Related papers: Smooth surface interpolation using patches with ra…
The existing combinatorial methods for iso-surface computation are efficient for pure visualization purposes, but it is known that the resulting iso-surfaces can have holes, and topological problems like missing or wrong connectivity can…
In this talk we review the problem of constructing a developable surface patch bounded by two rational or NURBS (Non-Uniform Rational B-spline) curves.
Smooth real cubic surfaces are birationally trivial (over $\R$) if and only if their real locus is connected or, equivalently, if and only if they have two skew real lines or two skew complex conjugate lines. In such a case a…
I propose a vertex patch smoother where local problems are solved inexactly by a nested, matrix-free p-multigrid, creating a multigrid-within-multigrid framework. A single iteration of the local solver can be evaluated with…
The ability to tailor a coherent surface plasmon polariton (SPP) field is an important step towards a number of new opportunities for a broad range of nanophotonic applications such as sensing [1,2], nano-circuitry [3,4], optical data…
In this paper, we give several simple methods for drawing a whole rational surface (without base points) as several Bezier patches. The first two methods apply to surfaces specified by triangular control nets and partition the real…
We present a novel method for isogeometric analysis (IGA) to directly work on geometries constructed by Boolean operations including difference (i.e., trimming), union and intersection. Particularly, this work focuses on the union…
We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \ge \b_2-2$ disjoint smooth rational curves with self-intersection -2, where $\b_2$ is the…
Generating continuous surfaces from discrete point cloud data is a fundamental task in several 3D vision applications. Real-world point clouds are inherently noisy due to various technical and environmental factors. Existing data-driven…
We propose and compare various techiques available to produce smooth cubic hypersurfaces over a non-algebraically-closed field which have rational points but which are not stably rational over their ground field.
A determination of the fixed components, base points and irregularity is made for arbitrary numerically effective divisors on any smooth projective rational surface having an effective anticanonical divisor. All of the results are proven…
Special curves in the Minkowski space such as Minkowski Pythagorean hodographs play an important role in Computer Aided Geometric Design, and their usages have been thoroughly studied in the recent years. Also, several papers have been…
We introduce a polynomial invariant of graphs on surfaces, $P_G$, generalizing the classical Tutte polynomial. Topological duality on surfaces gives rise to a natural duality result for $P_G$, analogous to the duality for the Tutte…
In order to generate novel 3D shapes with machine learning, one must allow for interpolation. The typical approach for incorporating this creative process is to interpolate in a learned latent space so as to avoid the problem of generating…
A simple characterization is given of open subsets of a complex surface that smoothly perturb to Stein open subsets. As applications, complex 2-space C^2 contains domains of holomorphy (Stein open subsets) that are exotic R^4's, and others…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
With the burst development of neural networks in recent years, the task of normal estimation has once again become a concern. By introducing the neural networks to classic methods based on problem-specific knowledge, the adaptability of the…
We construct over a given bilinear multi-patch domain a novel $C^s$-smooth mixed degree and regularity isogeometric spline space, which possesses the degree $p=2s+1$ and regularity $r=s$ in a small neighborhood around the edges and…
The reconstruction of real-world surfaces is on high demand in various applications. Most existing reconstruction approaches apply 3D scanners for creating point clouds which are generally sparse and of low density. These points clouds will…
We propose a novel architecture that learns an end-to-end mapping function to improve the spatial resolution of the input natural images. The model is unique in forming a nonlinear combination of three traditional interpolation techniques…