1 | %'tps_eval_dxy': calculate the derivatives of thin plate spline (tps) interpolation at a set of points (limited to the 2D case) |
---|

2 | %------------------------------------------------------------------------ |
---|

3 | % function [DMX,DMY] = tps_eval_dxy(dsites,ctrs) |
---|

4 | %------------------------------------------------------------------------ |
---|

5 | % OUTPUT: |
---|

6 | % DMX: Mx(N+3) matrix representing the contributions to the X |
---|

7 | % derivatives at the M sites from unit sources located at each of the N |
---|

8 | % centers, + 3 columns representing the contribution of the linear gradient part. |
---|

9 | % DMY: idem for Y derivatives |
---|

10 | % |
---|

11 | % INPUT: |
---|

12 | % dsites: M x s matrix of interpolation site coordinates (s=space dimension=2 here) |
---|

13 | % ctrs: N x s matrix of centre coordinates (initial data) |
---|

14 | % |
---|

15 | % related functions: |
---|

16 | % tps_coeff, tps_eval |
---|

17 | |
---|

18 | function [DMX,DMY] = tps_eval_dxy(dsites,ctrs) |
---|

19 | %% matrix declarations |
---|

20 | [M,s] = size(dsites); [N,s] = size(ctrs); |
---|

21 | Dsites=zeros(M,N); |
---|

22 | DM = zeros(M,N); |
---|

23 | % DMXY = zeros(M,N+1+s); |
---|

24 | |
---|

25 | %% Accumulate sum of squares of coordinate differences |
---|

26 | % The ndgrid command produces two MxN matrices: |
---|

27 | % Dsites, consisting of N identical columns (each containing |
---|

28 | % the d-th coordinate of the M interpolation sites) |
---|

29 | % Ctrs, consisting of M identical rows (each containing |
---|

30 | % the d-th coordinate of the N centers) |
---|

31 | |
---|

32 | [Dsites,Ctrs] = ndgrid(dsites(:,1),ctrs(:,1));%d coordinates of interpolation points (Dsites) and initial points (Ctrs) |
---|

33 | DX=Dsites-Ctrs;% set of x wise distances between sites and centres |
---|

34 | [Dsites,Ctrs] = ndgrid(dsites(:,2),ctrs(:,2));%d coordinates of interpolation points (Dsites) and initial points (Ctrs) |
---|

35 | DY=Dsites-Ctrs;% set of y wise distances between sites and centres |
---|

36 | DM = DX.*DX + DY.*DY;% add d component squared |
---|

37 | |
---|

38 | %% calculate matrix of tps derivatives |
---|

39 | DM(DM~=0) = log(DM(DM~=0))+1; %=2 log(r)+1 derivative of the tps r^2 log(r) |
---|

40 | |
---|

41 | DMX=[DX.*DM zeros(M,1) ones(M,1) zeros(M,1)];% effect of mean gradient |
---|

42 | DMY=[DY.*DM zeros(M,1) zeros(M,1) ones(M,1)];% effect of mean gradient |
---|

43 | |
---|