Related papers: Polyhedral Splines for Analysis
This paper proposes to generalize linear subdivision schemes to nonlinear subdivision schemes for curve and surface modeling by refining vertex positions together with refinement of unit control normals at the vertices. For each round of…
The P-splines of Eilers and Marx (1996) combine a B-spline basis with a discrete quadratic penalty on the basis coefficients, to produce a reduced rank spline like smoother. P-splines have three properties that make them very popular as…
We give a full classification of continuous flexible discrete axial cone-nets, which are called axial C-hedra. The obtained result can also be used to construct their semi-discrete analogs. Moreover, we identify a novel subclass within the…
Using the normalized B-bases of vector spaces of trigonometric and hyperbolic polynomials of finite order, we specify control point configurations for the exact description of higher dimensional (rational) curves and (hybrid) multivariate…
We present computational methods for constructing orthogonal/orthonormal polynomials over arbitrary polygonal domains in $\mathbb{R}^2$ using bivariate spline functions. Leveraging a mature MATLAB implementation which generates spline…
We analyze the space of differentiable functions on a quad-mesh $\cM$, which are composed of 4-split spline macro-patch elements on each quadrangular face. We describe explicit transition maps across shared edges, that satisfy conditions…
In this paper, we consider $C^1$ cubic Powell-Sabin splines for the numerical solution of boundary value problems on planar and spatial surface domains. We first review the construction and basic properties of polynomial and rational $C^1$…
A "blendstring" is a piecewise polynomial interpolant with high-degree two-point Hermite interpolational polynomials on each piece, analogous to a cubic spline. Blendstrings are smoother and can be more accurate than cubic splines, and can…
Spherical $t$-designs are finite point sets on the unit sphere that enable exact integration of polynomials of degree at most $t$ via equal-weight quadrature. This concept has recently been extended to spherical $t$-design curves by the use…
The paper is concerned with three types of cubic splines over a triangulation that are characterized by three degrees of freedom associated with each vertex of the triangulation. The splines differ in computational complexity, polynomial…
This survey gives an overview of three central algebraic themes related to the study of splines: duality, group actions, and homology. Splines are piecewise polynomial functions of a prescribed order of smoothness on some subdivided domain…
When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is…
In this article, we survey the primary research on polyhedral computing methods for constrained linear control systems. Our focus is on the modeling power of convex optimization, featured to design set-based robust and optimal controllers.…
Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission critical systems. For such applications, the identification of an appropriate…
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…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…
We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…
The control polygon of a Bezier curve is well-defined and has geometric significance---there is a sequence of weights under which the limiting position of the curve is the control polygon. For a Bezier surface patch, there are many possible…
This paper introduces a novel framework for constructing $C^r$ basis functions for polynomial spline spaces of degree $d$ over arbitrary planar polygonal partitions, overturning the belief that basis functions cannot be constructed on…
This article studies families of curves with monotonic curvature function (MC-curves) and their applications in geometric modelling and aesthetic design. Aesthetic analysis and assessment of the structure and plastic qualities of…