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Explanation of the parameters in the line intersection code

I am trying to understand a C code that moves the mesh nodes for each time step and i am totally struck on the parameters t1 and t2 please help me sorting this out. So here is what the function gets ...
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Ray-Triangle Intersection Detection using Barycentric Coordinates

I am attempting to convert the algorithm from http://www.cbloom.com/3d/techdocs/fast_ray_tri.txt to java code, but my solution does not function correctly. The only intentional change I made was for ...