This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: B ezier Curves James Keesling 1 Definition of a B ezier Curve A B ezier curve is a parametric curve that is used widely in computer graphics. They were originally used as an aid in design in the automobile industry. The B ezier curves are based on the Bernstein polynomials. The Bernstein polynomial of degree n is given by the following formula. B n ( t ) = n X i =0 n i t i (1 t ) n i In themselves the Bernstein polynomials are not very interesting. They are just the binomial expansion of ( t + (1 t )) n 1. However, for B ezier curves we will restrict t to the interval [0 , 1]. Then the individual terms in the expansion will be nonnegative and will sum to one. We will use them to produce a convex combination of points in R k . Let { P ,P 1 ,...,P n } be a set of n + 1 points in R k . The B ezier curve with control points { P ,P 1 ,...,P n } is given by the following formula. B ( t ) = n X i =0 n i t i (1 t ) n i P i The curve begins at the point P and ends at point P n , but will not generally go through the other control points. The curve will lie in the convex hull of determined by the setthe other control points....
View
Full
Document
This note was uploaded on 11/12/2011 for the course STA 3032 taught by Professor Kyung during the Summer '08 term at University of Florida.
 Summer '08
 Kyung
 Statistics

Click to edit the document details