X		Y		f

21		45		4.50E-01
21		39		4.50E-01
22		46		4.50E-01
21		31		4.50E-01
21		25		4.50E-01
22		24		0.45
20		46		4.75E-02
21.00		45.2321053	0.45
21		44.8400345	4.50E-01
21		44.6606522	4.50E-01
21		44.3508148	4.50E-01
21		43.7041512	4.50E-01
21		42.4068146	4.50E-01
21		40.670639	4.50E-01
22.007236	39.0728455	4.50E-01
22		46.4337692	4.50E-01
21.9539146	45.6999245	4.50E-01
21.8245602	45.434227	4.50E-01
21.6405773	45.2321053	4.50E-01
21.4521828	45.1080742	4.50E-01
21.2619286	45.0349121	4.50E-01
21.0865746	45.0037537	4.50E-01
21		37.4604988	4.50E-01
21		35.6463318	4.50E-01
21		33.9629593	4.50E-01
21		32.7155151	4.50E-01
21		31.8072739	4.50E-01
21.8686123	30.9459		4.50E-01
21		29.5364704	4.50E-01
21		28.1712418	4.50E-01
21		27.0972404	4.50E-01
21		26.2143383	4.50E-01
21		25.5662842	4.50E-01
21		25.1802902	4.50E-01
21.1502075	24.9886551	4.50E-01
21.3930035	24.9195366	4.50E-01
21.6465435	24.7628765	4.50E-01
21.8392906	24.5436821	4.50E-01
21.9584904	24.2851257	4.50E-01
20.2846222	24.6987381	2.36E-01
20.7573738	24.9701195	3.81E-01
20.9446869	45.0015297	4.27E-01
20.8130207	45.0176353	3.88E-01
20.5383778	45.1129227	3.06E-01
20.3055191	45.2804909	2.30E-01
20.2252884	45.3676834	1.97E-01
20.1977367	45.4030304	1.83E-01
20.1776428	45.4310303	1.74E-01
20.1585255	45.4597015	1.64E-01
20.133955	45.5000343	1.51E-01
20.0563316	45.6691055	1.02E-01
21.8656254	43.0926704	4.50E-01
21.7812004	43.7808723	0.45
21.2216797	44.6766052	0.45
21.3599567	44.9134827	0.45
21.7116566	44.9711227	0.45
21.9401073	44.725956	0.45
21.9212055	45.1420784	0.45
21.5404415	44.9976387	0.45
21.9398232	41.3490257	0.45
21.5472736	44.765831	0.45
21.5179386	44.3136864	0.45
21.1550236	44.9020462	0.45
21.9723816	33.4518661	0.45
21.7236691	31.5223541	0.45
21.9124794	32.3144646	0.45
22.0523205	34.8014908	0.45
21.648035	25.1297436	0.45
21.9322319	24.8675117	0.45
22.021616	25.2606735	0.45
21.9197674	28.7174358	0.45
21.6183758	25.6778183	0.45
21.9837494	27.6462231	0.45
21.7187138	26.7011585	0.45
21.3016033	25.243721	0.45
21.6281891	26.1863308	0.45
20.2532806	26.6364803	3.08E-01
20.4923344	25.6127872	3.28E-01
20.4693279	44.4552307	3.18E-01
20.0611458	45.3602486	1.53E-01
20.0452824	45.3889198	1.46E-01
20.032032	45.3458977	1.48E-01
20.0423832	45.2461967	1.59E-01
20.5548248	44.8751678	3.20E-01
19.9649849	45.3444481	1.35E-01
20.0667		45.4976578	1.36E-01
20.0942211	45.3479156	1.63E-01
20.1328106	45.3750687	1.69E-01
20.0875912	45.3906708	1.56E-01
20.1437569	45.4322205	1.64E-01
20.1575699	45.4060097	1.72E-01
20.1882706	45.3114052	1.91E-01
20.1711597	45.3533287	1.82E-01
20.1582565	45.2417297	1.88E-01
20.1437244	45.2955933	1.80E-01
20.0970211	45.299427	1.68E-01
20.0154095	45.3861847	1.40E-01
20.1118031	45.4503098	1.54E-01
20.0720043	45.4301529	1.47E-01
20.1213436	45.4125175	1.61E-01
20.1378689	45.3304558	1.75E-01
20.065691	45.3312111	1.58E-01
20.0499744	45.3067894	1.56E-01
20.001339	45.3604164	1.40E-01
20.0181427	45.3207512	1.48E-01
19.9863453	45.4271088	1.30E-01
20.1769123	45.3810234	1.80E-01
20.0981846	45.4209137	1.55E-01
20.0322933	45.4392357	1.37E-01
20.1682034	45.022541	2.02E-01
20.7674351	44.7697449	3.86E-01
20.0087757	45.5133514	1.22E-01
21.8234138	43.4367714	4.50E-01
21.1883507	44.7893257	4.50E-01
21.2908173	44.7950439	4.50E-01
21.2574902	44.9077644	4.50E-01
21.4060707	45.0107803	4.50E-01
21.3589249	45.0666351	4.50E-01
21.3109436	44.9741974	4.50E-01
21.825882	44.8485413	4.50E-01
21.9306564	44.9340172	4.50E-01
21.816431	45.0566025	4.50E-01
21.6761169	45.1016159	4.50E-01
21.5905094	45.114872	4.50E-01
21.626049	44.9843826	4.50E-01
21.6808548	40.4831314	4.50E-01
21.5036182	39.8717422	4.50E-01
21.899107	45.5622711	4.50E-01
21.9764881	45.4274445	4.50E-01
21.8728828	45.2881546	4.50E-01
21.7395077	45.3268509	4.50E-01
21.7808914	45.1870918	4.50E-01
21.5498886	45.1647606	4.50E-01
21.4963112	45.0528564	4.50E-01
21.9884109	45.8482018	4.50E-01
22.0248108	45.2813721	4.50E-01
22		46.2168846	4.50E-01
22		46.7226181	4.50E-01
21.6495705	44.0472794	4.50E-01
21.2589684	44.0089188	4.50E-01
21.3906002	43.7425117	4.50E-01
21.8327942	44.256218	4.50E-01
21.9644241	43.9898109	4.50E-01
21.4328117	43.3984108	4.50E-01
21		43.055481	4.50E-01
21.4328117	42.7497406	4.50E-01
21.729023	44.5198212	4.50E-01
21		41.5387268	4.50E-01
21.4699116	41.0098343	4.50E-01
21.4699116	41.8779221	4.50E-01
21.657671	42.2995796	4.50E-01
21		39.8353195	4.50E-01
21.5049343	39.0182343	4.50E-01
21		44.0274811	4.50E-01
21.2589684	44.3322525	4.50E-01
21.1208		44.9528999	4.50E-01
21.0432873	44.9736176	4.50E-01
21.0775108	44.9227676	4.50E-01
21.0433273	45.0009384	4.50E-01
21		44.9717407	4.50E-01
21		44.8917618	4.50E-01
21.0775108	44.8710403	4.50E-01
21.1108398	44.7583199	4.50E-01
21		44.7503433	4.50E-01
21.1108398	44.6686287	4.50E-01
21		44.5057335	4.50E-01
21.1108398	44.51371	4.50E-01
21.3844757	44.7212181	4.50E-01
21.3698082	44.4951477	4.50E-01
21.5326061	44.5397568	4.50E-01
21.4501991	44.9555588	4.50E-01
21.208477	44.9684792	4.50E-01
21.4536152	44.8396568	4.50E-01
21.5438576	44.8817368	4.50E-01
21.6294651	44.8684769	4.50E-01
21.7436905	44.7458954	4.50E-01
21.1749458	45.0154228	4.50E-01
21.8180733	31.9184093	4.50E-01
21.3618355	31.2611771	4.50E-01
21.4351482	30.9864616	4.50E-01
21.7961407	31.234127	4.50E-01
21.4562397	32.5149918	4.50E-01
21.9424305	32.8831635	4.50E-01
21.4861908	33.0836906	4.50E-01
21.6575661	37.5989532	4.50E-01
21.6357422	36.9123688	4.50E-01
22.012352	34.1266785	4.50E-01
21.6357422	36.0052834	4.50E-01
21.5261612	35.2239113	4.50E-01
21.4562397	32.0608673	4.50E-01
21.3618355	31.664814	4.50E-01
21.5036182	38.2666702	4.50E-01
21		38.2302475	4.50E-01
21		31.4036369	4.50E-01
21		32.2613945	4.50E-01
21		36.5534134	4.50E-01
21.4861908	33.7074127	4.50E-01
21		33.3392372	4.50E-01
21		34.8046455	4.50E-01
21.5261612	34.382225	4.50E-01
21.6472893	24.94631	4.50E-01
21.7893867	24.8151932	4.50E-01
21.7901344	24.9986267	4.50E-01
21.9769249	25.0640926	4.50E-01
21.7509575	24.6603508	4.50E-01
21.8857613	24.7055969	4.50E-01
22.0487442	24.4266701	4.50E-01
21.6332054	25.4037819	4.50E-01
21.8348255	25.1952095	4.50E-01
21.8199959	25.4692459	4.50E-01
21.8512306	27.1736908	4.50E-01
21.5205193	25.0246391	4.50E-01
21.5256424	24.8507061	4.50E-01
21.8970222	25.9149132	4.50E-01
21.901825	25.6522789	4.50E-01
21		30.2682343	4.50E-01
21.4343071	30.2411842	4.50E-01
21.9891434	24.5559483	4.50E-01
21.9081402	24.4186687	4.50E-01
21.9895687	24.1440659	4.50E-01
22.035614	24.7178631	4.50E-01
21		25.8903122	4.50E-01
21.3091888	25.6220512	4.50E-01
21.3091888	25.9460793	4.50E-01
21.6734505	26.4437447	4.50E-01
21.3593559	26.4577484	4.50E-01
21.3140945	26.2003345	4.50E-01
21.3593559	26.8992004	4.50E-01
21.4918747	27.3717308	4.50E-01
21.9471931	26.4265823	4.50E-01
21.4598846	29.1269531	4.50E-01
21		28.8538551	4.50E-01
21.4598846	28.4443398	4.50E-01
21.5573349	29.5105209	4.50E-01
22.0172176	29.1010017	4.50E-01
21.9517593	28.1818295	4.50E-01
21		25.0901451	4.50E-01
21.0753174	24.99716	4.50E-01
21.0751038	25.0844727	4.50E-01
21.5497398	29.8366528	4.50E-01
21.3473034	25.0816288	4.50E-01
21.4748192	25.1867332	4.50E-01
21.9840469	30.5413666	4.50E-01
21.2259064	25.116188	4.50E-01
21.2737961	24.9617882	4.50E-01
21.1508026	25.2120056	4.50E-01
21.4599895	25.4607697	4.50E-01
21.1508026	25.4050026	4.50E-01
21		25.3732872	4.50E-01
21.4918747	27.9087334	4.50E-01
21		27.6342411	4.50E-01
21.6232834	25.9320755	4.50E-01
21		26.6557884	4.50E-01
21.9019299	26.1691704	4.50E-01
20.8786869	25.0752048	4.15E-01
20.8777695	24.9925022	4.16E-01
20.7461662	25.5895348	3.88E-01
20.7461662	25.3965378	3.85E-01
20.624855	25.2914543	3.50E-01
20.3884773	25.1557617	2.84E-01
20.3106804	28.1619911	3.39E-01
20.3106804	27.6249905	3.33E-01
20.6266403	26.8668594	3.78E-01
19.9373207	27.3946114	2.73E-01
20.3728065	26.1246338	3.18E-01
20.7461662	25.9135628	3.92E-01
20.3106804	28.8446045	3.46E-01
19.9509277	30.9209423	3.15E-01
19.9627762	30.1110134	3.11E-01
20.6266403	26.4254093	3.73E-01
20.5021496	24.8672638	3.11E-01
20.073885	24.3772411	1.58E-01
20.3318176	33.3557549	3.69E-01
20.0661659	34.2924271	3.40E-01
20.3318176	32.7320328	3.68E-01
20.3318176	32.2779121	3.66E-01
20.0661659	35.1341095	3.40E-01
20.1656075	36.1329689	3.51E-01
20.1656075	37.0400543	3.49E-01
19.9627762	31.2464142	3.19E-01
20.053215	45.3745842	1.50E-01
20.0386581	45.3674088	1.47E-01
20.0465889	45.3530731	1.51E-01
20.6839218	44.9464035	3.55E-01
20.6722183	45.0552483	3.47E-01
20.5466003	44.9940453	3.12E-01
20.2368622	45.151516	2.14E-01
20.2318878	45.2611084	2.08E-01
20.1632309	45.1321335	1.95E-01
20.1003189	45.2439651	1.73E-01
20.1052933	45.1343689	1.81E-01
20.388958	43.6091232	3.25E-01
20.7346649	44.079689	3.90E-01
20.1236229	43.9846649	2.57E-01
20.0209389	41.2530212	3.06E-01
20.0209389	42.121109	2.94E-01
20.9723434	44.920784	4.41E-01
20.8785858	45.0073967	4.08E-01
20.9065094	44.928833	4.22E-01
19.9554901	45.5235062	1.12E-01
19.9975605	45.4702301	1.26E-01
20.2067795	45.3395462	1.94E-01
20.1982231	45.3605042	1.89E-01
20.1797142	45.3323669	1.87E-01
20.2468948	45.295948	2.10E-01
20.2641106	45.3228989	2.13E-01
20.9723434	44.9725075	4.39E-01
20.1135159	45.3614922	1.66E-01
20.1102009	45.3828697	1.62E-01
20.0909061	45.3692932	1.59E-01
20.1506634	45.4191132	1.68E-01
20.1676064	45.4185181	1.73E-01
20.1606998	45.4316254	1.69E-01
20.1548615	45.3780441	1.74E-01
20.1519852	45.3641968	1.75E-01
20.174036	45.3671761	1.81E-01
20.6183815	44.6124878	3.50E-01
20.7346649	44.5579414	3.83E-01
20.8837166	44.7151985	4.20E-01
20.8837166	44.8048897	4.19E-01
20.7902279	44.893692	3.88E-01
20.3532906	45.0677338	2.51E-01
20.4159069	45.1883125	2.67E-01
20.1003265	45.498848	1.43E-01
20.0912037	45.5827599	1.24E-01
20.0615158	45.5833817	1.18E-01
20.1509895	45.2686615	1.84E-01
20.1203728	45.2975082	1.74E-01
20.1276398	45.2705765	1.78E-01
19.975666	45.3857803	1.32E-01
19.9831619	45.3524323	1.37E-01
19.9938431	45.3937607	1.35E-01
20.972332	45.0003815	4.36E-01
20.0892525	45.4739838	1.44E-01
20.0693512	45.4639053	1.41E-01
20.0919037	45.4402313	1.50E-01
20.1679611	45.445282	1.69E-01
20.1511421	45.445961	1.64E-01
20.2010994	45.3743515	1.88E-01
20.2113152	45.3852043	1.90E-01
20.1873245	45.3920288	1.82E-01
20.1672401	45.3935165	1.76E-01
20.1451912	45.3905411	1.70E-01
20.1776543	45.4045181	1.77E-01
20.1875687	45.4169426	1.79E-01
20.1270771	45.3937912	1.65E-01
20.1394577	45.4092636	1.66E-01
20.1732635	45.2765656	1.90E-01
20.122879	45.475174	1.53E-01
20.1165733	45.4314117	1.58E-01
20.1325493	45.4223709	1.63E-01
20.1277809	45.4412651	1.59E-01
20.1545143	45.3418922	1.79E-01
20.1630707	45.3209305	1.83E-01
20.0928879	45.4057922	1.55E-01
20.1044674	45.4015961	1.59E-01
20.1097641	45.4167175	1.58E-01
20.1353397	45.3527603	1.72E-01
20.0743675	45.3754578	1.55E-01
20.0664368	45.3897934	1.51E-01
20.1659966	45.3034973	1.86E-01
20.1407967	45.3130264	1.78E-01
20.0956211	45.3236694	1.65E-01
20.117445	45.3149414	1.72E-01
20.116045	45.3391876	1.69E-01
20.1049938	45.4356117	1.54E-01
20.0850945	45.4255333	1.51E-01
20.0799561	45.3395615	1.60E-01
20.0776825	45.3540802	1.58E-01
20.0634193	45.3457298	1.56E-01
20.0734978	45.3031082	1.62E-01
20.081356	45.3153191	1.63E-01
20.0578327	45.3190002	1.57E-01
20.0697021	45.2728119	1.64E-01
20.0387878	45.4140778	1.42E-01
20.0586433	45.4095383	1.47E-01
20.0521488	45.4346924	1.42E-01
20.0797977	45.4104118	1.52E-01
20.0238514	45.4127121	1.39E-01
20.0303459	45.3875504	1.43E-01
20.0488625	45.3385544	1.53E-01
20.0166855	45.353157	1.44E-01
20.0237198	45.3660431	1.44E-01
20.0083733	45.3732986	1.40E-01
19.9915638	45.3325996	1.41E-01
20.003685	45.2953224	1.47E-01
20.030262	45.283474	1.54E-01
20.0097408	45.3405838	1.44E-01
20.0410042	45.3263435	1.52E-01
20.0250874	45.3333244	1.48E-01
20.0340576	45.3137703	1.52E-01
20.0461788	45.2764931	1.58E-01
20.0093193	45.4331741	1.33E-01
20.0008774	45.4066467	1.35E-01
19.9978905	45.1328735	1.56E-01
19.9792671	45.6013794	1.03E-01
20.014183	45.8321724	7.03E-02
19.9511013	45.7668304	7.62E-02
20.0205345	45.4762955	1.30E-01
20.361515	44.9488525	2.58E-01
20.7346649	44.4030228	3.86E-01
20.3187656	44.738884	2.58E-01
20.5120773	44.6651993	3.18E-01
20		46.7143631	2.23E-02
20.1351643	45.4550056	1.59E-01
20.1460018	45.4797249	1.58E-01
19.9496841	44.5972824	1.83E-01
20.388958	42.9604568	3.38E-01
20.0494957	45.4684448	1.36E-01
20.0377388	45.5055046	1.28E-01
20.661129	44.8224564	3.54E-01
20.0325546	45.5912285	1.12E-01


clear all;
close all;
clc;

load disppoints.txt;                            %load the X Y and displacement points.
data = disppoints;
numpoints = length(data);                       % Number of Points
dim=2;                                          % 2 Dimensional data
global RBFtype
RBFtype=5
datapoints= [data(:,1) data(:,2)];              % Data points x y in [-3,3]*[-3,3] for interpolation
disp=data(:,3);                                 % Data to be approximated
coefficients= rbfsolver(datapoints,disp);       % RBF coefficients
approxdisp=rbfeval(datapoints, datapoints, coefficients) % Approximated displacements



function coeff = rbfsolver(xypoints, values)
[numpoints,dim] = size(xypoints);
coeff=(rbf(pointstodistances(xypoints))+eye(numpoints,numpoints))\values; % RBF constant = inverse(rbf)*given values (displacements)
end



function distancematrix = pointstodistances(xypoints)
[numpoints,dim]=size(xypoints)                          % Get dimensions
distances = xypoints*xypoints' ;                        %ineer product between points
lsq=diag(distances);                                    %vectoe of squares of points
distancematrix = sqrt(repmat(lsq,1,numpoints)+repmat(lsq,1,numpoints)'-2*distances); % distance matrix r of Radial Basis Function
end



function y  = rbf(r)

global RBFtype;     % 1=Multiquadric, 2=Guassian, 3=Inverse Multiquadric, 4=Wendland, 5= Thin Plate Spline
if RBFtype ==1
    y=(1+r.*r).^(1/2);          % Multiquadric
    return;
end
if RBFtype ==2
    y=exp(-r.*r);               %Guassian
    return;
end
if RBFtype ==3
    y=(1+r.*r).^(-1/2);         % inverse multiquadric
    return;
end
if RBFtype ==4              
    y=(1+4*r).*max(0,(1-r)).^4; %Wendland 
    return;
end
if RBFtype ==5
    y = r.*r.*log(r+eps);       %TPS
    return;
end


error('NOT a Radial Basis Function')




function values = rbfeval(evalpoints, datapoints, coeff)

[numeval, evaldim] = size(evalpoints);
[numdata, datadim] = size(datapoints);
[numcoeff, coeffdim] = size(coeff);

if evaldim~=datadim
    error('Dimension is not equal')
end
if numcoeff~=numdata
    error('datapoints and coefficients much match')
end
if coeffdim~=1
    error('Coefficients must be a vector')
end
evalsquares = sum(evalpoints.^2,2);
datasquares = sum(datapoints.^2,2);

phimat= rbf(sqrt(repmat(evalsquares,1,numdata)+repmat(datasquares,1,numeval)'-2*evalpoints*datapoints'));

values = phimat*coeff;
end