1 | % 'DXYMatrix': calculate the matrix of thin-plate shell derivatives |
---|

2 | % |
---|

3 | % function DMXY = DXYMatrix(dsites,ctrs) |
---|

4 | % |
---|

5 | % INPUT: |
---|

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

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

8 | % |
---|

9 | % OUTPUT: |
---|

10 | % DMXY: Mx(N+1+s)xs matrix corresponding to M interpolation sites and |
---|

11 | % N centres, with s=space dimension, DMXY(:,:,k) gives the derivatives |
---|

12 | % along dimension k (=x, y,z) after multiplication by the N+1+s tps sources. |
---|

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

14 | %% matrix declarations |
---|

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

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

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

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

19 | |
---|

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

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

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

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

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

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

26 | |
---|

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

28 | DX=Dsites-Ctrs; |
---|

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

30 | DY=Dsites-Ctrs; |
---|

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

32 | |
---|

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

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

35 | |
---|

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

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

38 | |
---|