Hi
I have created this table based on some measurements:
t1 = {{59.38367090333329`, 460.6078253228267`,
805.`}, {302.1048538104013`, 461.72905098444113`,
805.`}, {547.9488192843321`, 463.02864907223164`,
805.`}, {796.9515493592204`, 464.5131337727569`,
805.`}, {1044.117089366742`, 466.15405911851997`,
805.`}, {1292.7722081900117`, 467.9731580365426`,
805.`}, {1539.9999999896709`, 469.94915430816627`,
805.`}, {1782.0000034310413`, 472.044969384517`,
805.`}, {105.00000808358162`, 407.8152230640072`,
737.`}, {334.9999977206025`, 408.4233494537993`,
737.`}, {567.057308415782`, 409.3090295247622`,
737.`}, {802.8580589648042`, 410.48897193863866`,
737.`}, {1037.237337936031`, 411.94146966973227`,
737.`}, {1273.0152354809818`, 413.6839584671484`,
737.`}, {1507.2762537494054`, 415.69468027459317`,
737.`}, {1739.3711147816339`, 417.9614994255005`,
737.`}, {142.9271728348491`, 362.98142270385904`,
674.`}, {361.8612671904232`, 363.3384564434068`,
674.`}, {583.9999999985181`, 364.0357576492104`,
674.`}, {809.4574404989381`, 365.08855244434045`,
674.`}, {1033.856348762275`, 366.4815945372955`,
674.`}, {1257.468760868694`, 368.2123237190352`,
674.`}, {1481.4381598843315`, 370.28860344494564`,
674.`}, {1701.6216781072417`, 372.66419814881544`,
674.`}, {178.32843037296428`, 321.1835833890642`,
609.`}, {388.484889977956`, 321.40820726451074`,
609.`}, {600.5275027421441`, 321.9861796041954`,
609.`}, {813.9999990985353`, 322.9245291080465`,
609.`}, {1029.620634032539`, 324.2354156312897`,
609.`}, {1243.9085285088286`, 325.8997356407203`,
609.`}, {1455.7605555458435`, 327.8994299932857`,
609.`}, {1666.292540689685`, 330.23564664161484`,
609.`}, {216.10802746667068`, 275.4492342523438`,
532.`}, {416.6558516294634`, 275.53342140572823`,
532.`}, {617.2563281659676`, 275.9827994908636`,
532.`}, {820.0000037082533`, 276.80806921626737`,
532.`}, {1023.7722087242142`, 278.0134315659101`,
532.`}, {1225.9999999741383`, 279.5822418581565`,
532.`}, {1428.9999989295727`, 281.5303375439369`,
532.`}, {1629.999999430509`, 283.8277373940662`,
532.`}, {248.53724652823018`, 238.54981863976835`,
463.`}, {439.18925324851625`, 238.80612906023327`,
463.`}, {631.3706009533535`, 239.34532844098712`,
463.`}, {825.8134355079837`, 240.17782399245382`,
463.`}, {1020.2897379509311`, 241.29916698823834`,
463.`}, {1213.1360344651664`, 242.69622059131342`,
463.`}, {1407.999741042584`, 244.39626900334042`,
463.`}, {1599.5687709712263`, 246.35014380799012`,
463.`}, {1787.4226509663818`, 248.53819038476695`,
463.`}, {271.0657662088092`, 211.71898893993335`,
408.`}, {456.43050079006576`, 211.7850360139266`,
408.`}, {641.7978478536077`, 212.19359072836482`,
408.`}, {828.8237814737055`, 212.95292078111146`,
408.`}, {1017.3333344006862`, 214.07109991436857`,
408.`}, {1204.5618400789936`, 215.53229717347673`,
408.`}, {1390.9054195586284`, 217.33353626938685`,
408.`}, {1575.2612110747373`, 219.45616854238585`,
408.`}, {1759.7862978322516`, 221.91999800068285`,
408.`}, {292.1315335958507`, 186.860580906395`,
355.`}, {471.0719872967465`, 186.91834150625527`,
355.`}, {651.658904114947`, 187.2968252823938`,
355.`}, {831.6428571428572`, 187.9940941811421`,
355.`}, {1012.1436516800293`, 189.0142565906517`,
355.`}, {1194.6990204908377`, 190.37288999778892`,
355.`}, {1375.9999881839437`, 192.0475161121808`,
355.`}, {1556.257081082542`, 194.03391237137524`,
355.`}, {1732.999677302721`, 196.2927518829849`,
355.`}, {316.46464970605615`, 157.9294056863523`,
288.`}, {487.67430489981774`, 157.97024516892282`,
288.`}, {661.0000002430351`, 158.3268201771229`,
288.`}, {835.3009439778589`, 159.00525027047658`,
288.`}, {1010.7077015613859`, 160.0117893929858`,
288.`}, {1185.0000016603942`, 161.33367302079085`,
288.`}, {1358.145993619255`, 162.96441993659712`,
288.`}, {1531.2029453576997`, 164.91059363852386`,
288.`}, {1702.8944365878237`, 167.15386331428869`,
288.`}, {338.33333451334795`, 132.14915289101697`,
223.`}, {503.2459262374899`, 132.11558120751215`,
223.`}, {671.0004795976905`, 132.40819052501732`,
223.`}, {840.5536375302611`, 133.03880707003157`,
223.`}, {1008.4570411555752`, 133.99504573065738`,
223.`}, {1175.963574325552`, 135.2779906894148`,
223.`}, {1343.5513506868613`, 136.8903742788726`,
223.`}, {1510.0000115678417`, 138.817348670245`,
223.`}, {1674.9999999999918`, 141.0477686774915`,
223.`}, {350.99999380302603`, 116.90822053720866`,
183.`}, {514.0671171059885`, 116.94958608049276`,
183.`}, {676.9667769861602`, 117.28513179747299`,
183.`}, {841.4065832838452`, 117.92210507789608`,
183.`}, {1006.1637933285251`, 118.8608344427576`,
183.`}, {1170.9999969124117`, 120.10104661260853`,
183.`}, {1334.6666665674518`, 121.63036720685305`,
183.`}, {1497.9995757246722`, 123.45250897186023`,
183.`}, {1660.0000007727779`, 125.55181543446656`,
183.`}, {364.7129157021116`, 102.22121405756394`,
142.`}, {523.6258843337882`, 102.20699149959746`,
142.`}, {683.3584648784453`, 102.5035187262144`,
142.`}, {843.0006545034189`, 103.11123631583024`,
142.`}, {1004.2382784506284`, 104.04097907092071`,
142.`}, {1165.0000026512294`, 105.2840959415858`,
142.`}, {1325.5485837220508`, 106.84058825739507`,
142.`}, {1486.2243923682963`, 108.71350297461456`,
142.`}, {1643.7398466655393`, 110.85565093405619`,
142.`}, {375.109403394961`, 88.98827071333633`,
103.`}, {531.2145477204673`, 88.99097566632297`,
103.`}, {688.000036392037`, 89.29811127924387`,
103.`}, {844.8739037593392`, 89.91075882235305`,
103.`}, {1003.0671171395852`, 90.8378475529598`,
103.`}, {1158.9670988358632`, 92.05535977785408`,
103.`}, {1316.868292022846`, 93.59597795412076`,
103.`}, {1475.0752419264852`, 95.44991694512463`,
103.`}, {1629.138732798296`, 97.55384189474498`,
103.`}, {384.6394986714535`, 79.623859374394`,
74.`}, {537.354005992903`, 79.6358542340854`,
74.`}, {691.8007090754759`, 79.93754807064624`,
74.`}, {846.7639291247217`, 80.5329091391809`,
74.`}, {1001.6954882282583`, 81.42120556164625`,
74.`}, {1156.5889867600415`, 82.60220284883054`,
74.`}, {1312.3711148995847`, 84.08538390189248`,
74.`}, {1466.0000058498538`, 85.83820360292621`,
74.`}, {1620.5773498531064`, 87.89263846120302`,
74.`}, {395.6905989158953`, 65.59518831071114`,
30.`}, {546.905419535318`, 65.66473219542159`,
30.`}, {698.3506406256911`, 66.01366071117941`,
30.`}, {847.6932719721631`, 66.63144260934908`,
30.`}, {1000.8047566046254`, 67.54697432996589`,
30.`}, {1152.6010754848905`, 68.73664705295923`,
30.`}, {1303.0146371379062`, 70.19244633900956`,
30.`}, {1453.6976229284448`, 71.92729087564645`,
30.`}, {1606.1682370292974`, 73.96434484848521`, 30.`}};
It looks fairly regular and smooth, even though the grid is not evenly spaced:
I make the Interpolation:
In[309]:= f1 = Interpolation[t1]
During evaluation of In[309]:= Interpolation::udeg: Interpolation on unstructured grids is currently only supported for InterpolationOrder->1 or InterpolationOrder->All. Order will be reduced to 1.
Out[309]= InterpolatingFunction[{{59.38, 1787.42}, {65.6, 472.04}}, <>]
-and get the warning that the Interpolation is reduced to 1. This is fine.
However, it seems that Mathematica makes some bumps in the Interpolating function:
p1 = Plot3D[f1[x, y], {x, 300, 1600}, {y, 320, 375}];
p2 = ListPointPlot3D[t1, AxesLabel -> {"x", "y", "f1"},
PlotStyle -> {Red, PointSize[0.02], Mesh -> None}];
Show[p1, p2]
I don't quite understand why Mathematica makes these fine bumps between the interpolation points. Can anyone help?
Henrik