Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Accuracy, limits, and approximation

Accuracy, limits, and approximation

Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...

Circular Shaft - Stresses in Linear Range

Circular Shaft - Stresses in Linear Range

Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.

Generalized Hooke's Law

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Bridging annotated microscopy imaging data and analysis method development for scientific discovery.

Patterns (New York, N.Y.)·2026

Same author

Revisiting deep information propagation: Fractal frontier and finite-size effects.

Neural networks : the official journal of the International Neural Network Society·2026

Same author

Revisiting PSF models: Unifying framework and high-performance implementation.

Journal of microscopy·2025

Same author

From images to understanding: Advances in deep learning for cellular dynamics analysis.

Current opinion in cell biology·2025

Same author

Perturbative Fourier ptychographic microscopy for fast quantitative phase imaging.

Optics express·2025

Same author

MIFA: Metadata, Incentives, Formats and Accessibility guidelines to improve the reuse of AI datasets for bioimage analysis.

Nature methods·2025

Search research articles

Related Experiment Video

Updated: Dec 24, 2025

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Support and approximation properties of Hermite splines.

Julien Fageot¹, Shayan Aziznejad¹, Michael Unser¹

¹Biomedical Imaging Group, École polytechnique fédérale de Lausanne (EPFL), Station 17, 1015 Lausanne, Switzerland.

Journal of Computational and Applied Mathematics

|April 8, 2020

Summary

Hermite splines offer minimal support size and optimal approximation power, matching B-splines. These properties make Hermite splines highly suitable for computer graphics and geometric design applications.

Keywords:

Approximation error Hermite interpolation Minimum-support property

More Related Videos

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Published on: October 20, 2023

Related Experiment Videos

Last Updated: Dec 24, 2025

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Published on: October 20, 2023

Area of Science:

Mathematics
Computer Science
Geometric Design

Background:

Hermite splines are essential in various applications.
Understanding their mathematical properties is crucial for optimization.

Purpose of the Study:

To formally investigate the localization and approximation power of Hermite splines.
To compare Hermite splines with B-spline approximation schemes.

Main Methods:

Demonstrating maximal localization of Hermite splines.
Quantifying the approximation error for function and derivative reconstruction.
Analyzing asymptotic approximation error constants.

Main Results:

Hermite splines exhibit minimal support size for given reproduction properties.
Hermite and B-spline schemes share identical approximation orders and asymptotic error constants.
Hermite splines possess optimal localization and approximation power.

Conclusions:

Hermite splines offer a compelling combination of properties, including interpolation and closed-form expressions.
These findings highlight the utility of Hermite splines in computer graphics and geometric design.