9
/21
Mean Value
In 2D
\(\displaystyle \omega_i = \frac{\tan(\alpha_{i-1}/2)+\tan(\alpha_i/2)}{\|p_i-p\|} \)
Michael S. Floater. Mean value coordinates. CAGD, 2003
In 3D
\(\displaystyle \omega_i=\frac{n_i \cdot m}{n_i \cdot (p_i-v)}\)
\(\displaystyle m=\frac{1}{2} \sum_i \theta_i\,n_i\)
Michael S. Floater, Géza Kos, Martin Reimers. Mean value coordinates in 3D. CAGD, 2005
Tao Ju, Scott Schaefer, Joe Warren. Mean Value Coordinates for Closed Triangular Meshes. SIGGRAPH 2005