Related papers: PH-CPF: Planar Hexagonal Meshing using Coordinate …
We introduce a novel method for directional-field design on meshes, enabling users to specify singularities at any location on a mesh. Our method uses a piecewise power-linear representation for phase and scale, offering precise control…
We present a method for designing smooth cross fields on surfaces that automatically align to sharp features of an underlying geometry. Our approach introduces a novel class of energies based on a representation of cross fields in the…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
We present a method for generating orthogonal quadrilateral meshes subject to user-defined feature alignment and sizing constraints. The approach relies on computing integrable orthogonal frame fields, whose symmetries are implicitly…
In the past decade frame fields have emerged as a promising approach for generating hexahedral meshes for CFD and CAE applications. One important problem asks for construction of a boundary-aligned frame field with prescribed singularity…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
This paper presents a novel algorithmic framework for the computational design, simulation, and fabrication of a hexagonal grid-based double-curvature structure with planar hexagonal panels. The journey begins with constructing a robust…
Reconstruction of directional fields is a need in many geometry processing tasks, such as image tracing, extraction of 3D geometric features, and finding principal surface directions. A common approach to the construction of directional…
Field-guided parametrization methods have proven effective for quad meshing of surfaces; these methods compute smooth cross fields to guide the meshing process and then integrate the fields to construct a discrete mesh. A key challenge in…
The accurate and efficient evaluation of potentials is of great importance for the numerical solution of partial differential equations. When the integration domain of the potential is irregular and is discretized by an unstructured mesh,…
This paper proposes an automated method to detect, group and rectify arbitrarily-arranged coplanar repeated elements via energy minimization. The proposed energy functional combines several features that model how planes with coplanar…
The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D…
The I-patch is a multi-sided surface representation, defined as a combination of implicit ribbon and bounding surfaces, whose pairwise intersections determine the natural boundaries of the patch. Our goal is to show how a collection of…
We present a target field approach to analytically design magnetic fields using permanent magnets. We assume that their magnetisation is bound to a two-dimensional surface and is composed of a complete basis of surface modes. By posing the…
This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…
In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle…
Our goal is to provide a novel method of representing 2D shapes, where each shape will be assigned a unique fingerprint - a computable approximation to a conformal map of the given shape to a canonical shape in 2D or 3D space (see page 22…
We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature…
The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take…
Planar quadrilateral (PQ) mesh generation is a key process in computer-aided design, particularly for architectural applications where the goal is to discretize a freeform surface using planar quad faces. The conjugate direction field (CDF)…