Abstract
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.
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© 1992 EUROGRAPHICS The European Association for Computer Graphics
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Seidel, HP. (1992). A Geometric Approach to Bézier Curves. In: Falcidieno, B., Herman, I., Pienovi, C. (eds) Computer Graphics and Mathematics. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77586-4_3
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DOI: https://doi.org/10.1007/978-3-642-77586-4_3
Publisher Name: Springer, Berlin, Heidelberg
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