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What I am thinking is -- in pseudo code is:

for each M value in the line starting from 0:

if the M of the event is more then the M of the vertex:

move to the next vert

else:

find the point on the line between vertexes

move to the next vert

else:

find the point on the line between vertexes

add vertexes to my new event line as needed

So, I can find the distance between points no problem with:

d = ((x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2)^(1/2)

But I am not sure how to find the event points with just the M along the line. Can someone please point me to the right path?

Thanks for any help!