ListPlot[{{0, 0}, {1, 1}}, Joined -> True, PlotStyle -> Dashed]

Graphics3D[{
   Tube[{{0, 0, 0}, {1, 1, 1}}],
   Tube[BezierCurve[{{0, 0, 0}, {1/2, 1/2, 1}, {1, 1, 1}}]],
   Tube[BSplineCurve[{{0, 0, 0}, {1, 1, 1/2}, {1, 1, 1}}]]
   }]

bsf1 = BezierFunction[{{0, 0, 0}, {1/2, 1/2, 1}, {1, 1, 1}}];
bsf2 = BezierFunction[{{0, 0, 0}, {1, 1, 1/2}, {1, 1, 1}}];

ln1 = Tube[#, .01] & /@ Partition[Table[bsf1[n], {n, 0, 1, .01}], 2][[1 ;; -1 ;; 2]];
ln2 = Tube[#, .01] & /@ Partition[Table[bsf2[n], {n, 0, 1, .03}], 2][[1 ;; -1 ;; 1]];

Graphics3D[{Tube[{{0, 0, 0}, {1, 1, 1}}], ln1, ln2}]