computational geometry - Produce one smooth curve on one triangle mesh -

computational geometry - Produce one smooth curve on one triangle mesh -

i hope 1 smooth curve on 1 triangle mesh. 1 path on mesh @ first. path consists of vertices of mesh. can see path image below.

each 1 greenish dot indicates 1 vertex on mesh. method using fit 1 smooth curve using vertices , project smooth curve on mesh. project smooth curve, find closest point on mesh each vertex of smooth curve.

however curve not on mesh because intersects mesh. realize vertices need move along border of triangle shared previous vertex.

in view, there 2 kinds of methods produce smooth curve. first kind move points of curve along mesh create curve smooth. sec kind fit points obtain 1 smooth curve , project smooth curve on mesh,but projection should complex.

can give me advices or links websites or papers? in advance.

computational-geometry mesh curve-fitting smooth