Year: 2025
Type: article
Abstract: We introduce a novel class of G 2 continuous splines constructed using an innovative blending method, which guarantees precise interpolation of given control points. These splines are designed to achieve local curvature maxima specifically at these control points and possess compact local support, thereby eliminating the need for global optimization processes. The formulation ensures the splines are free from cusps and self-intersections and, notably, prevents adjacent segments from intersecting—a significant improvement over prior blending-based curve techniques. This framework utilizes quadratic Bézier splines in conjunction with quartic Bézier blending functions. A constructive algorithm is presented that generates these curvature-controlled curves without relying on global optimization. Through parametric adjustments of curvatures, the curve's geometry near control points can be tuned to create features ranging from smooth to sharp, thus broadening the design possibilities. Rigorous mathematical proofs and visual demonstrations validate all claimed properties of the framework.
Source: ACM Transactions on Graphics
DOI: 10.1145/3763316
Authors: Bowen Jiang, Renjie Chen
Institution: University of Science and Technology of China
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: bronze
Award: G5429786766
OpenAlex ID: W4417000488