I want to divide a surface f[x_, y_] := (1.4025 - (-0.2 + x)^2 - (-0.2 + y)^2)^0.5 + 0.15 into meshes corresponding to the region x0y
f[x_, y_] := (1.4025 - (-0.2 + x)^2 - (-0.2 + y)^2)^0.5 + 0.15;
X[x_, y_] := Evaluate@D[f[x, y], x]
Y[x_, y_] := Evaluate@D[f[x, y], y]
GetRegion[n_,
m_] := {TwoD$Points = Outer[List, #, #] &@Subdivide[0, 1, n];
TwoD$Points = (Flatten[#, 1][[{1, 2, 4, 3}]] & /@
Flatten[Partition[TwoD$Points, {2, 2}, 1], 1]);
TwoD$Points[[m]]} // Flatten[#, 1] &
GetLine[n_,
m_] := {TwoD$Points = Outer[List, #, #] &@Subdivide[0, 1, n];
TwoD$Points = (Flatten[#, 1][[{1, 2, 4, 3}]] & /@
Flatten[Partition[TwoD$Points, {2, 2}, 1], 1]);
ThreeD$Points = Map[Flatten[{#, 0}] &, TwoD$Points, {2}][[m]];
List[ThreeD$Points,
Apply[{#1, #2, f[#1, #2]} &, ThreeD$Points, 2]] // Transpose} //
Flatten[#, 1] &
NormalLine[n_,
m_] := {TwoD$Points = Outer[List, #, #] &@Subdivide[0, 1, n];
TwoD$Points = (Flatten[#, 1][[{1, 2, 4, 3}]] & /@
Flatten[Partition[TwoD$Points, {2, 2}, 1], 1]);
ThreeD$Points = Map[Flatten[{#, 0}] &, TwoD$Points, {2}][[m]];
List[ThreeD$Points,
Apply[{#1, #2, f[#1, #2]} &, ThreeD$Points, 2]] // Transpose} //
Flatten[#, 1] &
Manipulate[region = GetRegion[n, m];
Show[Plot3D[{f[x, y], 0}, {x, 0, 1}, {y, 0, 1},
MeshFunctions -> {#1 &, #2 &}, Mesh -> n - 1,
MeshShading ->
ReplacePart[
ConstantArray[Automatic, {n, n}], {Mod[m, n, 1], Ceiling[m/n]} ->
Red], PlotRange -> {{0, 1.6}, {-0.2, 1.4}, {0, 1.6}},
BoxRatios -> Automatic],
Plot3D[X[(region[[1, 1]] + region[[3, 1]])/
2, (region[[1, 2]] + region[[2, 2]])/
2] (x - (region[[1, 1]] + region[[3, 1]])/2) +
Y[(region[[1, 1]] + region[[3, 1]])/
2, (region[[1, 2]] + region[[2, 2]])/
2] (y - (region[[1, 2]] + region[[2, 2]])/2) +
f[(region[[1, 1]] + region[[3, 1]])/
2, (region[[1, 2]] + region[[2, 2]])/2], {x, region[[1, 1]],
region[[3, 1]]}, {y, region[[1, 2]], region[[2, 2]]},
Mesh -> None, PlotStyle -> {Blue, Opacity[0.6]}],
Graphics3D[{Thick, Dashed, Pink, Line@GetLine[n, m]}]], {{n, 4,
"Divide quantity"}, 3, 30, 1,
Appearance -> "Open"}, {{m, 1, "Division number of sub region j"},
1, n^2, 1, Appearance -> "Open"}]
But I can't match the jth red mesh in xoy with the surface f[x_, y_] := (1.4025 - (-0.2 + x)^2 - (-0.2 + y)^2)^0.5 + 0.15.What should I do to make the corresponding part of the surface red?
