Sequence of data in 3D, joining the points

Question

Let me just first say I am not actually trying to find a function for these set of data. All I am doing is joining the points to make a line.

Basically let's say I have some data, which I cleverly will call/name them as 'data' in Mathematica.

data:= {{1,0,0},{2,4,7},{2,6,7},{0,0,23}}

Now plotting them. (FYI, these data points are randomlly chosen)

ListPointPlot3D[data]

I should get a plot, but of course they are all disconnected. What I want to do is to join them. Unfortunately 'Joined -> True' does not exists in ListPointPlot3D, so I do not know how to join them

Any ideas?

EDIT

At the moment, I have a recursion. I will just show you the table

For instance

Table[x[n, t], {n, 1, 10}] 

prints out a list of 10 data points in 3D. It will not work with Graphics3D

EDIT

I will write out exactly what I have

x[1, t_] := {0,0,0};

A[t_] := {{1, -t, 1}, {t, 2, 0}, {0, 0,t}}

B[t_] := Inverse[A[t]];

x[n_Integer, t_] /; n > 0 := B[t].x[n - 1, t];

Table[x[n, t], {n, 1, 10}]

I want to plot the points and join them in a curve. If possilbe I would even like to manipulate the plot. The range for $t \in [0,1]$

Everything updated

Answer 1

t := RandomReal[]
x[n_, t_] := Sin@t
data = Table[{n, #, x[n, #]} &[t], {n, 1, 10}];

Graphics3D[{Line@data, PointSize[Large], Point@data}, 
           PlotRange -> ({Min@# - 1, Max@# + 1} & /@ Transpose@data), Axes -> True]

Edit

Also something like this shall do

f = Interpolation[#, InterpolationOrder -> 1] & /@ Transpose@data;
Show[{ParametricPlot3D[Through[f[t]], {t, 1, Length@data}], 
      Graphics3D[{PointSize[Large], Point@data}]}]

Answer 2

Of course the Graphics3D approach in belisarius' answer is very general and should always work. But maybe you want to stick with ListPointPlot3D for some reason. Then you could use Show to combine the isolated points with a plot of the linear Interpolation between the points:

data = {{1, 0, 0}, {2, 4, 7}, {2, 6, 7}, {0, 0, 23}}

(* ==> {{1, 0, 0}, {2, 4, 7}, {2, 6, 7}, {0, 0, 23}} *)

iData = 
  Interpolation[Transpose[{Range[Length[#]], #} &@data], 
   InterpolationOrder -> 1];

Show[
 ListPointPlot3D[data], ParametricPlot3D[iData[t], {t, 1, 4}]
 ]

It's worth mentioning here that Show always uses the options of the plot that comes first in the list, unless you specify additional options to Show (such as BoxRatios, if desired). You can also control the style of the points and curve separately using the usual options.