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I need to calculate the error resulting from approximating a parametric cubic Bezier curve using a quadratic B-spline.

For approximating the cubic Bezier we're using a quadratic B-spline with a control polygon made of the two anchor points of the cubic Bezier and the control points of the quadratic bezier curves that we are obtained when the DeCasteljou's subdivision algorithm is used two divide the cubic Bezier curve in t=0.5.

This technique was extracted from page 83 of the pdf found at:

http://docs.google.com/viewer?a=v&q=cache:OOe-uigEyVEJ:citeseerx.ist.psu.edu/viewdoc/download%3Fdoi%3D10.1.1.94.5523%26rep%3Drep1%26type%3Dpdf+font+rasterization+the+state+of+the+art&hl=en&gl=us&pid=bl&srcid=ADGEEShF6wZ4rNyfKMI5hGOR10_Q98t3SN6HHdKw-K6NO-GDjJTHaOb9D84Ie-7xyef2O6GmObBg7fFAd32Ln_sOMCUjDSiMUeHCbWw7hSUiqqP50tx6ql9yuDjfEkSE4WbC4WjLNAOF&sig=AHIEtbR7JvsphPDM_KuNTFFesq2OiK4qug

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I'm not sure this question should be closed, although it would benefit from the OP actually writing out some of the details (e.g. DeCasteljou's subdivision algorithm). Certainly splines seem a perfectly reasonable topic for MO, mathematically speaking – Yemon Choi Apr 22 2011 at 7:17

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