SOLID MODELING
Marcelo Bernal, Design Computing PhD Student. COA. GA Tech.
Abstract.
Since the early days the computer has been defined as an environment where represent
objects through models. The primary challenges were related to represent such objects
and develop series of techniques to manipulate them throughout design processes.
Some of the current challenges refer to improve geometry control, to explore interactive
techniques of design, and to administrate incremental amount of digital information. This
is a review of such solid modeling foundations and some emergent questions about the
next steps in CAD design.
Model.
Kalay Y, points out that the primary function of a model is to represent in the computer’s
memory an artifact or environment, in order to reason and operate about something
which doesn’t exist in reality. Models help designers and engineers to visualize,
evaluate, and optimize them, also are a significant source of documentation. Some
models are oriented to specific application, like energy analysis, and other more general
are used to do more than one task at a time. Derived from this wide range of application
increasing interoperability between models is being demanded in CAD environments.
Solid model properties.
A solid is a compact set of contiguous points in three dimensional space, it means that
there is a path between any two contiguous points, this doesn’t exclude cavities in the
solid. Solidity is the property to distinguish points which are not part of the solid. The set
of points that form a solid are compact and occupied a finite amount of space. A solid
model must have four basic properties in order to be represented and manipulated in the
computer’s memory.
- Well-formedness, to guaranty the correspondence with the physical object it
represents without ambiguity. The object’s shape is the complete set of point occupied in
the three dimensional space, the object’s surfaces, which enclose it, are only a subset of
the whole set of points. In order to verify the well-formedness of a polyhedron the
mathematician Euler suggested a rule based on the number of elements of a solid
embedded in a sphere. Faces + Vertices – Edges = 2. Further adaptations of such rule
have been made in order to include a wide rage of shapes.
- Completeness, to make the model useful for many applications, it means that it has
the data required explicitly or implicitly for different applications.
- Generality, to allow the model represent a wide variety of objects in three dimensional
space and forms derived from forms it can represent.
- Efficiency, to be implemented and using reasonable amount of resources.
All this four properties must be balanced in order to achieve specific model efficiency
every time.
Methods of solid representation.
There is no a unique method of representation for solids, they differ in terms of data
structure, storage and purposes.
- Spatial array or occupancy enumeration.
It is a simple set of contiguous cubes of fixed size distributed in a three dimensional grid.
The cubic unit is called “voxel”. This representation has two advantages: easy access to
any point in the grid and avoidance of two bodies using the same space. The
disadvantages are lacking of explicit relationship between the part of an object, limited
