Publication

NUMERICAL APPROXIMATION OF RIGID MAPS IN ORIGAMI THEORY

2023

Abstract

In origami theory, the problem of rigid maps consists in finding a paper folding from the two-dimensional space onto the three-dimensional space. This problem is an example of a first-order fully nonlinear equation. In this article, we present a general variational framework to solve the problem of rigid maps with Dirichlet boundary conditions. The numerical framework relies on the introduction of a regularized objective function and the penalization of the constraints. A splitting algorithm is advocated for the corresponding flow problem. The iterations sequence consists of local nonlinear problems and a global linear variational problem at each step. Numerical experiments validate the efficiency of the method for piecewise smooth exact solutions.

Official source

https://infoscience.epfl.ch/entities/publication/3f38f3ac-f5b9-4876-8e8d-afa521a4302f

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2023

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/3f38f3ac-f5b9-4876-8e8d-afa521a4302f

About this result

Related concepts (32)

Three-dimensional space

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, the Euclidean n-space of dimension n=3 that models physical space. More general three-dimensional spaces are called 3-manifolds. Technically, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n-dimensional Euclidean space.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Four-dimensional space

Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled x, y, and z).

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