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3D modeling systems,lecture topics:

terminology used in examining and

comparing systems

applying geometric modeling (especiallysolids) to engineering design

introduction to solid concepts

3D models create analogousrepresentations of an object.

Analogous implies similar, but different.

Therefore, 3D models are very similar tothe real world objects they arerepresenting but not necessarily identical.

Model is an approximation ofreal object.

Term for the quality of approximationis faithfulness.

Faithful model incorporates thoseattributes necessary to the design or tothe analysis being performed.

A model need not include all physical

real world features to be faithful

Model database

As previously noted, the heart of ageometric model is the model database.

The database can be considered as anorganized form of the information whichdescribes the model.

Database information for solids dividedinto two general categories, geometric

and topological.

Geometry

Geometric data relates to dimensionalinformation, e.g.

the location of points in space

the shape and size of geometric features.

Topology

Topology: refers to the connectivity ofthe elements which make up the model,

e.g. two faces intersect at an edge

Inclusion of topological data makessolid models computationally verifiable.

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Two objects with the sametopology but different

geometry.

Data format

model data may be stored:

explicitly (evaluated data)

Complete mathematical entity definitions arestored in the database

or implicitly (unevaluated data)

Definitions not stored, but rather computed asneeded

For example, the curve defined by intersectionof two surfaces or

an edge computed for display, then discardedwhen not needed (recomputed at next display)

Data / Format

In practice, database not strictlyevaluated or unevaluated but some

combination

Primary vs. Secondary models

Systems typically maintain multiple data

representations

The data used by fundamental modelingoperations is the primary model

Other representations (which may ormay not be solid) are referred to assecondary models

Secondary models

Secondary models derived from primarymodel for use is specific applications:

display, analysis (FEA), manufacturing,documentation (drawings), data exchange

Secondary models are maintained toreduce regeneration times when modelsare required.

Some modelers maintain a log of stepsperformed. This log may be considereda secondary model.

Associativity

One form of associativity is the directconnection of primary to secondary

models. Associativity can permit alteration of

one model when another is modified

e.g. top-down associativity: alter primary,secondary documentation file changes

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Associativity

An example of this would be the updateof display information when a change to

model geometry is made.

This concept (associativity) alsoappears in the relationship between

parent and child geometry and in theextraction of mechanical drawings froma solid model.

Model evaluation factors:

domain and expressive power

uniqueness

validity.

Domain and Expressivepower

domain refers to the range of modelgeometries which may be generated bya particular modeler.

some modeling system supply the userwith broader domain

expressive power: is the primary model

exact or approximate representation?

Uniqueness

Concept of singularity between modeland database

Two types of uniqueness may beconsidered.

Interpretation: Can the database representmore than one object.

Expression: Can more than one database

represent the same object?

Validity

whether or not the model represents anobject which can exist in the real world.

many solid modeling systems includechecks of model validity in theirarchitecture.

validity checks often involve topologicalchecks

Manifold vs.Non-manifold geometry

Mathematically manifold geometrymeans every point on a surface hasneighborhood (infinitesimal sphere)

around it that can be deformed onto alocally planar surface.

More simply: manifold geometry rulesout objects which are not physicallyrealizable such as those with featuresjoined along a single edge or vertex.

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Non-manifold geometry Manifolds in solid modeling

Class of manifolds comprises real

world, manufacturable objects.

When computationally modeling solids,is possible to create non-manifolds.

One case would be a self-intersectingmodel.

Software may perform diagnosticchecks but user should be aware ofwhat non-manifold geometry is.

Solid Modeling

Just as a set of 2D lines and curvesdoes not need to describe the boundaryof a closed area, a collection of 3Dsurfaces and planes does notnecessarily bound a closed volume.

Solid Modeling

Many engineering applications ofgeometric modeling require the ability todistinguish between the inside, outside andsurface of an object.

Several techniques for the computerizedmodeling of solid geometries exist and arein use today.

The various techniques have differentadvantages disadvantages and uses.

Solid Modeling

What properties are considered important forof an effective solid modeling system

Bounded - the boundary must limit and contain the

interior of the solid. Finite - Finite in size, model can be defined by a

limited set of information

Homogeneously 3-dimensional or more simply, nodangling faces or edges, boundary must alwaysbe in contact with the interior