Constructing spherical curves by interpolation

Based on a composite conical surface patch, we develop new simple methods for up to G2 continuous interpolation of an arbitrary sequence of points on a sphere with a specified tangent direction and curvature vector at every point. The resulting interpolation curve is the intersection of the given sphere and the composite conical surface patch. Unlike some existing methods, introduced into the method are several free parameters that can be used in subsequent interactive modification such that the resulting curve’s shape hits our demand, and the resulting curve can be expressed explicitly. Experiments demonstrate the method is effective and potentially useful in pattern design on sphere, sphere trim, robot, and other industrial and research fields.