Interpolate between two 3D lines of scattered points and delete false interpolation results

Hello,

I have two sets of Data. data1(x,y,z) and data2(x,y,z). the following code shows the data and plots it to help visualize it.

I want to interpolate between these two sets and cut away invalid interpolated data points.

the colums are the x,y and z values

data1 = [0	-71.1483620540933	152.800376024537
1	-70.8317205107499	152.648260076248
2	-70.5155832191710	152.495476065991
3	-70.1999540969100	152.342025751664
4	-69.8848370615203	152.187910891162
5	-69.5702360305551	152.033133242383
6	-69.2561549215678	151.877694563222
7	-68.9425976521115	151.721596611576
8	-68.6295681397398	151.564841145341
9	-68.3170703020057	151.407429922414
10	-68.0051080564627	151.249364700691
11	-67.6936853206640	151.090647238068
12	-67.3828060121630	150.931279292442
13	-67.0724740485130	150.771262621710
14	-66.7626933472672	150.610598983767
15	-66.4534678259790	150.449290136510
16	-66.1448014022017	150.287337837835
17	-65.8366979934885	150.124743845640
18	-65.5291615173928	149.961509917820
19	-65.2221958914679	149.797637812271
20	-64.9158050332671	149.633129286890
21	-64.6099928603436	149.467986099574
22	-64.3047632902509	149.302210008219
23	-64.0001202405421	149.135802770721
24	-63.6960676287706	148.968766144977
25	-63.3926093724897	148.801101888882
26	-63.0897493892528	148.632811760334
27	-62.7874915966130	148.463897517229
28	-62.4858399121238	148.294360917464
29	-62.1847982533384	148.124203718933
30	-61.8843705378101	147.953427679535
31	-61.5845606830922	147.782034557166
32	-61.2853726067380	147.610026109721
33	-60.9868102263009	147.437404095097
34	-60.6888774593341	147.264170271191
35	-60.3915782233910	147.090326395899
36	-60.0949164360248	146.915874227118
37	-59.7988960147888	146.740815522743
38	-59.5035208772364	146.565152040672
39	-59.2087949409208	146.388885538800
40	-58.9147221233954	146.212017775024
41	-58.6213063422135	146.034550507241
42	-58.3285515149283	145.856485493346
43	-58.0364615590932	145.677824491237
44	-57.7450403922614	145.498569258809
45	-57.4542919319863	145.318721553960
46	-57.1642200958212	145.138283134585
47	-56.8748288013194	144.957255758580
48	-56.5861219660342	144.775641183843
49	-56.2981035075189	144.593441168270
50	-56.0107773433267	144.410657469756
51	-55.7241473910111	144.227291846199
52	-55.4382175681252	144.043346055495
53	-55.1529917922225	143.858821855540
54	-54.8684739808561	143.673721004230
55	-54.5846680515795	143.488045259463
56	-54.3015779219459	143.301796379134
57	-54.0192075095086	143.114976121140
58	-53.7375607318210	142.927586243377
59	-53.4566415064362	142.739628503741
60	-53.1764537509077	142.551104660130
61	-52.8970013827887	142.362016470439
62	-52.6182883196326	142.172365692565
63	-52.3403184789926	141.982154084404
64	-52.0630957784220	141.791383403853
65	-51.7866241354742	141.600055408808
66	-51.5109074677024	141.408171857165
67	-51.2359496926600	141.215734506821
68	-50.9617547279003	141.022745115672
69	-50.6883264909765	140.829205441614
70	-50.4156688994420	140.635117242545
71	-50.1437858708500	140.440482276360
72	-49.8726813227540	140.245302300956
73	-49.6023591727070	140.049579074229
74	-49.3328233382626	139.853314354076
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76	-48.7961262863945	139.459167465076
77	-48.5289729040773	139.261288812022
78	-48.2626215075758	139.062875697127
79	-47.9970760144434	138.863929878287
80	-47.7323403422332	138.664453113400
81	-47.4684184084987	138.464447160361
82	-47.2053141307930	138.263913777067
83	-46.9430314266696	138.062854721414
84	-46.6815742136817	137.861271751298
85	-46.4209464093826	137.659166624617
86	-46.1611519313257	137.456541099266
87	-45.9021946970641	137.253396933142
88	-45.6440786241513	137.049735884141
89	-45.3868076301406	136.845559710159
90	-45.1303856325851	136.640870169094
91	-44.8748165490383	136.435669018841
92	-44.6201042970535	136.229958017296
93	-44.3662527941839	136.023738922357
94	-44.1132659579829	135.817013491920
95	-43.8611477060037	135.609783483880
96	-43.6099019557997	135.402050656135
97	-43.3595326249242	135.193816766580
98	-43.1100436309304	134.985083573113
99	-42.8614388913717	134.775852833629
100	-42.6137223238013	134.566126306026
101	-42.3668978457727	134.355905748198
102	-42.1209693748390	134.145192918044
103	-41.8759408285536	133.933989573458
104	-41.6318161244698	133.722297472338
105	-41.3885991801410	133.510118372580
106	-41.1462939131202	133.297454032081
107	-40.9049042409611	133.084306208736
108	-40.6644340812167	132.870676660442
109	-40.4248873514404	132.656567145096
110	-40.1862679691855	132.441979420594
111	-39.9485798520054	132.226915244832
112	-39.7118269174532	132.011376375707
113	-39.4760130830824	131.795364571116
114	-39.2411422664462	131.578881588953
115	-39.0072183850980	131.361929187117
116	-38.7742453565910	131.144509123503
117	-38.5422270984785	130.926623156008
118	-38.3111675283139	130.708273042528
119	-38.0810705636504	130.489460540959
120	-37.8519401220413	130.270187409199
121	-37.6237801210400	130.050455405143
122	-37.3965944781998	129.830266286687
123	-37.1703871110739	129.609621811729
124	-36.9451619372157	129.388523738164
125	-36.7209228741785	129.166973823889
126	-36.4976738395155	128.944973826801
127	-36.2754187507801	128.722525504795
128	-36.0541615255256	128.499630615768
129	-35.8339060813053	128.276290917617
130	-35.6146563356724	128.052508168238
131	-35.3964162061804	127.828284125527
132	-35.1791896103824	127.603620547381
133	-34.9629804658319	127.378519191696
134	-34.7477926900820	127.152981816369
135	-34.5336302006861	126.927010179296
136	-34.3204969151976	126.700606038372
137	-34.1083967511696	126.473771151496
138	-33.8973336261556	126.246507276563
139	-33.6873114577088	126.018816171469
140	-33.4783341633825	125.790699594111
141	-33.2704056607301	125.562159302386
142	-33.0635298673047	125.333197054189
143	-32.8577107006598	125.103814607417
144	-32.6529520783487	124.874013719967
145	-32.4492579179246	124.643796149735
146	-32.2466321369408	124.413163654617
147	-32.0450786529507	124.182117992510
148	-31.8446013835075	123.950660921310
149	-31.6452042461646	123.718794198914
150	-31.4468911584752	123.486519583217
151	-31.2496660379927	123.253838832117
152	-31.0535328022704	123.020753703509
153	-30.8584953688615	122.787265955291
154	-30.6645576553195	122.553377345358
155	-30.4717235791975	122.319089631607
156	-30.2799970580488	122.084404571935
157	-30.0893820094269	121.849323924237
158	-29.8998823508849	121.613849446410
159	-29.7115019999763	121.377982896350
160	-29.5242448742542	121.141726031955
161	-29.3381148912721	120.905080611120
162	-29.1531159685831	120.668048391741
163	-28.9692520237406	120.430631131716
164	-28.7865269742980	120.192830588940
165	-28.6049447378085	119.954648521310
166	-28.4245092318254	119.716086686723
167	-28.2452243739020	119.477146843074
168	-28.0670940815916	119.237830748260
169	-27.8901222724476	118.998140160178
170	-27.7143128640232	118.758076836723
171	-27.5396697738717	118.517642535793
172	-27.3661969195465	118.276839015284
173	-27.1938982186008	118.035668033092
174	-27.0227775885880	117.794131347113
175	-26.8528389470613	117.552230715244
176	-26.6840862115740	117.309967895381
177	-26.5165232996796	117.067344645421
178	-26.3501541289312	116.824362723260
179	-26.1849826168821	116.581023886795
180	-26.0210126810857	116.337329893922
181	-25.8582482390953	116.093282502536
182	-25.6966932084642	115.848883470536
183	-25.5363515067457	115.604134555816
184	-25.3772270514930	115.359037516275
185	-25.2193237602595	115.113594109806
186	-25.0626455505985	114.867806094309
187	-24.9071963400634	114.621675227678
188	-24.7529800462073	114.375203267810
189	-24.6000005865836	114.128391972601
190	-24.4482618787456	113.881243099948
191	-24.2977678402466	113.633758407748
192	-24.1485223886400	113.385939653896
193	-24.0005294414789	113.137788596290
194	-23.8537929163168	112.889306992825
195	-23.7083167307069	112.640496601397
196	-23.5641048022025	112.391359179904
197	-23.4211610483570	112.141896486242
198	-23.2794893867236	111.892110278307
199	-23.1390937348556	111.642002313995];

data2 = [0	-71.9804043784130	150.229949132353
1	-71.5071436226507	150.022252001755
2	-71.0346264796777	149.814795110696
3	-70.5628588161522	149.607578417341
4	-70.0918464987326	149.400601879855
5	-69.6215953940771	149.193865456404
6	-69.1521113688439	148.987369105152
7	-68.6834002896913	148.781112784264
8	-68.2154680232776	148.575096451907
9	-67.7483204362610	148.369320066243
10	-67.2819633952999	148.163783585440
11	-66.8164027670525	147.958486967661
12	-66.3516444181770	147.753430171072
13	-65.8876942153318	147.548613153838
14	-65.4245580251750	147.344035874124
15	-64.9622417143650	147.139698290094
16	-64.5007511495600	146.935600359915
17	-64.0400921974184	146.731742041751
18	-63.5802707245983	146.528123293768
19	-63.1212925977580	146.324744074129
20	-62.6631636835558	146.121604341002
21	-62.2058898486500	145.918704052549
22	-61.7494769596988	145.716043166937
23	-61.2939308833605	145.513621642331
24	-60.8392574862935	145.311439436895
25	-60.3854626351558	145.109496508795
26	-59.9325521966058	144.907792816195
27	-59.4805320373019	144.706328317262
28	-59.0294080239021	144.505102970160
29	-58.5791860230649	144.304116733053
30	-58.1298719014484	144.103369564108
31	-57.6814715257110	143.902861421488
32	-57.2339907625109	143.702592263360
33	-56.7874354785064	143.502562047889
34	-56.3418115403558	143.302770733238
35	-55.8971248147172	143.103218277574
36	-55.4533811682490	142.903904639062
37	-55.0105864676095	142.704829775866
38	-54.5687465794569	142.505993646151
39	-54.1278673704495	142.307396208084
40	-53.6879547072456	142.109037419828
41	-53.2490144565033	141.910917239549
42	-52.8110524848811	141.713035625411
43	-52.3740746590371	141.515392535581
44	-51.9380868456297	141.317987928223
45	-51.5030949113170	141.120821761502
46	-51.0691047227574	140.923893993583
47	-50.6361221466091	140.727204582631
48	-50.2041530495304	140.530753486812
49	-49.7732032981796	140.334540664290
50	-49.3432787592150	140.138566073231
51	-48.9143852992947	139.942829671799
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54	-47.6339500603829	139.357049186919
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57	-46.3630057325684	138.773410902629
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60	-45.1017107156244	138.191913689386
61	-44.6834507123528	137.998556883308
62	-44.2662863213666	137.805437806673
63	-43.8502234093240	137.612556417647
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187	-2.70448139520336	115.523725873194
188	-2.47230328497106	115.360225985133
189	-2.24196585262413	115.196958513479
190	-2.01347496482082	115.033923416397
191	-1.78683648821939	114.871120652052
192	-1.56205628947812	114.708550178610
193	-1.33914023525527	114.546211954235
194	-1.11809419220911	114.384105937092
195	-0.898924026997904	114.222232085347
196	-0.681635606279926	114.060590357164
197	-0.466234796713451	113.899180710709
198	-0.252727464956735	113.738003104147
199	-0.0411194776680333	113.577057495643];

plot3(data1(:,1),data1(:,2),data1(:,3)); hold on
plot3(data2(:,1),data2(:,2),data2(:,3)); 
grid on
legend('data1','data2')
hold off

When i tried the interp2 function, it told me that a ndgrid structure is needed, so i checked an found out, that the y- values of the data are not evenly spaced. so i turned to the griddata function.

[xq,yq] = meshgrid(0:200,-80:0);
data_int = griddata([1:200 ;1:200]',[data1(:,2) data2(:,2)],[data1(:,3) data2(:,3)],xq,yq );

contour(xq,yq,data_int); hold on
grid minor
plot3(data1(:,1),data1(:,2),data1(:,3),LineWidth=3); 
plot3(data2(:,1),data2(:,2),data2(:,3),LineWidth=3);
legend('interpolated data', 'data1','data2')
hold off

it does its job but i realized the data below the blue line is not valid, but it still interpolates z values there.

does anyone has a idea how to get rid of this interpolated data?

my guess is that it is a side product of the triangulation. is there maybe a solution by deleting the data below the blue line?

thank you in advance

kind regards

Answer 1

[Githin George]

Hi Lukas,

I understand you would like to cut away the invalid datapoints in the final grid obtained. These datapoints are generated by the contour and can be eliminated by setting those specific values to ‘NaN’. I have added a few lines of code to the script in order to do the same.

[xq,yq] = meshgrid(0:200,-80:0);
data_int = griddata([1:200 ;1:200]',[data1(:,2) data2(:,2)],[data1(:,3) data2(:,3)],xq,yq );

% Code to Remove the invalid data points.
mask = yq < interp1(data1(:,1), data1(:,2), xq);
data_int(mask) = NaN

% Code for plotting
contour(xq,yq,data_int); hold on
grid minor
plot3(data1(:,1),data1(:,2),data1(:,3),LineWidth=3); 
plot3(data2(:,1),data2(:,2),data2(:,3),LineWidth=3);
legend('interpolated data', 'data1','data2')
hold off

I hope this helps.