How to draw a guide line in 3-dimensional space by Mathematca?

Question

I want to use mma to draw this picture: original picture.

Here is my code:

Show[Graphics3D[{Opacity[0.5], LightBlue, InfinitePlane[{0, 0, 0}, {{0, 0, 1}, {1, 0, 0}}]}, Axes -> True], 
 Plot3D[Labeled[x^2 + y^2, "surface z=f(x,y)"], {x, -1, 1}, {y, -1, 1}, PlotStyle -> Directive[Gray, Opacity[0.4]], Mesh -> None ], 
 ParametricPlot3D[{x, 0, x^2}, {x, -1, 1}] , 
 ParametricPlot3D[Labeled[{x, 0, 0}, "tangent line, slope  \!\(\*SubscriptBox[\(f\), \\(x\)]\)(\!\(\*SubscriptBox[\(x\), \(0\)]\),\!\(\*SubscriptBox[\(y\), \\(0\)]\))"], {x, -1, 1}, PlotStyle -> {Black}], 
 ParametricPlot3D[{x, 0, -1.5}, {x, -1, 1}, PlotStyle -> {LightBlue, Opacity[1]}], AxesLabel -> {x, y, z}, 
 BoxRatios -> {1, 2, 1}, Boxed -> False, Axes -> False]

And here is the result: my result

As you can see, the biggest differences between them are the guide lines. In original picture, there are guide lines connecting the graph and the label. I've searched "guide line" and "inspector" in documentation, but both get no results. How can I draw these lines in mma?

Answer 1

You could use "Callout" instead of "Labeled". Here is an example:

Show[
 Graphics3D[{Opacity[0.5], LightBlue, 
   InfinitePlane[{0, 0, 0}, {{0, 0, 1}, {1, 0, 0}}]}, Axes -> True],
 Plot3D[Callout[x^2 + y^2, "surface z=f(x,y)", Above], {x, -1, 
   1}, {y, -1, 1}, PlotStyle -> Directive[Gray, Opacity[0.4]], 
  Mesh -> None], 
 ParametricPlot3D[Callout[{x, 0, x^2}, "{x,0,x^2}"], {x, -1, 1}], 
 ParametricPlot3D[
  Callout[{x, 0, 0}, 
   "tangent line, slope  \!\(\*SubscriptBox[\(f\), \(x\)]\), \
\!\(\*SubscriptBox[\(x\), \(0\)]\)", LeaderSize -> 10, 
   Appearance -> "Frame", CalloutMarker -> "Arrow"], {x, -1, 1}, 
  PlotStyle -> {Black}], 
 ParametricPlot3D[{x, 0, -1.5}, {x, -1, 1}, 
  PlotStyle -> {LightBlue, Opacity[1]}], AxesLabel -> {x, y, z}, 
 BoxRatios -> {1, 2, 1}, Boxed -> False, Axes -> False]