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I want to subdivide a cubic Bezier curve at a point which may not be the curve's midpoint. I'm using the plain and slow incremental method to plot the curve from its parametric equations.

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Try Adaptive Subdivision of Bezier Curves. –  lhf Mar 14 '12 at 12:49
    
You can subdivide at any parameter value. See cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/Bezier/… for instance. –  lhf Mar 14 '12 at 12:50
    
What I'm looking for is two sets of parametric equations -- one for each subdivided part of the curve. –  Omer Hassan Mar 14 '12 at 12:53
    
That's what subdivision does: it gives you two new control polygons, from which you get the parametric equations using the Bezier formulation. –  lhf Mar 14 '12 at 13:01
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Thanks for those links guys! I now understand De Casteljau's algorithm. –  Omer Hassan Mar 15 '12 at 18:58
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