# Paralel bezier curve

If I have a cubic Bezier curve specified by two endpoints and two control points, how can I find an offset curve which is "parallel" to the original at some given distance, after i have determined the other 2 endpoints ? The red dots in the image http://s11.postimg.org/n44nmqzoj/bezier_question.png are the endpoints, and the red squares are the control points of the initial bezier segment. Everything red is known, and i need to find the blue squares, that is, the control points of the second curve, such that the second curve is parallel to the first one(must also take into account that the dimension varies, as if it was below the original bezier, the second curve would be smaller).

I am sorry for the graphics of the image, it has only a illustrative purpose and i am not good at drawing. Thank you for the help!

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Take a look at this: math.stackexchange.com/questions/302076/… – bubba Jul 24 '14 at 13:14
I found another reference which mentions this: the very old (2003) comp.graphics.algorithms FAQ at faqs.org/faqs/graphics/algorithms-faq says in question 4.01: "How do I generate a Bezier curve that is parallel to another Bezier? You can't. The only case where this is possible is when the Bezier can be represented by a straight line. And then the parallel 'Bezier' can also be represented by a straight line." – Zsbán Ambrus Feb 4 at 15:40