KEYWORDS

MT (Multi-Tesselation)

A multiresolution model for spatial objects represented as k-dimensional simplicial complexes (here called tesselations) embedded in d-dimensional space, for generic k and d.

Extractor

An engine which extracts tesselations at variable resolution from an MT according to user-defined requirements.
An extractor can be either global (static or dynamic) or local.

Extraction conditions

User-defined functions used within an extractor for expressing: They are boolean functions answering the questions: "is the resolution of this tile sufficient?" and "is this tile an interesting one?", respectively. We call:

Global extractor

It extracts a tesselation covering the whole object, such that the resolution filter condition is satisfied by every active tile: "The resolution of every interesting tile is sufficient". The resolution of other tiles is as coarse as possible compatibly with the constraint that active and non-active tiles must glue together with continuity into a tesselation.

A global extractor is either static or dynamic:

Local extractor

It extracts a tesselation covering just the part of the object which is of interest for the focus condition (thus, a tesselation made up of active tiles only), such that all tiles in it are feasible.
It is convenient when the area of interest is a small portion of the object.

Building Interface

An MT is built from the sequence of update operations performed on a tesselation during an iterative process of refinement or coarsening. Examples are, for triangulations, refinement processes based on vertex insertion, coarsening processes based on either edge collapse or vertex decimation.

The building interface provides a set of functions which must be called within a program for iterative refinement or coarsening of a tesselation, in order to build the corresponding MT.

Attributes

Additional information (beside tile vertices and vertex coordinates) that can be associated with the tiles and the vertices of an MT. Attributes are application dependent. For instance: field values, approximation errors, surface normals, colors, etc.

Attributes remain attached to the vertices and tiles of tesselations extracted from an MT, and may be useful in processing such tesselations by the application programs (e.g., colors and normals for rendering).
They may also be used within extraction conditions to decide when a tile is feasible (e.g., based on its approximation error) or active (e.g., when it contains a certain field value).

Attributes can be explicitly stored in tables associated with an MT (see Attribute Table below), or derived from geometry (e.g., bounding box, volume...)

Attribute Table

A structure which stores, for each vertex or tile of an MT, a value of a certain type, representing the attribute of that vertex or tile.