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:
- the resolution requirements that an extracted tesselation must
satisfy (resolution filter condition)
- a subset of tiles on which to focus the attention in generating
the extracted tesselation, e.g., those tiles lying within a certain
area of interest (focus condition)
They are boolean functions answering the questions: "is the resolution of
this tile sufficient?" and "is this tile an interesting one?", respectively.
We call:
- feasible tile a tile satisfying the resolution filter condition
- active tile a tile satisfying the focus condition
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:
- a static extractor recomputes a new tesselation by scratch at
each extraction query (represented by a resolution filter and a
focus condition);
- a dynamic extractor computes the solution of a new extraction
query by modifying the solution of the previous query; convenient when
extraction conditions change gradually, and thus the new tesselation is
expected to be very close to the previous one.
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.