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Concept

Spline (mathematics)

Related publications (28)

Hessian Splines For Scanning Transmission X-Ray Microscopy

Michaël Unser, Thomas Jean Debarre

Scanning transmission X-ray microscopy (STXM) produces images in which each pixel value is related to the measured attenuation of an X-ray beam. In practice, the location of the illuminated region does not exactly match the desired uniform pixel grid. This ...

IEEE2020

A Low-Parametric Rhombic Microstructure Family for Irregular Lattices

Francis Julian Panetta

New fabrication technologies have significantly decreased the cost of fabrication of shapes with highly complex geometric structure. One important application of complex fine-scale geometric structures is to create variable effective elastic material prope ...

2020

Deep Neural Networks With Trainable Activations and Controlled Lipschitz Constant

Michaël Unser, Shayan Aziznejad, Harshit Gupta, Joaquim Gonçalves Garcia Barreto Campos

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output relation. To that end, ...

2020

A hierarchical approach to the a posteriori error estimation of isogeometric Kirchhoff plates and Kirchhoff–Love shells

Annalisa Buffa, Pablo Antolin Sanchez, Luca Coradello

This work focuses on the development of a posteriori error estimates for fourth-order, elliptic, partial differential equations. In particular, we propose a novel algorithm to steer an adaptive simulation in the context of Kirchhoff plates and Kirchhoff–Lo ...

2020

Seamless integration of design and Kirchhoff-Love shell analysis using analysis-suitable unstructured T-splines

Xiaodong Wei

Analysis-suitable T-splines (ASTS) including both extraordinary points and T-junctions are used to solve Kirchhoff-Love shell problems. Extraordinary points are required to represent surfaces with arbitrary topological genus. T-junctions enable local refin ...

ELSEVIER SCIENCE SA2020

Volumetric untrimming: Precise decomposition of trimmed trivariates into tensor products

Pablo Antolin Sanchez

3D objects, modeled using Computer Aided Geometric Design (CAGD) tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physic ...

2019

Domain-Informed Spline Interpolation

Dimitri Nestor Alice Van De Ville, Hamid Behjat, Zafer Dogan

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a single homogeneous domain. In contrast, many naturally occurring signals lie on an inhomogeneous domain, such as brain activity associated to different brain ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

A finite element framework based on bivariate simplex splines on triangle configurations

Xiaodong Wei

Recently, triangle configuration based bivariate simplex splines (referred to as TCB-spline) have been introduced to the geometric computing community. TCB-splines retain many attractive theoretic properties of classical B-splines, such as partition of uni ...

ELSEVIER SCIENCE SA2019