Managed to implement a decent solution thanks to the formula found here: http://www.doc.ic.ac.uk/~dfg/AndysSplineTutorial/Parametrics.html
They also provide a nice Java applet to check out the different parameters.
For my problem I set the t1 value to 0.5 and check if t is above/below this threshold, since I only want to draw one segment of the curve! Works out nicely.