Lets say V1-V2 is 1 unit long and V2-V3 is 1 unit long, if D is say 4; then the new location for the camera starting in line V1-V2 is past V3; so you have to place in on the line V3-V4 - but it might also be past V4 - understand.
Thanks. I have implemented as per your suggestion. At each frame equal amount of distance v*t is travelled. Checking each time among which vertices pair the center and cameral position lie and giving new positions for each. I think this makes travel same amount of distance and result is more uniform.
Glad to hear you are making progress.