3D plot of concave data set

Question

I have the following data set

regionpt={{1.98549, -9.63663, 0.000175534}, {1.98549, 9.63663, 0.000175534},
{1.88018, -8.53927, 0.0000752711}, {1.88018, 8.53927, 0.0000752711}, 
{1.76991, -7.52454, 0.000259522}, {1.76991, 7.52454, 0.000259522}, 
{1.65418, -6.59002, 0.000428226}, {1.65418, 6.59002, 0.000428226}, 
{1.53246, -5.7332, 0.000239152}, {1.53246, 5.7332, 0.000239152}, 
{1.40408, -4.9514, 0.000916734}, {1.40408, 4.9514, 0.000916734}, 
{1.26824, -4.24183, 0.00135667}, {1.26824, 4.24183, 0.00135667}, 
{1.12393, -3.60157, 0.00115797}, {1.12393, 3.60157, 0.00115797}, 
{0.969869, -3.02756, 0.00179841}, {0.969869, 3.02756, 0.00179841}, 
{0.804309, -2.51667, 0.00323765}, {0.804309, 2.51667, 0.00323765}, 
{0.624759, -2.06561, 0.0039468}, {0.624759, 2.06561, 0.0039468}, 
{0.427375, -1.67104, 0.00303385}, {0.427375, 1.67104, 0.00303385}, 
{0.205564, -1.32947, 0.00235364}, {0.205564, 1.32947, 0.00235364}, 
{-0.0537818, -1.03737, 0.0256703}, {-0.0537818, 1.03737, 0.0256703}, 
{-0.383654, -0.791088, 0.123001}, {-0.383654, 0.791088, 0.123001}, 
{-0.922168, -0.586907, 0.259956}, {-0.922168, 0.586907, 0.259956}}

This data set is extracted from a larger set of which it constitutes the boundary region, that is the region for which the coordinate y gets its minimum and maximum values.

The boundary of this surface is concave, so when I ask Mathematica to ListPlot3D the data above I get the following result

ListPlot3D[regionpt, PlotRange -> All]

Is there a way to have Mathematica remove the artificially added "wings"?

Answer 1

We can create a MeshRegion of your region in this case and an interpolation ifn that can be used in Plot3D:

reg = MeshRegion[regionpt[[All, 1 ;; 2]], Polygon@FindCurvePath[regionpt]];
ifn = Interpolation[regionpt, InterpolationOrder -> 1];

Show[
 Plot3D[ifn[x, y], {x, y} ∈ reg, PlotRange -> All],
 Graphics3D[{Red, PointSize[Medium], Point[regionpt]}]
 ]