An interpolation scheme with C1 Overhauser-type interpolation splines over hierarchical T-meshes

Yuanpeng Zhu and Kaichen Li

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 82-95

Abstract: We present a surface interpolation scheme employing a kind of C1 Overhauser-type interpolation splines over hierarchical T-meshes. The introduced spline surfaces exhibit C1 continuity and possess the capability to interpolate all basis vertices within hierarchical T-meshes, making them well-suited for surface modeling applications. Initially, we develop a set of linearly parametrized basis surfaces over hierarchical T-meshes. Furthermore, through the blending of the basis functions with these linearly parametrized basis surfaces, we propose C1 Overhauser-type interpolation splines over hierarchical T-meshes. Examples are provided to demonstrate the comparison of interpolation performance between PHT-splines and C1 Overhauser-type interpolation splines. The C1 Overhauser-type interpolation splines exhibit good properties such as affine invariance, interpolation property, and C1 continuity. Some experiments on surface reconstruction of 3D triangular mesh models applying the new C1 Overhauser-type interpolation splines are presented. The experimental results show that the new C1 Overhauser-type interpolation splines are suitable for surface modeling.

Keywords: Interpolation scheme; Hierarchical T-mesh; Interpolation spline; Surface reconstruction (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:82-95

DOI: 10.1016/j.matcom.2025.06.026

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