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[3] viXra:2607.0043 [pdf] submitted on 2026-07-11 10:32:59
Authors: Abdelmajid Ben Hadj Salem
Comments: 2 Pages. In French. Comments welcome.
In this note, we present a problem in the theory of surfaces. The equations for the surface $(Sigma)$ were inspired by the monograph cited in the references, published by the eminent Japanese mathematicians Katsumi Nomizu and Takeshi Sasaki.
Category: Geometry
[2] viXra:2607.0035 [pdf] submitted on 2026-07-11 22:57:23
Authors: Zitao Xu
Comments: 10 Pages.
This article presents a least-squares optimization model for quadrilateral mesh offsets. Starting from an initial offset mesh generated from a base quad mesh, the method improves offset quality by introducing tangential corrections at offset vertices and solving for them globally. Each correction is represented by two scalar variables associated with two independent directions taken from the corresponding base quad, so that the optimization preserves the intended offset distance while allowing the offset mesh to adjust tangentially.For each quad, the objective function is constructed from local shape-preservation terms together with a center-consistency term, so that the optimized offset quad remains as consistent as possible with the shape and size of the corresponding base quad while reducing local crimping and shearing. The resulting formulation is a global least-squares problem over the mesh and leads to a sparse linear system. Examples in both convex and concave regions show that the method can significantly improve the quality of quad-mesh offsets and can be applied iteratively for further improvement.
Category: Geometry
[1] viXra:2607.0009 [pdf] submitted on 2026-07-03 22:24:16
Authors: Zitao Xu
Comments: 7 Pages.
Classical offset algorithms focus on constructing offset curves and surfaces. Optimization-based geometry processing has also been extensively studied for mesh fairing, deformation, and parameterization. The present work differs from both directions by introducing a least-squares formulation whose unknowns are tangential displacements of offset vertices, yielding a globally optimized offset configuration.
Category: Geometry
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