Related papers: Corner-based implicit patches
We introduce trimmed NURBS surfaces with accurate boundary control, briefly called ABC-surfaces, as a solution to the notorious problem of constructing watertight or smooth ($G^1$ and $G^2)$ multi-patch surfaces within the function range of…
Dupin cyclides are interesting algebraic surfaces used in geometric design and architecture to join canal surfaces smoothly and to construct model surfaces. Dupin cyclides are special cases of Darboux cyclides, which in turn are rather…
The recent surge of utilizing deep neural networks for geometric processing and shape modeling has opened up exciting avenues. However, there is a conspicuous lack of research efforts on using powerful neural representations to extend the…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
A translational surface is a tensor product surface constructed from two space curves by translating one along the other. These surfaces are common within geometric modeling and, since their description is parametric, it is desirable to…
Basket weaving is a traditional craft used to create practical three-dimensional (3D) structures. While the geometry and aesthetics of baskets have received considerable attention, the underlying mechanics and modern engineering potential…
We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter…
This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In…
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…
Given a surface with boundary and some points on its boundary, a polygon diagram is a way to connect those points as vertices of non-overlapping polygons on the surface. Such polygon diagrams represent non-crossing permutations on a surface…
Based on the computation of a superset of the implicit support, implicitization of a parametrically given hyper-surface is reduced to computing the nullspace of a numeric matrix. Our approach exploits the sparseness of the given parametric…
We introduce a new implicit shape representation called Primary Ray-based Implicit Function (PRIF). In contrast to most existing approaches based on the signed distance function (SDF) which handles spatial locations, our representation…
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped…
We introduce a new way to implicitly represent swept volumes in 3D. We first implicitize the base volume and then apply the time-dependent rigid transformation to build an implicit representation of the swept volume. This way, we build a…
In conventional formulations of multilayer feedforward neural networks, the individual layers are customarily defined by explicit functions. In this paper we demonstrate that defining individual layers in a neural network \emph{implicitly}…
Implicit copulas are the most common copula choice for modeling dependence in high dimensions. This broad class of copulas is introduced and surveyed, including elliptical copulas, skew $t$ copulas, factor copulas, time series copulas and…
Reconstructing general dynamic scenes is important for many computer vision and graphics applications. Recent works represent the dynamic scene with neural radiance fields for photorealistic view synthesis, while their surface geometry is…
Illumination of scenes is usually generated in computer graphics using polygonal meshes. In this paper, we present a geometric method using projections. Starting from an implicit polynomial equation of a surface in 3-D or a curve in 2-D, we…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
Implicit surfaces are known for their ability to represent smooth objects of arbitrary topology thanks to hierarchical combinations of primitives using a structure called a blobtree. We present a new tile-based rendering pipeline well…