# Bezier Curve

## Description

“Bezier Curve” is a method of generating smooth curve in computer graphics. Note that it is a method of curve representation, and not a curve in the usual sense in math contexts.

The Bezier Curve method is named after the engineer Pierre Bézier.

Given 4 points P0, P1, P2, P3, find a parametric formula in polynomial such that it passes P0 with tangent vector[P0,P1], and passes P2 with tangent vector[P3,P2].

Solution, written in complex number notation:

z[t]=(1-t)^3*P0 + 3*t(1-t)^2*P1 + 3*t^2(1-t)*P2 + t^3*P3

We verify that

z[0]==P0, z'[0]==3*(P1-P0) z[1]=P2, z'[1]==3*(P2-P3)

see Bézier curve

See: Websites on Plane Curves, Plane Curves Books.

2006-05

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