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Jan M.
Jan M.
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Jan M.
Jan M.
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Say I have a set of oriented points at locations $\vec{v_i}$ with each some direction $\vec{n_i}$, in practice they represent a surface with its normals. How would I calculate the divergence of this vector field? Standard finite-difference methods would obviously not work because there is no grid.

Can I perhaps assume a grid and use nearest neighbours to infer the vector field at each point? The discretized vector field would then have at each point a weighted average of nearby points. This would then allow me to use standard FD-methods to calculate the divergence at each gridpoint. Is this a common method, or are there better methods?

Say I have a set of oriented points at locations $\vec{v_i}$ with each some direction $\vec{n_i}$, in practice they represent a surface with its normals. How would I calculate the divergence of this vector field? Standard finite-difference methods would obviously not work because there is no grid.

Can I perhaps assume a grid and use nearest neighbours to infer the vector field at each point? The discretized vector field would then have at each point a weighted average of nearby points. This would then allow me to use standard FD-methods to calculate the divergence at each gridpoint.

Say I have a set of oriented points at locations $\vec{v_i}$ with each some direction $\vec{n_i}$, in practice they represent a surface with its normals. How would I calculate the divergence of this vector field? Standard finite-difference methods would obviously not work because there is no grid.

Can I perhaps assume a grid and use nearest neighbours to infer the vector field at each point? The discretized vector field would then have at each point a weighted average of nearby points. This would then allow me to use standard FD-methods to calculate the divergence at each gridpoint. Is this a common method, or are there better methods?

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Jan M.
Jan M.
  • 143
  • 5

Numerically calculating the divergence of a set of oriented points

Say I have a set of oriented points at locations $\vec{v_i}$ with each some direction $\vec{n_i}$, in practice they represent a surface with its normals. How would I calculate the divergence of this vector field? Standard finite-difference methods would obviously not work because there is no grid.

Can I perhaps assume a grid and use nearest neighbours to infer the vector field at each point? The discretized vector field would then have at each point a weighted average of nearby points. This would then allow me to use standard FD-methods to calculate the divergence at each gridpoint.