Mahadevan, L.Rycroft, Chris H.Choi, Pui Tung2020-10-162020-052020-05-132020Choi, Pui Tung. 2020. Metamaterials, Morphometrics, Morphogenesis, and Mappings. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37365874In this thesis, we develop mathematical tools to tackle important problems in metamaterials, morphometrics, morphogenesis, and mappings. Specifically, we propose novel methods with a solid theoretical foundation to control the geometry and topology of kirigami and origami metamaterials. We also analyze the growth and form of biological shapes including insect wing and ferret brain using computational geometry. We further propose physically-based methods for producing mappings and deformations of two- and three-dimensional objects and explore their applications to geometry processing, medical imaging and data visualization. Altogether, this thesis brings in new mathematical insights and techniques for advancing our understanding of the physical world, the biological world, and the digital world.application/pdfenapplied mathematicscomputational geometrymathematical modellingmetamaterialskirigamiorigamiquantitative biologymorphometricsmorphogenesismedical imaginggeometry processingscientific computingThesis or Dissertation2020-10-160000-0001-5407-9111