The Multi-Triangulation (MT)

General Information


What is a Multi-Triangulation?

A Multi-Triangulation (MT) is a tool which provides representations of a surface through triangle meshes at variable resolution, i.e., meshes which can be more or less refined according to user-defined requirements. The user queries an MT by specifying two parameters:

The MT answers the query by returning a triangle mesh which represents the surface with the required accuracy inside the focus area.

A large number of relevant spatial operations can be performed at variable resolution on a surface by querying an MT built for such a surface. Examples of such queries are:

A variable resolution means that the resolution (density) of the triangle mesh can be locally adapted to the needs of the application. For instance:


An example

In the following example we can see a triangle mesh by two different viewpoints. The mesh is extracted considering a conical region with resolution decreasing with distance from the vertex of the cone.


What does an MT look like?

An MT is made of a collection of elementary triangle meshes, each representing a portion of the surface at a certain resolution. Many alternative representations of the same piece of surface exist in an MT. A mesh representing the whole surface at variable resolution can be obtained by assembling the elementary triangle meshes. The triangle meshes forming an MT are arranged in a directed acyclic graph, which provides all the ways in which they can be combined to provide consistent surface descriptions.

How to build an MT

The construction of an MT is based on iterative methods for the generation of triangle meshes representing a surface. Such methods are of two kinds:


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