LinePositionToPoint
From Solid Graphics Wiki

The LinePositionToPoint function translates point's position on a line to the point coordinates.
The point position t is translated to point coordinates depending on coordinates of the specified points P0 and P1 defining the line. If the point position value is 0.0 then the function will translate the position into coordinates equal to the specified line point P0. If the point position is 1.0 then the function will translate the position into coordinates equal to the specified line point P1. Other point position values are linearly scaled, value 0.5 is translated into coordinates of a point which lies in equal distance (centre) to points P0 and P1, value 2.0 is translated into coordinates of a point lying from the point P0 in twice of P0 distance to P1 in direction of point P1, and so on.
void LinePositionToPoint ( float t, const float P0[ 3 ], const float P1[ 3 ], float pnt[ 3 ] );
void LinePositionToPoint ( double t, const double P0[ 3 ], const double P1[ 3 ], double pnt[ 3 ] );
Parameters
t  the line point position to translate. 
P0  x,y,z coordinates of first point defining the line 
P1  x,y,z coordinates of second point defining the line 
pnt  the function stores into the variable pointed by pnt the coordinates of the line point specified by point's position t. 
See Also