Research


Our current research interests include:



1. Computational geometry and visualization


Spherical conformal parameterization

Disk conformal parameterization

Rectangular conformal parameterization

Conformal parameterization onto a non-convex domain

Free-boundary conformal parameterization

Conformal and quasi-conformal parameterization of multiply-connected surfaces

Spherical quasi-conformal parameterization

Spherical landmark aligned optimized conformal parameterization

Disk landmark-based quasi-conformal parameterization

Ellipsoidal conformal and quasi-conformal parameterization

Teichmüller extremal map

Higher-dimensional quasi-conformal map

Density-equalizing map (area-preserving/with controllable area distortion)

Optimal mass transport map

Image triangulation and registration

Mappings and deep learning

Surface harmonics

Mappings for astronomy

Mappings for robotics



2. Mathematics of materials


Kirigami metamaterials

Origami metamaterials

Structural assemblies

Floppy networks

Droplets



3. Quantitative biology


Brain morphometry and morphogenesis

Face shape analysis

Shape analysis of carotid artery

Insect wing morphometry

Tooth morphometry

Avian beak morphometry and morphogenesis

Egg patterns

Flower morphology

Bacterial biofilms

Collective dynamics

Quasi-conformal flows for morphodynamics



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