Smooth and Discrete Cone-Nets

Article Computer Science, Software Engineering

Planar Panels and Planar Supporting Beams in Architectural Structures

Caigui Jiang et al.

Summary: In this article, the geometric properties and modeling capabilities of quad meshes with planar faces are investigated, where the mesh polylines are contained in a single plane. This planarity is advantageous in architectural design and building construction. The design of meshes under the requirement that one half of the mesh polylines are planar (P meshes) is discussed, as well as the geometry and design of meshes where all polylines enjoy this property (PP meshes). Geometric insights, explicit constructions, and an approach to geometric modeling of both P meshes and PP meshes are provided.

ACM TRANSACTIONS ON GRAPHICS (2023)

添加到收藏夹

Article Mathematics, Applied

Discrete curvature and torsion from cross-ratios

Christian Mueller et al.

Summary: The study investigates a curvature notion for discrete curves inspired by a Mobius invariant subdivision scheme for polygons, using the cross-ratio in key definitions. Circles are constructed along discrete curves using a specific Mobius invariant point-insertion-rule, with asymptotic analysis showing convergence to smooth curvature circles as sampling density increases. The study also expresses discrete torsion for space curves, not a Mobius invariant notion, using the cross-ratio and shows its asymptotic behavior similar to the curvature.

ANNALI DI MATEMATICA PURA ED APPLICATA (2021)

添加到收藏夹

Article Computer Science, Theory & Methods