The speed and storage requirements of the geometry for subsequent representation sometimes forced to make simplifying models.

Multiresolution techniques can face the problem by establishing models with different levels of detail for use depending on the size of the representation (distance to the camera), allowing the visualization of complex models in real time.

The use of multiresolution involves obtaining simplified models from the original, and select the level of detail in each case. In this article we focus on the simplification phase addressing one of the simplest techniques: The collapse of vertices, edges and faces.

## Mallas polygonal

We must distinguish in a mesh between the basic components that comprise:

**Geometric mesh**: Contains the vertices of the same, elements that spatially define the geometry we are representing.**Connectivity mesh**: Contains the edges and faces”bind” vertices, by setting the object's shape, and giving rise to holes, cavities and tunnels in the same, namely, defining topology.

Denominate “**Genus**” the number of “holes” that is the surface of the mesh. A sphere and a cube are **topologically equivalent** and having **same “Genus”**.

## Simplification techniques

Los **criteria **for simplification technique furnishes good results are:

- Keep topology (surface continuity)
- Keep the genus and not “open new holes”.

The approach can be made from a continuous or discrete perspective; in the discrete model are obtained “versions” with different degrees of simplification are stored in memory for use when needed while in the continuous model simplification is done in real time with different degree of simplification in areas close to the observer that you are further from.

## Simplification of polygonal meshes

In general the algorithms are geared to work with triangular elements. The objective is to reduce the number of triangles that form the mesh, minimizing errors of simplification to preserve the original appearance. The important thing is that I do not appreciate big difference from a visual standpoint.

Simplification is addressed mainly two criteria:

- Fidelity
- Budget

Fidelity is a measure of the approximation of the surfaces, where raw perception of the object, while the budget affects the maximum number of areas to ensure real-time interaction.

## Operators simplification

The idea is to establish a set of operators to apply the simplified model. These operators can be applied in different order and number of times to bring the surface to a sufficiently simplified model for our interests.

The main operators are:

- Collapse of Vertices
- Edge collapse
- Faces collapse (triangles)
- Cell collapse
- Vertex decimation

We will see later how these techniques arise in detail, and how to apply it from a practical point of view mainly with Blender animation software.

- Modeled Multiresolución By Susana Mata Fernández: Professor URJC (Primary basis for this article)
- 3D scanning Capture, assembly and simplification of three-dimensional models.
- LOD Leveo of detail Work I've done for the Master of Graphical Programming, Games and Virtual Reality taught in URJC

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