You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: inflate.m
    path of file: ./repos/gptoolbox/mesh
    
    the code of the file until where you have to start completion: function [VH] = inflate(varargin)
  %INFLATE a planar 2D mesh into a 3D "pillow" with the original silhouette 
  %
  % [VH] = inflate(V,F,'ParameterName',ParameterValue,...)
  %
  % Inputs:
  %   V  #V by 2 list of mesh vertices
  %   F  #F by 3 list of triangle indices into
  %  Optional:
  %    'Method' followed by one of the following: {'BiXYThenBaran'}
  %      'Baran' Follow "Notes on Inflating Curves" [Baran and Lehtinen 2009].
  %        Leave X and Y coordinates as is and solve Δ(z^2) = f, that is solve
  %        Δw = f and set z = sqrt(w), 
  %      'BiXYHarmonic', solve Δ²XY = 0 with implicit neumann conditions and
  %        simultaneous solve Δz = f, 
  %      'BiXYThenBaran', solve Δ²XY = 0 with implicit neumann conditions,
  %        stop, recompute cotmatrix and solve z as in 'Baran', 
  %      'MixedFEM' solve Δ²XYZ = 0 with ∂XY/∂n = 0 and ∂Z/∂n = f, 
  %      'Repousse' follow "Repousse: Automatic Inflation of 2D Artwork"

    
function [VH] = inflate(varargin)
  %INFLATE a planar 2D mesh into a 3D "pillow" with the original silhouette 
  %
  % [VH] = inflate(V,F,'ParameterName',ParameterValue,...)
  %
  % Inputs:
  %   V  #V by 2 list of mesh vertices
  %   F  #F by 3 list of triangle indices into
  %  Optional:
  %    'Method' followed by one of the following: {'BiXYThenBaran'}
  %      'Baran' Follow "Notes on Inflating Curves" [Baran and Lehtinen 2009].
  %        Leave X and Y coordinates as is and solve Δ(z^2) = f, that is solve
  %        Δw = f and set z = sqrt(w), 
  %      'BiXYHarmonic', solve Δ²XY = 0 with implicit neumann conditions and
  %        simultaneous solve Δz = f, 
  %      'BiXYThenBaran', solve Δ²XY = 0 with implicit neumann conditions,
  %        stop, recompute cotmatrix and solve z as in 'Baran', 
  %      'MixedFEM' solve Δ²XYZ = 0 with ∂XY/∂n = 0 and ∂Z/∂n = f, 
  %      'Repousse' follow "Repousse: Automatic Inflation of 2D Artwork"
  %        [Joshi and Carr 2008], that is solve Δ²XY = 0 with ∂XYZ/∂n = 0, but
  %        explicitly treat ΔZ|∂Ω = f/2
  %    'PuffFactor' followed by a scale value corresponding to different amount of
  %      "puffiness". See f value in 'Method' descriptions {f=-8}
  % Outputs:
  %   VH  #V by 3 list of new "height" field vertices, but note that depend