wolfram mathematica - Plot3D: Drawing Points at Mesh Intersections -

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i want draw points @ visible mesh intersections, this: 

plot3d[sin[x + y^2], {x, -3, 3}, {y, -2, 2}, mesh -> {1, 4}, boxed -> false]

desired output:

enter image description here

i calculate mesh going be, based on plotrange , mesh cardinality, , draw points there, think there should easier alternative way.

a big plus able chose point color based upon function value. also, labeling points wonderful.

any ideas?

for it's worth, simple solution well. plus easy use same coloring function both surface , points:

g = plot3d[sin[x + y^2], {x, -3, 3}, {y, -2, 2}, mesh -> {1, 4}, boxed -> false, colorfunction -> "rainbow"]; p = listpointplot3d[table[{x, y, sin[x + y^2]}, {x, -3, 3, (3 - (-3))/(1 + 1)}, {y, -2, 2, (2 - (-2))/(4 + 1)}], colorfunction -> "rainbow", plotstyle -> pointsize[large]]; show[g, p]

enter image description here

edit: if want make customized myplot3d, think following should do:

myplot3d[f_, {x_, xmin_, xmax_}, {y_, ymin_, ymax_},     mesh -> {i_integer, j_integer}, opts : optionspattern[]] :=    module[{g =       plot3d[f, {x, xmin, xmax}, {y, ymin, ymax}, mesh -> {i, j},        evaluate@filterrules[{opts}, options[plot3d]]],     stx = (xmax - xmin)/(i + 1),     sty = (ymax - ymin)/(j + 1), pts},    pts = listpointplot3d[      table[{x, y, f}, {x, xmin + stx, xmax - stx, stx}, {y,         ymin + sty, ymax - sty, sty}],       evaluate@filterrules[{opts}, options[listpointplot3d]]];    show[g, pts]];

note options applied both plots, filtered first. removed points on contour of plot. example, 

myplot3d[sin[x + y^2], {x, -3, 3}, {y, -2, 2}, mesh -> {4, 10},   boxed -> false, colorfunction -> "rainbow", axes -> false,   plotstyle -> pointsize[large]]

will give result

enter image description here


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