Question

have two line segment in the space, how to construct a surface with two line segment as the boundary?

Answer 1

You may do this parametrically.

Supose your two segments described by:

{s1(t)} = t {a1} + {b1}   (0 <= t <= 1)

{s2(t)} = t {a2} + {b2}   (0 <= t <= 1)

where the {} indicates vector quantities, {a},{b} constants.

Then, for any t you have two points in space, one in each segment.

The straight line between them can be described by:

{r(v)} = ({s2(t)} - {s1(t)}) v + {s1(t)}  (0 <= v <= 1 )  

We are almost there. Now we write the function describing the surface, replacing s1 and s2 by their values:

{K(v,t)} = t v ( {a2} - {a1} )+ v ({b2} - {b1})  + t {a1} + {b1}  (0<= t,v <=1)

HTH!

Edit

An Example:

a1 = {1, 1, 1};
b1 = {0, 0, 0};
a2 = {1, 1, 0};
b2 = {0, 0, 0};

Show[ParametricPlot3D[
  t v a1 (a2 - a1) + v (b2 - b1) + t a1 + b1, {t, 0, 1}, {v, 0, 1}, 
  AxesLabel -> {"x", "y", "z"}], 
   Graphics3D[{Thick, Red, Line[{b1, a1 + b1}]}], 
   Graphics3D[{Thick, Red, Line[{b2, a2 + b2}]}]]

Another example, showing a non-flat surface:

a1 = {1, 1, 1};
b1 = {0, 0, 1};
a2 = {1, 0, 0};
b2 = {0, 1, 0};