A Construction of Interpolating Space Curves with Any Degree of Geometric Continuity

2024/05/17 by Tsung-Wei Hu, Hu, Tsung-Wei, Ming-Jun Lai +1
Computer Science · Engineering · #30C60 #31A05 #35J25 #53A10 #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2405.11123

openalex publication_date 2024/05/17 · openalex created_date 2024/05/22 · openalex updated_date 2026/07/28

Abstract

This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in ℝ^d applicable to oriented and flattenable points with d≥ 2. The construction involves four essential components: local functions, blending functions, redistributing functions, and gluing functions. The resulting curve possesses favorable attributes, including G² geometric smoothness, locality, the absence of cusps, and no self-intersection. Moreover, the algorithm is adaptable to various scenarios, such as preserving convexity, interpolating sharp corners, and ensuring sphere preservation. The paper substantiates the efficacy of the proposed method through the presentation of numerous numerical examples, offering a practical demonstration of its capabilities.

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