Let $f(x,y) = \frac{x^2}{2}+\frac{y^2}{2}$ and $M:=\{(x,y)\in\mathbb R^2 | \frac{x^2}{2}+y^2\leq1\}$
I'd like to plot $f, M$ and the points $p_1=(0,0,1), \ p_2=(\sqrt{2},0,1), \ p_3=(-\sqrt{2},0,1)$
What I got:
u1 = Plot3D[x^2/2 + y^2/2, {x, -2, 2}, {y, -2, 2}]
u2 = RegionPlot3D[x^2/2 + y^2/2 <= 1, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]
Show[u1,u2]
I read a bit in the docs and that I can use Point[] for it. But I just can't figure out how this works. Also, I'd like to make them very bright. Any help is appreciated.
Graphics3D + Point– Kuba Jan 19 '17 at 09:53Show[Plot3D[(* stuff *)], RegionPlot3D[(* stuff *)], Graphics3D[{Green, Point[(* stuff *)]}]]– J. M.'s missing motivation Jan 19 '17 at 09:57u3 = ListPointPlot3D[{{0, 0, 1}, {Sqrt[2], 0, 1}, {-Sqrt[2], 0, 1}}, PlotStyle -> PointSize[0.3]];oru3 = Graphics3D[{PointSize[0.5], Point[{{0, 0, 1}, {Sqrt[2], 0, 1}, {-Sqrt[2], 0, 1}}]}];, but considering the fact that the points have to be large to be visible, you might want to consider an implementation withSphere. – Feyre Jan 19 '17 at 10:01