%'filter_tps': find the thin plate spline coefficients for interpolation-smoothing %------------------------------------------------------------------------ % [SubRange,NbCentre,Coord_tps,U_tps,V_tps,W_tps,U_smooth,V_smooth,W_smooth,FF] =filter_tps(Coord,U,V,W,SubDomainSize,Rho,Threshold) % % OUTPUT: % SubRange(NbCoord,NbSubdomain,2): range (min, max) of the coordiantes x and y respectively, for each subdomain % NbCentre(NbSubdomain): number of source points for each subdomain % FF: false flags % U_smooth, V_smooth: filtered velocity components at the positions of the initial data % Coord_tps(NbCentre,NbCoord,NbSubdomain): positions of the tps centres % U_tps,V_tps: weight of the tps for each subdomain % to get the interpolated field values, use the function calc_field.m % % INPUT: % coord=[X Y]: matrix whose first column is the x coordinates of the initial data, the second column the y coordiantes % U,V: set of velocity components of the initial data % Rho: smoothing parameter % Threshold: max diff accepted between smoothed and initial data % Subdomain: estimated number of data points in each subdomain %======================================================================= % Copyright 2008-2019, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France % http://www.legi.grenoble-inp.fr % Joel.Sommeria - Joel.Sommeria (A) legi.cnrs.fr % % This file is part of the toolbox UVMAT. % % UVMAT is free software; you can redistribute it and/or modify % it under the terms of the GNU General Public License as published % by the Free Software Foundation; either version 2 of the license, % or (at your option) any later version. % % UVMAT is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License (see LICENSE.txt) for more details. %======================================================================= function [SubRange,NbCentre,Coord_tps,U_tps,V_tps,W_tps,U_smooth,V_smooth,W_smooth,FF] =filter_tps(Coord,U,V,W,SubDomainSize,Rho,Threshold) %% adjust subdomain decomposition warning off NbVec=size(Coord,1);% nbre of vectors in the field to interpolate NbCoord=size(Coord,2);% space dimension MinCoord=min(Coord,[],1);%lower coordinate bounds MaxCoord=max(Coord,[],1);%upper coordinate bounds Range=MaxCoord-MinCoord; AspectRatio=Range(2)/Range(1); NbSubDomain=NbVec/SubDomainSize;% estimated number of subdomains NbSubDomainX=max(floor(sqrt(NbSubDomain/AspectRatio)),1);% estimated number of subdomains in x NbSubDomainY=max(floor(sqrt(NbSubDomain*AspectRatio)),1);% estimated number of subdomains in y NbSubDomain=NbSubDomainX*NbSubDomainY;% new estimated number of subdomains in a matrix shape partition in subdomains Siz(1)=Range(1)/NbSubDomainX;%width of subdomains Siz(2)=Range(2)/NbSubDomainY;%height of subdomains CentreX=linspace(MinCoord(1)+Siz(1)/2,MaxCoord(1)-Siz(1)/2,NbSubDomainX);% X positions of subdomain centres CentreY=linspace(MinCoord(2)+Siz(2)/2,MaxCoord(2)-Siz(2)/2,NbSubDomainY);% Y positions of subdomain centres [CentreX,CentreY]=meshgrid(CentreX,CentreY); CentreX=reshape(CentreX,1,[]);% X positions of subdomain centres CentreY=reshape(CentreY,1,[]);% Y positions of subdomain centres %% smoothing parameter rho=Siz(1)*Siz(2)*Rho/1000;%optimum rho increase as the area of the subdomain (division by 1000 to reach good values with the default GUI input) %% default output SubRange=zeros(NbCoord,2,NbSubDomain);%initialise the boundaries of subdomains Coord_tps=zeros(1,NbCoord,NbSubDomain);% initialize coordinates of interpolated data U_tps=zeros(1,NbSubDomain);% initialize interpolated u component V_tps=zeros(1,NbSubDomain);% initialize interpolated v component NbCentre=zeros(1,NbSubDomain);%number of interpolated field values per subdomain, =0 by default W_tps=[];%default (2 component case) U_smooth=zeros(NbVec,1); % smoothed velocity U at the initial positions V_smooth=zeros(NbVec,1);% smoothed velocity V at the initial positions W_smooth=[];%default (2 component case) FF=zeros(NbVec,1); nb_select=zeros(NbVec,1); check_empty=zeros(1,NbSubDomain); %% calculate tps coeff in each subdomain for isub=1:NbSubDomain isub SubRange(1,:,isub)=[CentreX(isub)-0.55*Siz(1) CentreX(isub)+0.55*Siz(1)];%bounds of subdomain #isub in x coordinate SubRange(2,:,isub)=[CentreY(isub)-0.55*Siz(2) CentreY(isub)+0.55*Siz(2)];%bounds of subdomain #isub in y coordinate ind_sel_previous=[]; ind_sel=0;%initialize set of vector indices in the subdomain %increase iteratively the subdomain if it contains less than SubDomainNbVec/4 source vectors while numel(ind_sel)>numel(ind_sel_previous) ind_sel_previous=ind_sel;% record the set of selected vector indices for next iteration ind_sel=find(Coord(:,1)>=SubRange(1,1,isub) & Coord(:,1)<=SubRange(1,2,isub) & Coord(:,2)>=SubRange(2,1,isub) & Coord(:,2)<=SubRange(2,2,isub)); numel(ind_sel) % if no vector in the subdomain #isub, skip the subdomain if isempty(ind_sel) check_empty(isub)=1; break % go to next subdomain % if too few selected vectors, increase the subrange for next iteration elseif numel(ind_sel)Threshold);%put FF value to 20 to identify the criterium of elimmination ind_ind_sel=find(FF(ind_sel)==0); % select the indices of ind_sel corresponding to the remaining vectors end % if no value exceeds threshold, the result is recorded if isequal(numel(ind_ind_sel),numel(ind_sel)) U_smooth(ind_sel)=U_smooth(ind_sel)+U_smooth_sub; V_smooth(ind_sel)=V_smooth(ind_sel)+V_smooth_sub; NbCentre(isub)=numel(ind_sel); Coord_tps(1:NbCentre(isub),:,isub)=Coord(ind_sel,:); U_tps(1:NbCentre(isub)+3,isub)=U_tps_sub; V_tps(1:NbCentre(isub)+3,isub)=V_tps_sub; nb_select(ind_sel)=nb_select(ind_sel)+1; display(['tps done in subdomain # ' num2str(isub) ' among ' num2str(NbSubDomain)]) break % if too few selected vectors, increase the subrange for next iteration elseif numel(ind_ind_sel)