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This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility…
We develop a formalism to study the use of Level Set Method (LSM) in the investigation of evolution of observables in terms of parameters of the Hamiltonian, both of the system itself and the control part. A simple example with an analytic…
General skinning techniques aim to deform the surface of an articulated model following the pose change of a skeleton. Their rapidity makes them ideal tools for real-time animation purposes. However, popular skinning algorithms are simple,…
In this paper, we propose a novel gradient-based method to optimize curvilinear masks in optical lithography. The mask pattern is represented by periodic B-spline curves. We apply Delaunay triangulation to discretize the domains circled by…
Duchon's method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain integral functional. For transfinite interpolation, i.e. interpolation of continuous data prescribed on curves…
For large-scale data fitting, the least-squares progressive iterative approximation is a widely used method in many applied domains because of its intuitive geometric meaning and efficiency. In this work, we present a randomized progressive…
We propose a novel method to generate a small set of ruled surfaces that do not collide with the input shape for linear hot-wire rough machining. Central to our technique is a new observation: the ruled surfaces constructed by vertical…
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…
Tile B-splines in $\mathbb{R}^d$ are defined as autoconvolutions of the indicators of tiles, which are special self-similar compact sets whose integer translates tile the space $\mathbb{R}^d$. These functions are not piecewise-polynomial,…
There are many methods for image enhancement. Image inpainting is one of them which could be used in reconstruction and restoration of scratch images or editing images by adding or removing objects. According to its application, different…
One little-explored frontier of image generation and editing is the task of interpolating between two input images, a feature missing from all currently deployed image generation pipelines. We argue that such a feature can expand the…
A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…
The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit…
We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space (Vuong et al.,…
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…
We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The…
Given a system of triangles in the plane $\mathbb{R}^2$ along with given data of function and gradient values at the vertices, we describe the general pattern of local linear methods invoving only four smooth standard shape functions which…
This article presents a new mathematical framework to perform statistical analysis on time-indexed sequences of 2D or 3D shapes. At the core of this statistical analysis is the task of time interpolation of such data. Current models in use…
Quantitative MRI methods that estimate multiple physical parameters simultaneously often require the fitting of a computational complex signal model defined through the Bloch equations. Repeated Bloch simulations can be avoided by matching…
Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In…