# G2 Continuity in Bezier Curve?

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Is it reasonable to achieve? Can it be done with a cubic curve while still having an arbitrary shape? My math is showing my that G2 continuity between two segments will mean that the first segment constrains the start point and control points of the second segment. What about quartic curves?

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Absolutely. A cubic B-Spline has both G2 and C2 continuity. Check out this document for construction details.

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Aren't G2 and C2 continuity the same thing?

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Quote:
 Original post by halfpowerAren't G2 and C2 continuity the same thing?

Not quite. From Wikipedia:

Quote:
 A curve with Cn parametric continuity usually also has Gn geometric continuity (exceptions include situations arising when using null vectors). Geometric continuity describes the shape of a curve or surface; parametric continuity also describes this, but adds restrictions on the speed with which the parameter traces out the curve.

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Okay, so Cn is a special case of Gn. Is it practical to design G2 continuous bezier curves? It seems like there would be to many contraints on the control points, and that something like hermite interpolation might work better.

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