gistfile1.txt

% DEFORM_SURFACE_TPS - Given a set of control points and mapping
% coefficients, compute a deformed surface f(S) using a thin plate spline
% radial basis function phi(r) as shown in [1].
%
% Usage:    [fX, fY, fZ] = deform_surface_tps(X, Y, Z, control_points, ...
%           mapping_coeffs, poly_coeffs)
%
% Arguments:
%           X, Y, Z        - h by w matrices of X, Y, Z components of the
%                            surface.
%           control_points - p by 3 vector of control points. Same as
%                            vector c in [1]. 
%           mapping_coeffs - p by 3 vector of weights of the basis
%                            functions. Same as vector w in [1].
%           poly_coeffs    - 4 by 3 vector of weights of the polynomial.
%                            Same as vector v in [1].
%
% Returns:
%           fX, fY, fZ     - h by w vectors of X, Y, Z compoments of the
%                            deformed surface.
%
% References:
%           1. http://en.wikipedia.org/wiki/Polyharmonic_spline
%
% Author:
% Daeyun Shin
% dshin11@illinois.edu  daeyunshin.com
%
% April 2014