Related papers: Polyhedral design with blended $n$-sided interpola…
We present a new method for performing Boolean operations on volumes represented as triangle meshes. In contrast to existing methods which treat meshes as 3D polyhedra and try to partition the faces at their exact intersection curves, we…
We develop a theory of simple pentagonal subdivision of quadrilateral tilings, on orientable as well as non-orientable surfaces. Then we apply the theory to answer questions related to pentagonal tilings of surfaces, especially those…
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
We produce implicit equations for general biquadratic (order 2x2) B\'ezier triangle and quadrilateral surface patches and provide function evaluation code, using modern computing resources to exploit old algebraic construction techniques.
In this short note we describe a simple adaptation of biharmonic surfaces to interpolate boundary cross-derivatives given in ribbon form, and compare with the recently proposed Generalized B-spline patches.
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
Membrane-metasurfaces, formed by periodic arrangements of holes in a dielectric layer, are gaining attention for their easier manufacturing via subtractive techniques, unnecessity of substrates, and access to resonant near-fields. Despite…
New interpolation and quasi-interpolation operators of Cl\'ement- and Scott-Zhang-type are analyzed on anisotropic polygonal and polyhedral meshes. Since no reference element is available, an appropriate linear mapping to a reference…
We address the unsolved problem of unfolding prismatoids in a new context, viewing a "topless prismatoid" as a convex patch---a polyhedral subset of the surface of a convex polyhedron homeomorphic to a disk. We show that several natural…
In this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate $C^1$ quadratic splines on…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
We propose an end-to-end pipeline to robustly generate high-quality quadrilateral meshes for complex CAD models. An initial quad-dominant mesh is generated with frontal point insertion guided by a locally integrable cross field and a scalar…
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…
We analyze surface patches with a corner that is rounded in the sense that the partial derivatives at that point are antiparallel. Sufficient conditions for $G^1$ smoothness are given, which, up to a certain degenerate case, are also…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
We study the use of polyhedral discretizations for the solution of heat diffusion and elastodynamic problems in computer graphics. Polyhedral meshes are more natural for certain applications than pure triangular or quadrilateral meshes,…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
We introduce a new technique to create a mesh of convex polyhedra representing the interior volume of a triangulated input surface. Our approach is particularly tolerant to defects in the input, which is allowed to self-intersect, to be…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…