A biarc joins two points with two circular arcs, following a prescribed tangent vector at each endpoint. The arcs meet with continuous position and tangent direction, producing a smooth transition. section 5.3.1
Constructing a biarc turns the geometric requirements into a solvable system:
- Represent the two arc centers and radii as six unknowns. section 5.3.1
- Place each center along the endpoint’s rotated, normalized tangent direction, scaled by its radius. section 5.3.1
- Require the circle centers’ distance to equal the sum of the radii, so the arcs touch smoothly. section 5.3.1
- Use symbolic solving to obtain the centers and radii, while avoiding unnecessary quadratic constraints that can multiply solutions. section 5.3.1
Choosing biarcs in a composite curve
Combine biarcs with arc-and-segment pieces: use the arc-and-segment option when endpoint tangents are less than 90 degrees apart, and use the biarc otherwise. The resulting pieces can form complex curves and support equal parameter intervals that correspond to equal travel, making constant-speed motion straightforward. section 5.3.3
