Biarc
A biarc is a smooth curve formed from two circular arcs. In order to make the biarc smooth (G1 continuous), the two arcs should have the same tangent at the connecting point where they meet.
Biarcs are commonly used in geometric modeling and computer graphics. They can be used to approximate splines and other plane curves by placing the two outer endpoints of the biarc along the curve to be approximated, with a tangent that matches the curve, and then choosing a middle point that best fits the curve. This choice of three points and two tangents determines a unique pair of circular arcs, and the locus of middle points for which these two arcs form a biarc is itself a circular arc. In particular, to approximate a Bézier curve in this way, the middle point of the biarc should be chosen as the incenter of the triangle formed by the two endpoints of the Bézier curve and the point where their two tangents meet. More generally, one can approximate a curve by a smooth sequence of biarcs; using more biarcs in the sequence will in general improve the approximation's closeness to the original curve.
References
- Bolton, K. M. (1975). "Biarc curves". Computer-Aided Design. 7 (2): 89–92.
- Nutbourne, A. W.; Martin, R. R. (1988). Differential geometry applied to curve and surface design. Vol.1: Foundations. Ellis Horwood. ISBN 013211822X.
- Kurnosenko, A. I. (2013). "Biarcs and bilens". Computer-Aided Geometric Design. 30 (3): 310–330.