I have a 3D data set that I have represented in a graph. Subsequently, I have defined two planes that intersect the obtained figure at x and y, intersecting the data with a minimum value of z. I would like to obtain the graphs of the 2D curves that are projected in the initial figure under the intersection of the planes where in one the minimum of the new curve is the value of x for minimum z and in the other the value of y.
It has been proposed to me to do an interpolation, but it is not possible, since there are multiple data with the same value of x and different y.
The code is:
datos = {{2.3, 4.0, 1.212}, {2.3, 4.1, 1.005}, {2.3, 4.2, 0.88}{2.3,4.3, 0.828}, {2.3, 4.4, 0.8404}, {2.3, 4.5, 0.9091}, {2.3, 4.6, 1.027}, {2.1, 3.8, 1.279}, {2.1, 3.9, 1.0384}, {2.1, 4.0, 0.8887}, {2.1, 4.1, 0.82}, {2.1, 4.15, 0.813}, {2.1, 4.2, 0.8227}, {2.1, 4.3, 0.88844}, {2.1, 4.35, 0.9424}, {2.1, 4.4, 1.009}, {2.1, 4.45, 1.0881}, {2.1, 4.5, 1.178}, {2.2, 4.15, 0.8427}, {2.2, 4.2, 0.8217}, {2.3, 4.2, 0.8799669337077713`}, {2.4, 4.2, 0.9963}, {1.9, 4.2, 1.0199758812690207}, {1.8, 4.2, 1.5233}, {2.0, 4.2, 0.8856076060224287`}, {2.2, 3.8, 1.5646}, {2.2,4.3, 0.82964}, {2.2, 4.35, 0.8564}, {2.2, 4.4, 0.8971}, {2.2, 4.5, 1.016518265050807}, {2.2, 4.6, 1.181428279516127}, {2.0, 4.6, 1.6557430652615237}, {2.0, 4.5, 1.3990826842632}, {2.0, 4.4, 1.1812664252171354}, {2.0, 4.35, 1.0886626776777466}, {2.0, 4.3, 1.007962917838608}, {2.0, 4.2, 0.8856076060224287}, {2.0, 4.15, 0.845922223275994}, {2.0, 4.1, 0.8216559782498348}, {2.0, 4.0, 0.8237258088572351}, {2.0, 3.9, 0.900707731524648}, {2.0, 3.8, 1.0622674412720716}, {1.9, 4.35, 1.3075228435074677}, {1.9, 4.0, 0.8296262380492792}, {1.9, 4.25, 1.1036043673793587}, {2.0, 4.25, 0.9400136847425637}, {2.1, 4.25, 0.8482517670565681}, {2.2, 4.25, 0.8177531605442097}, {2.3, 4.25, 0.8454401150830607}, {1.8, 3.7, 0.9717940708671742}, {1.8, 3.9, 0.9879974492241449}, {1.8, 4, 1.1061402299909153}, {1.8, 4.1, 1.287126422049739}, {2.15, 4.3, 0.8517350572025426}, {2.15, 4.35, 0.8921846379723392}, {2.15, 4.4, 0.9460092405857214}, {2.15, 4.25, 0.8255974118165675}, {2.15, 4.2, 0.8147302884679374}, {2.15, 4.15, 0.8202313032580684}, {2.15, 4.1, 0.8431140507584328}, {1.95, 4., 0.8167974459299269}, {1.95, 3.95, 0.8277902096574934}, {2.05, 4.0, 0.8478984024702497}, {2.05, 4.05, 0.8211048969554303}, {2.05, 4.1, 0.8126006353994589}, {2.05, 4.15, 0.8212675830473939}};
puntoMinimo = First[MinimalBy[datos, Last]];
plano = InfinitePlane[puntoMinimo, {{0, 1, 0}, {0, 0, 1}}];
minx = pchi = Show[
ListPlot3D[datos, InterpolationOrder -> 7, Mesh -> Full],
Graphics3D[{Opacity[0.5], plano}]]
plano = InfinitePlane[puntoMinimo, {{1, 0, 0}, {0, 0, 1}}];
miny = pchi = Show[
ListPlot3D[datos, InterpolationOrder -> 7, Mesh -> Full],
Graphics3D[{Opacity[0.5], plano}]]
Show[miny, minx]