Presentation
$G^2$ Interpolating Spline with Local Maximum Curvature
DescriptionWe present \(G^2\) continuous splines formulated through spline blending, which interpolate a given list of control points. These splines attain local maximum curvatures at the control points, possess local support, and do not require global optimization. They ensure the absence of cusps, self-intersections, and, importantly, intersections between adjacent segments, which has not guaranteed by previous blending curve methods. We propose the use of quadratic \Bezier splines, where each spline passes through only one control point, as our interpolation functions, and quartic \Bezier splines as our blending functions. Based on these, we propose an algorithm that generates curves without requiring global optimization. Moreover, by simply adjusting the curvature of the interpolation functions, the curves near the control points can exhibit a smoother or sharper appearance, thereby substantially increasing the degree of freedom in curve design. Finally, we exhibit the results and provide proofs for the aforementioned properties.
Event Type
Technical Papers
TimeTuesday, 16 December 20255:13pm - 5:24pm HKT
LocationMeeting Room S426+S427, Level 4