Construction of G3 conic spline interpolation

In this paper, a new method to interpolate a sequence of ordered points with conic splines is presented. The degree of continuity at the joints of the resulting splines can reach G3; and the splines are faired by decreasing curvature extrema. The construction is not based on parametrization, but based on basic geometric elements, such as the directions of tangents and chord lengths. The weight of Rational Quadratic Bézier Spline is translated into an equivalent form called chord-tangent ratio. The main idea of the new method is converting the geometric construction problem into a conditional extrema problem through representing the curvature and the curvature changing rate at joints with tangent arguments and chord-tangent ratios, and then deriving the unknowns by solving the conditional extremum problem. Experiments show that splines constructed by the new method perform well not only in terms of continuity, but also in smoothness.