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janetournois committed Nov 21, 2023
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Expand Up @@ -24,6 +24,8 @@ The algorithm results in high-quality uniform isotropic meshes,
with the desired mesh density,
while preserving the input geometric curve and surface features.

\subsection ssecAlgorithm Remeshing Algorithm

Specific remeshing rules have been designed to satisfy the following criteria.
First, the algorithm preserves the geometric complex topology, including
multi-material surface patches and polyline features. Polyline features
Expand All @@ -37,7 +39,7 @@ preserve the input topology of the geometric complex.

The tetrahedral remeshing algorithm improves the quality of dihedral angles,
while targeting the user-defined uniform sizing field and preserving the
topology of the feature complex, as highlighted by Figure \cgalFigureRef{Remesh_liver}.
topology of the feature complex, as highlighted by \cgalFigureRef{Remesh_liver}.

Experimental evidence shows that a higher number of remeshing iterations
leads to a mesh with a improved fidelity to the sizing criterion,
Expand All @@ -50,12 +52,33 @@ Tetrahedral mesh, modified by our uniform tetrahedral remeshing method.
dihedral angles are in the interval [12,7; 157.7].
\cgalFigureEnd

\subsection ssecSizing Sizing Field

Tetrahedral isotropic remeshing algorithm is led by a target sizing field,
that can be either uniform, adaptive, or custom.

The sizing field establishes the local target edge length for the remeshed
tetrahedra. Two sizing fields are provided: a uniform and a mesh-adaptive sizing field.
With `CGAL::Tetrahedral_remeshing::Uniform_sizing_field`,
all tetrahedra edges are targeted to have equal lengths,
as depicted in Section \secTetRemeshing .
With `CGAL::Tetrahedral_remeshing::Adaptive_remeshing_sizing_field`,
tetrahedra edge lengths remain locally close to the local size of simplices in the input mesh.

The difference between remeshing with uniform and adaptive
sizing fields is depicted in \cgalFigureRef{uniform_and_adaptive}.

The same sizing field can be used for initial tetrahedral mesh generation
using the \cgal \ref PkgMesh3 package, and consecutive consistent isotropic remeshing,
as shown by \cgalFigureRef{sphere_sizing_field}.


\section secTetRemeshingAPI API

The tetrahedral remeshing algorithm is implemented as a single free function
`CGAL::tetrahedral_isotropic_remeshing()` that
takes only two required parameters: the input triangulation, and the desired edge length,
takes only two required parameters: the input triangulation, and the desired edge length
or sizing field,
which drives the remeshing process.

\ref BGLNamedParameters are used to deal with optional parameters.
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