tNormal</code> function.  However, these expressions
    become uncomfortably large.  For the scenario demonstrated above, 
    where the tangent expression consists of 65 lines of R code, 
    the unit tangent expression is 193 lines of R code and the unit normal
    expression is 4,458 lines of R code.  
    Consequently, the implementation
    in the 'vwline' package only uses the R expressions that were generated for
    X-spline tangents and then divides by the tangent lengths and performs
    a 90 deg