Mesh generation | Geometry processing

Laplacian smoothing

Laplacian smoothing is an algorithm to smooth a polygonal mesh. For each vertex in a mesh, a new position is chosen based on local information (such as the position of neighbours) and the vertex is moved there. In the case that a mesh is topologically a rectangular grid (that is, each internal vertex is connected to four neighbours) then this operation produces the Laplacian of the mesh. More formally, the smoothing operation may be described per-vertex as: Where is the number of adjacent vertices to node , is the position of the -th adjacent vertex and is the new position for node . (Wikipedia).

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C79 Linear properties of the Laplace transform

The linear properties of the Laplace transform.

From playlist Differential Equations

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C75 Introduction to the Laplace Transform

Another method of solving differential equations is by firs transforming the equation using the Laplace transform. It is a set of instructions, just like differential and integration. In fact, a function is multiplied by e to the power negative s times t and the improper integral from ze

From playlist Differential Equations

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3 Properties of Laplace Transforms: Linearity, Existence, and Inverses

The Laplace Transform has several nice properties that we describe in this video: 1) Linearity. The Laplace Transform of a linear combination is a linear combination of Laplace Transforms. This will be very useful when applied to linear differential equations 2) Existence. When functions

From playlist Laplace Transforms and Solving ODEs

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C80 Solving a linear DE with Laplace transformations

Showing how to solve a linear differential equation by way of the Laplace and inverse Laplace transforms. The Laplace transform changes a linear differential equation into an algebraical equation that can be solved with ease. It remains to do the inverse Laplace transform to calculate th

From playlist Differential Equations

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Laplace Transform and Piecewise or Discontinuous Functions

Watch the Intro to the Laplace Transform in my Differential Equations playlist here: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 This video deals particularly with how the Laplace Transform works with piecewise functions, a type of discontinuous functions. T

From playlist Laplace Transforms and Solving ODEs

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Laplace transform of 1/sqrt(t), *SPEED RUN*

laplace transform of 1/sqrt(t), L{1/sqrt(t)}, laplace transform examples, laplace transform lessons, blackpenredpen

From playlist Properties of Laplace Transform (Nagle's Sect7.3)

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Laplace Transform Explained and Visualized Intuitively

Laplace Transform explained and visualized with 3D animations, giving an intuitive understanding of the equations. My Patreon page is at https://www.patreon.com/EugeneK

From playlist Physics

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Periodic Functions and the Laplace Transform

Watch the Intro to the Laplace Transform in my Differential Equations playlist here: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 We've seen previously in the playlist that Laplace Transforms work great with piecewise functions, functions that have discontinui

From playlist Laplace Transforms and Solving ODEs

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Differential Equations | The Laplace Transform of a Derivative

We establish a formula involving the Laplace transform of the derivative of a function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist The Laplace Transform

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Rafe Mazzeo - Minicourse - Lecture 2

Rafe Mazzeo Conic metrics on surfaces with constant curvature An old theme in geometry involves the study of constant curvature metrics on surfaces with isolated conic singularities and with prescribed cone angles. This has been studied from many points of view, ranging from synthetic geo

From playlist Maryland Analysis and Geometry Atelier

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AMMI 2022 Course "Geometric Deep Learning" - Seminar 1 (Physics-based GNNs) - Francesco Di Giovanni

Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 Seminar 1 - Graph neural networks through the lens of multi-particle dynamics and gradient flows - Francesco Di Giovanni (Twitter) Slides: https://www.dropbox.com/s/

From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)

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Camillo De Lellis: Ill-posedness for Leray solutions of the ipodissipative Navier-Stokes equations

Abstract: In a joint work with Maria Colombo and Luigi De Rosa we consider the Cauchy problem for the ipodissipative Navier-Stokes equations, where the classical Laplacian −Δ is substited by a fractional Laplacian (−Δ)α. Although a classical Hopf approach via a Galerkin approximation shows

From playlist Partial Differential Equations

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T. Richard - Advanced basics of Riemannian geometry 3

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the Bochner formula and basics of Ricci flow.

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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T. Richard - Advanced basics of Riemannian geometry 3 (version temporaire)

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the Bochner formula and basics of Ricci flow.

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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The Hypoelliptic Laplacian: An Introduction - Jean-Michel Bismut

Jean-Michel Bismut Universite de Paris-Sud March 26, 2013 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Rafe Mazzeo - Minicourse - Lecture 1

Rafe Mazzeo Conic metrics on surfaces with constant curvature An old theme in geometry involves the study of constant curvature metrics on surfaces with isolated conic singularities and with prescribed cone angles. This has been studied from many points of view, ranging from synthetic geo

From playlist Maryland Analysis and Geometry Atelier

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Lecture 9: GNNs as Dynamic Systems - Francesco Di Giovanni

Video recording of the First Italian School on Geometric Deep Learning held in Pescara in July 2022. Slides: https://www.sci.unich.it/geodeep2022/slides/GRAFF_presentation%20(17).pdf

From playlist First Italian School on Geometric Deep Learning - Pescara 2022

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Yilin Wang - 3/3 The Loewner Energy at the Crossroad of Random Conformal Geometry (...)

The Loewner energy for Jordan curves first arises from the large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is

From playlist Yilin Wang - The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory

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The Laplace Transform - A Graphical Approach

Get the map of control theory: https://www.redbubble.com/shop/ap/55089837 Download eBook on the fundamentals of control theory (in progress): https://engineeringmedia.com A lot of books cover how to perform a Laplace Transform to solve differential equations. This video tries to show grap

From playlist Fourier

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Hermitian and Non-Hermitian Laplacians and Wave Equaions by Andrey shafarevich

Non-Hermitian Physics - PHHQP XVIII DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Phys

From playlist Non-Hermitian Physics - PHHQP XVIII

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Polygon mesh | Smoothing | Tutte embedding