An Efficient Approach for Solving Mesh Optimization Problems Using Newton’s Method

Algorithm 5

Surface mesh optimization using Newton’s method.

Map the vertex coordinate to a parametric space [3]

while  not converged  do

 Compute the gradient and Hessian of

 if   is not positive definite  then

   Perform Hessian modification

 end if

 Newton direction:

 Update the vertex position: such that satisfies the   

 if   satisfies both the mesh validity and surface constraints  then

   Update the vertex position and map to

 else

  if   does not satisfy the mesh validity  then

    Backtracking Line Search: set ,

    such that satisfies mesh validity

  end if

  if   does not satisfy the surface constraints  then

    Change the parametric space to the neighborhood parametric space

  end if

  Update the vertex position and map to

 end if

end while