A Geometric Approach to Bézier Curves
Using techniques from classical geometry we present a purely geometric approach to Bézier curves and B-splines. The approach is based on the intersection of osculating flats: The osculating 1-flat is simply the tangent line, the osculating 2-flat is the osculating plane, etc. The intersection of osculating flats leads to the so-called polar form. We discuss the main properties of the polar form and show how polar forms lead to a simple new labeling scheme for Bézier curves and B-splines.
KeywordsGeometric Approach Polar Form Spline Curve Bezier Curve Quadratic Case
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