Density

• \(\rho_i\): Replace A(p) as \(\rho\)

• • \(\rho(p_i) = \sum_j \rho(p_j) \, m_j / \rho_j \; W_h(\|p_i-p_j\|)\)

• • \(\Rightarrow\)
    \(\displaystyle \rho_i = \sum_j m_j \, W_h(\|p_i-p_j\|)\)

• Choice of weight functions

• • Use a smooth polynomial:
  • ex. \(W_h^{poly6}(d)=\frac{315}{64\,\pi\,h^9}\;(h^2-d^2)^3\;\;\;\;0\leq d \leq h\)