Bézier

Also called bezier, bézier curve, cubic bezier, bezier handle

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A polynomial curve defined by control points and evaluated by repeated linear interpolation between them — de Casteljau's algorithm. It passes through its first and last points, is merely pulled toward the rest, and never leaves their convex hull. Cubic, four points, is the standard: the lowest degree admitting an inflection.

A cubic Bézier curve with its four control points joined by a dashed polygon, the curve touching the first and last points and pulled toward but not through the two interior ones.

In practice

'Bézier handle' is the vector-tool name for the two interior control points of a cubic. TrueType outlines are quadratic; PostScript and OpenType CFF are cubic, which is why converting between them is lossy.

Not to be confused with

NURBSA curve or surface defined by control points, a degree, a knot vector, and a weight per point. Non-uniform knots allow unequal spans and local sharpening; rational weights let it represent conics exactly — a true circle, which no polynomial Bézier can produce. That exactness is why it became the CAD standard.

Origin

Pierre Bézier published the method at Renault in the 1960s for car body panels. Paul de Casteljau had derived it earlier at Citroën, but Citroën kept it a trade secret — the name follows publication, not invention.

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In practice

Not to be confused with

Origin

Related

How this term connects

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