Constructing Bézier curves

Linear curves

Animation of a beeline Bézier curve, t in 0,1

The t in the action for a beeline Bézier ambit can be anticipation of as anecdotic how far B(t) is from P0 to P1. For archetype if t=0.25, B(t) is one division of the way from point P0 to P1. As t varies from 0 to 1, B(t) describes a beeline band from P0 to P1.

editQuadratic curves

For boxlike Bézier curves one can assemble average credibility Q0 and Q1 such that as t varies from 0 to 1:

Point Q0 varies from P0 to P1 and describes a beeline Bézier curve.

Point Q1 varies from P1 to P2 and describes a beeline Bézier curve.

Point B(t) varies from Q0 to Q1 and describes a boxlike Bézier curve.

Construction of a boxlike Bézier curve Animation of a boxlike Bézier curve, t in 0,1

editHigher-order curves

For higher-order curves one needs appropriately added average points. For cubic curves one can assemble average credibility Q0, Q1, and Q2 that call beeline Bézier curves, and credibility R0 & R1 that call boxlike Bézier curves:

Construction of a cubic Bézier curve Animation of a cubic Bézier curve, t in 0,1

For fourth-order curves one can assemble average credibility Q0, Q1, Q2 & Q3 that call beeline Bézier curves, credibility R0, R1 & R2 that call boxlike Bézier curves, and credibility S0 & S1 that call cubic Bézier curves:

Construction of a quartic Bézier curve Animation of a quartic Bézier curve, t in 0,1

For fifth-order curves, one can assemble agnate average points.