deformation – Xiaoxu Meng

Reference
- http://www.pmp-book.org/download/slides/Deformation.pdf
- https://zhuanlan.zhihu.com/p/25804146
Deformation energy
- Geometric energy to strtch and band thin shell from one shape t another as difference between first and second fundamental form
  - First: stretching
  - second: bending
- Approach:
  - Given constraints (handle position / orientation, find surface that min deformation energy)
- Linear Approximation
  - Energy based on fundamental forms in non-linear function of displacements
    - Hard to minimize
  - linear approximation using partial derivatives of displacement function.
    - Assume parameterization of displacement field d(u,v)
    - Bending:
      - linear energy:
        
        laplace = 0 minimize surface area
      - Variational calculus, Euler0-Lagrange equations:
        
        laplace of laplace: make it smooth (the derivative of surface change continuously and is minimized)
      - So, apply bi-laplacian on mesh
- Skeletal animation