Local Averaging Region General idea:spatial averages over a local neighborhood (x)of a point x. ·x:one mesh vertex .(x):n-ring neighborhoods of mesh vertex or local geodesic balls. The size of the (x):stability and accuracy ·Large size:smooth Small size:accurate for clean mesh data Local Averaging Region • General idea: spatial averages over a local neighborhood Ω(𝒙) of a point 𝒙. • 𝒙: one mesh vertex • Ω(𝒙): n-ring neighborhoods of mesh vertex or local geodesic balls. • The size of the Ω(𝒙): stability and accuracy • Large size: smooth • Small size: accurate for clean mesh data 𝒙