Processing?
3) In what sense is graphics a mathematical discipline?