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I have a question about "smoothing" the surface created on the basis of a set of points. I would like to get an effect similar to that from the Documentation Center. enter link description here enter image description here

The collection of points that I have:

POINTS={{0.005, 0.938338, 0.005}, {0.00740971, 0.937049, 0.005}, {0.015, 
  0.939004, 0.005}, {0.0181504, 0.940752, 0.005}, {0.025, 0.938894, 
  0.005}, {0.0279244, 0.939622, 0.005}, {0.035, 0.938968, 
  0.005}, {0.0385932, 0.942966, 0.005}, {0.045, 0.934363, 
  0.005}, {0.0475352, 0.937676, 0.005}, {0.0536817, 0.925, 
  0.005}, {0.0493282, 0.896641, 0.005}, {0.055, 0.89578, 
  0.005}, {0.059262, 0.89631, 0.005}, {0.065, 0.895392, 
  0.005}, {0.069092, 0.89546, 0.005}, {0.075, 0.894647, 
  0.005}, {0.0789294, 0.894647, 0.005}, {0.085, 0.894647, 
  0.005}, {0.088916, 0.89458, 0.005}, {0.095, 0.895392, 
  0.005}, {0.0989739, 0.89487, 0.005}, {0.105, 0.89578, 
  0.005}, {0.106318, 0.925, 0.005}, {0.115, 0.934363, 
  0.005}, {0.116374, 0.931869, 0.005}, {0.125, 0.938968, 
  0.005}, {0.127652, 0.93826, 0.005}, {0.135, 0.938894, 
  0.005}, {0.137456, 0.937279, 0.005}, {0.145, 0.939004, 
  0.005}, {0.148084, 0.940418, 0.005}, {0.155, 0.938338, 
  0.005}, {0.005, 0.124057, 0.005}, {0.00970599, 0.125, 
  0.005}, {0.015, 0.139654, 0.005}, {0.019963, 0.149815, 
  0.005}, {0.025, 0.159013, 0.005}, {0.0328758, 0.164379, 
  0.005}, {0.035, 0.164588, 0.005}, {0.0371566, 0.164217, 
  0.005}, {0.045, 0.166939, 0.005}, {0.0537177, 0.168588, 
  0.005}, {0.055, 0.168184, 0.005}, {0.0636262, 0.168131, 
  0.005}, {0.065, 0.167671, 0.005}, {0.0733614, 0.166807, 
  0.005}, {0.075, 0.166333, 0.005}, {0.0832665, 0.166333, 
  0.005}, {0.085, 0.166333, 0.005}, {0.0866386, 0.166807, 
  0.005}, {0.095, 0.167671, 0.005}, {0.103545, 0.167727, 
  0.005}, {0.105, 0.168184, 0.005}, {0.106282, 0.168588, 
  0.005}, {0.115, 0.166939, 0.005}, {0.122843, 0.164217, 
  0.005}, {0.125, 0.164588, 0.005}, {0.131857, 0.159285, 
  0.005}, {0.135, 0.159013, 0.005}, {0.139724, 0.148618, 
  0.005}, {0.145, 0.139654, 0.005}, {0.14703, 0.135151, 
  0.005}, {0.150294, 0.125, 0.005}, {0.154846, 0.124228, 
  0.005}, {0.155, 0.124057, 0.005}, {0.155, 0.0616616, 
  0.005}, {0.15259, 0.0629515, 0.005}, {0.145, 0.0609959, 
  0.005}, {0.14185, 0.059248, 0.005}, {0.135, 0.0611058, 
  0.005}, {0.127652, 0.0617398, 0.005}, {0.125, 0.0610324, 
  0.005}, {0.121407, 0.057034, 0.005}, {0.115, 0.0656366, 
  0.005}, {0.112465, 0.0623241, 0.005}, {0.106318, 0.075, 
  0.005}, {0.110672, 0.103359, 0.005}, {0.105, 0.104219, 
  0.005}, {0.098974, 0.10513, 0.005}, {0.095, 0.104608, 
  0.005}, {0.090908, 0.10454, 0.005}, {0.085, 0.105353, 
  0.005}, {0.0789294, 0.105353, 0.005}, {0.075, 0.105353, 
  0.005}, {0.071084, 0.10542, 0.005}, {0.065, 0.104608, 
  0.005}, {0.061026, 0.10513, 0.005}, {0.055, 0.104219, 
  0.005}, {0.0493282, 0.103359, 0.005}, {0.0536817, 0.075, 
  0.005}, {0.045, 0.0656366, 0.005}, {0.0436262, 0.068131, 
  0.005}, {0.035, 0.0610324, 0.005}, {0.032348, 0.0617398, 
  0.005}, {0.025, 0.0611058, 0.005}, {0.0225443, 0.0627214, 
  0.005}, {0.015, 0.0609959, 0.005}, {0.00740971, 0.0629515, 
  0.005}, {0.005, 0.0616616, 0.005}, {0.155, 0.875943, 
  0.005}, {0.150294, 0.875, 0.005}, {0.145, 0.860346, 
  0.005}, {0.140037, 0.850185, 0.005}, {0.135, 0.840987, 
  0.005}, {0.127124, 0.835621, 0.005}, {0.125, 0.835412, 
  0.005}, {0.116553, 0.832765, 0.005}, {0.115, 0.83306, 
  0.005}, {0.106282, 0.831412, 0.005}, {0.105, 0.831816, 
  0.005}, {0.0963738, 0.831869, 0.005}, {0.095, 0.832329, 
  0.005}, {0.0866386, 0.833193, 0.005}, {0.085, 0.833667, 
  0.005}, {0.0767335, 0.833667, 0.005}, {0.075, 0.833667, 
  0.005}, {0.0665525, 0.832762, 0.005}, {0.065, 0.832329, 
  0.005}, {0.0564545, 0.832273, 0.005}, {0.055, 0.831816, 
  0.005}, {0.0537177, 0.831412, 0.005}, {0.045, 0.83306, 
  0.005}, {0.0371566, 0.835783, 0.005}, {0.035, 0.835412, 
  0.005}, {0.028143, 0.840715, 0.005}, {0.025, 0.840987, 
  0.005}, {0.0202765, 0.851382, 0.005}, {0.015, 0.860346, 
  0.005}, {0.0129697, 0.864849, 0.005}, {0.00970599, 0.875, 
  0.005}, {0.00515436, 0.875772, 0.005}, {0.005, 0.875943, 
  0.005}, {0.0174972, 0.775, 0.005}, {0.021459, 0.757295, 
  0.005}, {0.025, 0.738803, 0.005}, {0.027436, 0.73718, 
  0.005}, {0.035, 0.725131, 0.005}, {0.0350262, 0.725131, 
  0.005}, {0.0352867, 0.725, 0.005}, {0.035, 0.724791, 
  0.005}, {0.0284029, 0.707986, 0.005}, {0.025, 0.70307, 
  0.005}, {0.0214563, 0.675, 0.005}, {0.0225636, 0.662818, 
  0.005}, {0.025, 0.632709, 0.005}, {0.0260742, 0.630371, 
  0.005}, {0.0276731, 0.625, 0.005}, {0.025, 0.611755, 
  0.005}, {0.0232384, 0.575, 0.005}, {0.0234339, 0.567169, 
  0.005}, {0.0243969, 0.525, 0.005}, {0.0243969, 0.478015, 
  0.005}, {0.0243969, 0.475, 0.005}, {0.0243118, 0.471559, 
  0.005}, {0.0232384, 0.425, 0.005}, {0.0235988, 0.417994, 
  0.005}, {0.025, 0.388248, 0.005}, {0.0264328, 0.382164, 
  0.005}, {0.0276738, 0.375, 0.005}, {0.0260746, 0.369627, 
  0.005}, {0.025, 0.367288, 0.005}, {0.0214565, 0.325, 
  0.005}, {0.0228891, 0.314445, 0.005}, {0.025, 0.296931, 
  0.005}, {0.028403, 0.292015, 0.005}, {0.035, 0.275211, 
  0.005}, {0.0350401, 0.2752, 0.005}, {0.0352897, 0.275, 
  0.005}, {0.035, 0.274868, 0.005}, {0.027436, 0.26282, 
  0.005}, {0.025, 0.261197, 0.005}, {0.0174972, 0.225, 
  0.005}, {0.022237, 0.211185, 0.005}, {0.025, 0.201214, 
  0.005}, {0.0298207, 0.199103, 0.005}, {0.035, 0.192407, 
  0.005}, {0.0384929, 0.192465, 0.005}, {0.045, 0.188643, 
  0.005}, {0.0478422, 0.189211, 0.005}, {0.055, 0.186653, 
  0.005}, {0.0574999, 0.187499, 0.005}, {0.065, 0.187584, 
  0.005}, {0.0677151, 0.188575, 0.005}, {0.075, 0.189919, 
  0.005}, {0.0820163, 0.189919, 0.005}, {0.085, 0.189919, 
  0.005}, {0.0877733, 0.188867, 0.005}, {0.095, 0.187584, 
  0.005}, {0.1025, 0.187499, 0.005}, {0.105, 0.186653, 
  0.005}, {0.107231, 0.186155, 0.005}, {0.115, 0.188643, 
  0.005}, {0.117719, 0.188593, 0.005}, {0.125, 0.192407, 
  0.005}, {0.130179, 0.199103, 0.005}, {0.135, 0.201214, 
  0.005}, {0.142503, 0.225, 0.005}, {0.138541, 0.242705, 
  0.005}, {0.135, 0.261197, 0.005}, {0.132564, 0.26282, 
  0.005}, {0.125, 0.274868, 0.005}, {0.124973, 0.274867, 
  0.005}, {0.12471, 0.275, 0.005}, {0.125, 0.275211, 
  0.005}, {0.125064, 0.275319, 0.005}, {0.135, 0.296931, 
  0.005}, {0.138544, 0.325, 0.005}, {0.137436, 0.337181, 
  0.005}, {0.135, 0.367288, 0.005}, {0.133925, 0.369627, 
  0.005}, {0.132326, 0.375, 0.005}, {0.135, 0.388248, 
  0.005}, {0.136762, 0.425, 0.005}, {0.136566, 0.432831, 
  0.005}, {0.135603, 0.475, 0.005}, {0.135603, 0.521985, 
  0.005}, {0.135603, 0.525, 0.005}, {0.135688, 0.528441, 
  0.005}, {0.136762, 0.575, 0.005}, {0.136401, 0.582006, 
  0.005}, {0.135, 0.611755, 0.005}, {0.133568, 0.617839, 
  0.005}, {0.132327, 0.625, 0.005}, {0.135, 0.632709, 
  0.005}, {0.138544, 0.675, 0.005}, {0.137111, 0.685555, 
  0.005}, {0.135, 0.70307, 0.005}, {0.125063, 0.724684, 
  0.005}, {0.125, 0.724791, 0.005}, {0.12496, 0.724802, 
  0.005}, {0.124713, 0.725, 0.005}, {0.125, 0.725131, 
  0.005}, {0.125031, 0.725154, 0.005}, {0.135, 0.738803, 
  0.005}, {0.142503, 0.775, 0.005}, {0.137763, 0.788815, 
  0.005}, {0.135, 0.798786, 0.005}, {0.130179, 0.800897, 
  0.005}, {0.125, 0.807593, 0.005}, {0.121507, 0.807535, 
  0.005}, {0.115, 0.811358, 0.005}, {0.112158, 0.81079, 
  0.005}, {0.105, 0.813348, 0.005}, {0.1025, 0.812501, 0.005}, {0.095,
   0.812416, 0.005}, {0.0922849, 0.811425, 0.005}, {0.085, 0.810081, 
  0.005}, {0.0820163, 0.810081, 0.005}, {0.075, 0.810081, 
  0.005}, {0.0722267, 0.811133, 0.005}, {0.065, 0.812416, 
  0.005}, {0.0626534, 0.813267, 0.005}, {0.055, 0.813348, 
  0.005}, {0.052769, 0.813845, 0.005}, {0.045, 0.811358, 
  0.005}, {0.0422816, 0.811408, 0.005}, {0.035, 0.807593, 
  0.005}, {0.0311259, 0.80563, 0.005}, {0.025, 0.798786, 
  0.005}, {0.0174972, 0.775, 0.005}, {0.005, 0.925, 
  0.015}, {0.00500001, 0.925, 0.015}, {0.015, 0.932794, 
  0.015}, {0.0166613, 0.933306, 0.015}, {0.025, 0.933724, 
  0.015}, {0.0269903, 0.934951, 0.015}, {0.035, 0.933925, 
  0.015}, {0.0372202, 0.936101, 0.015}, {0.045, 0.928613, 
  0.015}, {0.0459607, 0.929803, 0.015}, {0.049095, 0.925, 
  0.015}, {0.0489231, 0.894616, 0.015}, {0.055, 0.894132, 
  0.015}, {0.0589226, 0.894613, 0.015}, {0.065, 0.89363, 
  0.015}, {0.0687272, 0.893636, 0.015}, {0.075, 0.892713, 
  0.015}, {0.0785426, 0.892713, 0.015}, {0.085, 0.892713, 
  0.015}, {0.0885414, 0.892707, 0.015}, {0.095, 0.89363, 
  0.015}, {0.0986317, 0.893159, 0.015}, {0.105, 0.894132, 
  0.015}, {0.110905, 0.925, 0.015}, {0.115, 0.928613, 
  0.015}, {0.11556, 0.927799, 0.015}, {0.125, 0.933925, 
  0.015}, {0.12656, 0.932799, 0.015}, {0.135, 0.933724, 
  0.015}, {0.136638, 0.933191, 0.015}, {0.145, 0.932794, 
  0.015}, {0.146517, 0.932583, 0.015}, {0.155, 0.925, 0.015}, {0.005, 
  0.924999, 0.015}, {0.00729777, 0.886489, 0.015}, {0.0131251, 0.875, 
  0.015}, {0.0136617, 0.868309, 0.015}, {0.015, 0.859975, 
  0.015}, {0.0198621, 0.84931, 0.015}, {0.025, 0.8377, 
  0.015}, {0.0269757, 0.834878, 0.015}, {0.0319563, 0.825, 
  0.015}, {0.025, 0.798062, 0.015}, {0.0199859, 0.775, 
  0.015}, {0.0218332, 0.759166, 0.015}, {0.025, 0.729401, 
  0.015}, {0.0253864, 0.726932, 0.015}, {0.0256277, 0.725, 
  0.015}, {0.025512, 0.72244, 0.015}, {0.025, 0.712795, 
  0.015}, {0.0235316, 0.675, 0.015}, {0.0237064, 0.668532, 
  0.015}, {0.0247499, 0.625, 0.015}, {0.0247409, 0.623705, 
  0.015}, {0.0244305, 0.575, 0.015}, {0.0244429, 0.572215, 
  0.015}, {0.0246277, 0.525, 0.015}, {0.0246277, 0.476862, 
  0.015}, {0.0246277, 0.475, 0.015}, {0.0246192, 0.473096, 
  0.015}, {0.0244305, 0.425, 0.015}, {0.0244496, 0.422248, 
  0.015}, {0.0247497, 0.375, 0.015}, {0.0247113, 0.373556, 
  0.015}, {0.0235316, 0.325, 0.015}, {0.0237834, 0.318917, 
  0.015}, {0.025, 0.287205, 0.015}, {0.025512, 0.27756, 
  0.015}, {0.0256277, 0.275, 0.015}, {0.0253864, 0.273068, 
  0.015}, {0.025, 0.270599, 0.015}, {0.0199859, 0.225, 
  0.015}, {0.022645, 0.213225, 0.015}, {0.025, 0.201937, 
  0.015}, {0.0282724, 0.191362, 0.015}, {0.0319561, 0.175, 
  0.015}, {0.025, 0.1623, 0.015}, {0.0204421, 0.15221, 0.015}, {0.015,
   0.140025, 0.015}, {0.0131251, 0.125, 0.015}, {0.005, 0.0750008, 
  0.015}, {0.005, 0.075, 0.015}, {0.00500001, 0.075, 0.015}, {0.015, 
  0.0672059, 0.015}, {0.0233618, 0.0668089, 0.015}, {0.025, 0.066276, 
  0.015}, {0.0334401, 0.0672005, 0.015}, {0.035, 0.0660751, 
  0.015}, {0.0444402, 0.0722012, 0.015}, {0.045, 0.0713874, 
  0.015}, {0.049095, 0.075, 0.015}, {0.0489231, 0.105384, 
  0.015}, {0.055, 0.105868, 0.015}, {0.0613683, 0.106841, 
  0.015}, {0.065, 0.10637, 0.015}, {0.0714586, 0.107293, 
  0.015}, {0.075, 0.107287, 0.015}, {0.0785426, 0.107287, 
  0.015}, {0.085, 0.107287, 0.015}, {0.0912728, 0.106364, 
  0.015}, {0.095, 0.10637, 0.015}, {0.0986317, 0.106841, 
  0.015}, {0.105, 0.105868, 0.015}, {0.111077, 0.105384, 
  0.015}, {0.110905, 0.075, 0.015}, {0.114039, 0.0701967, 
  0.015}, {0.115, 0.0713874, 0.015}, {0.12278, 0.063899, 
  0.015}, {0.125, 0.0660751, 0.015}, {0.12656, 0.0672005, 
  0.015}, {0.135, 0.066276, 0.015}, {0.143339, 0.0666937, 
  0.015}, {0.145, 0.0672059, 0.015}, {0.155, 0.075, 0.015}, {0.155, 
  0.075, 0.015}, {0.155, 0.924999, 0.015}, {0.146875, 0.875, 
  0.015}, {0.145, 0.859975, 0.015}, {0.139558, 0.84779, 
  0.015}, {0.135, 0.8377, 0.015}, {0.128044, 0.825, 0.015}, {0.131728,
   0.808638, 0.015}, {0.135, 0.798062, 0.015}, {0.137355, 0.786775, 
  0.015}, {0.140014, 0.775, 0.015}, {0.135, 0.729401, 
  0.015}, {0.134372, 0.725, 0.015}, {0.135, 0.712795, 
  0.015}, {0.136217, 0.681083, 0.015}, {0.136468, 0.675, 
  0.015}, {0.135289, 0.626443, 0.015}, {0.13525, 0.625, 
  0.015}, {0.13555, 0.577752, 0.015}, {0.135569, 0.575, 
  0.015}, {0.135381, 0.526904, 0.015}, {0.135372, 0.525, 
  0.015}, {0.135372, 0.523138, 0.015}, {0.135372, 0.475, 
  0.015}, {0.135557, 0.427785, 0.015}, {0.135569, 0.425, 
  0.015}, {0.135259, 0.376296, 0.015}, {0.13525, 0.375, 
  0.015}, {0.136294, 0.331468, 0.015}, {0.136468, 0.325, 
  0.015}, {0.135, 0.287205, 0.015}, {0.134372, 0.275, 
  0.015}, {0.134614, 0.273068, 0.015}, {0.135, 0.270599, 
  0.015}, {0.138167, 0.240834, 0.015}, {0.140014, 0.225, 
  0.015}, {0.135, 0.201937, 0.015}, {0.131728, 0.191362, 
  0.015}, {0.128044, 0.175, 0.015}, {0.133024, 0.165122, 
  0.015}, {0.135, 0.1623, 0.015}, {0.140138, 0.15069, 0.015}, {0.145, 
  0.140025, 0.015}, {0.146338, 0.131691, 0.015}, {0.146875, 0.125, 
  0.015}, {0.152702, 0.113511, 0.015}, {0.155, 0.0750008, 
  0.015}, {0.0222369, 0.925, 0.025}, {0.0191423, 0.895712, 
  0.025}, {0.0198348, 0.875, 0.025}, {0.0211457, 0.855728, 
  0.025}, {0.022355, 0.825, 0.025}, {0.0217008, 0.808504, 
  0.025}, {0.0210809, 0.775, 0.025}, {0.0214448, 0.757224, 
  0.025}, {0.0214509, 0.725, 0.025}, {0.0214204, 0.707102, 
  0.025}, {0.0218008, 0.675, 0.025}, {0.0218703, 0.659351, 
  0.025}, {0.0217461, 0.625, 0.025}, {0.0217633, 0.608817, 
  0.025}, {0.0219595, 0.575, 0.025}, {0.0219686, 0.559843, 
  0.025}, {0.0219199, 0.525, 0.025}, {0.0219199, 0.4904, 
  0.025}, {0.0219199, 0.475, 0.025}, {0.0219108, 0.459554, 
  0.025}, {0.0219595, 0.425, 0.025}, {0.0219428, 0.409714, 
  0.025}, {0.0217461, 0.375, 0.025}, {0.0216752, 0.358376, 
  0.025}, {0.0218008, 0.325, 0.025}, {0.0218296, 0.309148, 
  0.025}, {0.0214509, 0.275, 0.025}, {0.0210873, 0.255437, 
  0.025}, {0.0210809, 0.225, 0.025}, {0.0217993, 0.208997, 
  0.025}, {0.022355, 0.175, 0.025}, {0.0212011, 0.156006, 
  0.025}, {0.0198348, 0.125, 0.025}, {0.0191423, 0.104288, 
  0.025}, {0.0222369, 0.075, 0.025}, {0.0245237, 0.0726185, 
  0.025}, {0.025, 0.0723498, 0.025}, {0.0344091, 0.0720457, 
  0.025}, {0.035, 0.0717341, 0.025}, {0.0415189, 0.075, 
  0.025}, {0.045, 0.090978, 0.025}, {0.0485852, 0.107074, 
  0.025}, {0.055, 0.106981, 0.025}, {0.061574, 0.10787, 
  0.025}, {0.065, 0.107395, 0.025}, {0.0717067, 0.108533, 
  0.025}, {0.075, 0.108639, 0.025}, {0.0782723, 0.108639, 
  0.025}, {0.085, 0.108639, 0.025}, {0.0915007, 0.107503, 
  0.025}, {0.095, 0.107395, 0.025}, {0.098426, 0.10787, 
  0.025}, {0.105, 0.106981, 0.025}, {0.111415, 0.107074, 
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  0.045}, {0.0253259, 0.275, 0.045}, {0.0253449, 0.276724, 
  0.045}, {0.025917, 0.325, 0.045}, {0.0260489, 0.369755, 
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  0.045}, {0.0263088, 0.425, 0.045}, {0.0263174, 0.431587, 
  0.045}, {0.0263571, 0.475, 0.045}, {0.0263571, 0.481785, 
  0.045}, {0.0263571, 0.525, 0.045}, {0.0263482, 0.531741, 
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  0.045}, {0.0254273, 0.775, 0.045}, {0.0254334, 0.777167, 
  0.045}, {0.0263075, 0.825, 0.045}, {0.0274388, 0.837194, 
  0.045}}

When I use the following command, the surface is displayed but it is not "elegant".

ListSurfacePlot3D[POINTS, MaxPlotPoints -> 50]

enter image description here

Does anyone have an idea how can I get a similar effect as in the example? Thank you in advance for your help.

$\endgroup$
  • 1
    $\begingroup$ have you tried ListSurfacePlot3D[POINTS, MaxPlotPoints -> Infinity]? $\endgroup$ – kglr Oct 22 '18 at 20:01
  • $\begingroup$ Yes - unfortunately the surface is not symmetrical then (relative to the vertical plane) which is a problem unfortunately. $\endgroup$ – Arek Oct 22 '18 at 20:05

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