Related papers: Spline surfaces with T-junctions

This paper is devoted to the construction of polynomial 2-surfaces which possess a polynomial area element. In particular we study these surfaces in the Euclidean space $\mathbb R^3$ (where they are equivalent to the PN surfaces) and in the…

We establish several fundamental properties of analysis-suitable T-splines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended…

A smooth T-surface can be thought of as a generalization of a surface of revolution in such a way that the axis of rotation is not fixed at one point but rather traces a smooth path on the base plane. Furthermore, the action, by which the…

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…

Motivated by applications in architecture and design, we present a novel method for increasing the developability of a B-spline surface. We use the property that the Gauss image of a developable surface is 1-dimensional and can be locally…

In this paper we address the issue of designing developable surfaces with Bezier patches. We show that developable surfaces with a polynomial edge of regression are the set of developable surfaces which can be constructed with Aumann's…

Computing occluding contours is a key building block of non-photorealistic rendering, but producing contours with consistent visibility has been notoriously challenging. This paper describes the first general-purpose smooth surface…

This paper further develops the Method of Matched Sections (MMS), a robust numerical framework for the solution of boundary value problems governed by partial differential equations. It demonstrates its unique applicability to the…

Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…

Spherical $t$-designs on $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ provide $N$ nodes for an equal weight numerical integration rule which is exact for all spherical polynomials of degree at most $t$. This paper considers the generation of…

We introduce a family of boundary conditions and point constraints for conformal immersions that increase the controllability of surfaces defined as minimizers of conformal variational problems. Our free boundary conditions fix the metric…

We study the geometry of the smooth projective surfaces that are defined by Frobenius forms, a class of homogenous polynomials in prime characteristic recently shown to have minimal possible F-pure threshold among forms of the same degree.…

In analogy to classical spherical t-design points, we introduce the concept of t-design curves on the sphere. This means that the line integral along a t-design curve integrates polynomials of degree t exactly. For low degrees we construct…

This paper addresses the linear independence of T-splines that correspond to refinements of three-dimensional tensor-product meshes. We give an abstract definition of analysis-suitability, and prove that it is equivalent to…

Several results on constrained spline smoothing are obtained. In particular, we establish a general result, showing how one can constructively smooth any monotone or convex piecewise polynomial function (ppf) (or any $q$-monotone ppf,…

We present a novel method named truncated hierarchical unstructured splines (THU-splines) that supports both local $h$-refinement and unstructured quadrilateral meshes. In a THU-spline construction, an unstructured quadrilateral mesh is…

Let $\Gamma_g$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We introduce a combinatorial structure of "core surfaces", that represent subgroups of $\Gamma_g$. These structures are (usually)…

We consider overlap splines that are defined by connecting the patches of piecewise functions via common values at given finite sets of nodes, without using any partitions of the computational domain. It is shown that some classical finite…

Given a graph $G$ whose edges are labeled by ideals of a commutative ring $R$ with identity, a generalized spline is a vertex labeling of $G$ by the elements of $R$ so that the difference of labels on adjacent vertices is an element of the…

Subdivision schemes are iterative methods for the design of smooth curves and surfaces. Any linear subdivision scheme can be identified by a sequence of Laurent polynomials, also called subdivision symbols, which describe the linear rules…