get.quantity.of.information

<p>An object of class <code>RcppSimplification</code>.</p>

<p>For each triangle $T$ in the mesh, the associated quantity of information $N_T$ is defined as: $$N_T := n_f + \frac{1}{2}n_e + \frac{1}{\# \big( T_{v_1} \big)} n_1 + \frac{1}{\# \big( T_{v_2} \big)} n_2 + \frac{1}{\# \big( T_{v_3} \big)} n_3 \, ,$$ where $n_f$ and $n_e$ denote the number of data points associated with the face and the edges of the triangle $T$, respectively. For $j = 1, \, 2, \, 3$, $n_j$ is the number of data points associated with the $j$-th vertex $v_j$ of $T$, $T_{v_j}$ is the patch of elements associated with $v_j$ (i.e., the elements sharing $v_j$), and $\# \big( T_{v_j} \big)$ denotes the cardinality of the patch $T_{v_j}$.</p>

Iterative simplification strategy for surface triangular meshes (2.5D meshes) with associated data. Each iteration corresponds to an edge collapse where the selection of the edge to contract is driven by a cost functional that depends both on the geometry of the mesh than on the distribution of the data locations over the mesh. The library can handle both zero and higher genus surfaces. The package has been designed to be fully compatible with the R package 'fdaPDE', which implements regression models with partial differential regularizations, making use of the Finite Element Method. In the future, the functionalities provided by the current package may be directly integrated into 'fdaPDE'.

Stefano Ubbiali

meshsimp

Simplification of Surface Triangular Meshes with Associated
Distributed Data

Franco Dassi

Bree Ettinger

Marco Martinolli

Simona Perotto

Laura M. Sangalli

get.quantity.of.information function

Get the quantity of information associated with each element of the triangulation, from an object of class <code>RcppSimplification</code>. — get.quantity.of.information

Get the quantity of information associated with each element of the triangulation, from an object of class <code>RcppSimplification</code>.

get.quantity.of.information: Get the quantity of information associated with each element of the triangulation, from an object of class `RcppSimplification`.

Description

Usage

Arguments

Value

See Also