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Which shape this wire frame drawing produces is arbitrary !

DQ:16.2.2 Surface Description

•The geometry is described with polygons which should represent an entire surface of an object.

•Generally these polygons do not indicate which side a volume lies on, but inside/outside is defined with tricks like defining polygon vertices so that counter-clockwise is out.

•STL is a good example of an engineering use of this surface representation.

•This method is also used in computer games where speed is important, and the overhead of the

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full solid information is not desired.

•Advantages,

-gives appearance of solids.

-well known, and fast software and hardware for drawing.

•Disadvantages,

-because objects are not solid, they may be subject to ambiguities

-hard to pass data to other systems, like FEA

-not well suited to CAD

-polygon selection is problematic

•Commonly used in graphics packages like HOOPS, PHIGS, CORE, etc. Also acts as the basis for the SGI computer graphics.

•An example of the polygon meshes is given below.

V3

P2

P1

V1

V4

• We can also define these geometries using edge meshes.

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•This still bears a remote resemblance to Surface Modelling.

•Major differences are that,

-inside/outside is defined for each surface

-the edges, and vertices of touching faces are defined

•Advantages,

-can store very complex geometries

-easy to propagate changes to faces, edges and vertices

-can easily generate and store complex surfaces

-many systems support this method, such as PARASOLIDS, ACIS, etc.

-can be used to mimic CSG

•Disadvantages,

-high Level information is still not present in model

-requires a powerful computer

-hard to recognize some simple features like a block

•A BRep object is pictured below,

•Each feature in a B-Rep object can be varied independently

•Geometry is kept in parallel with the object topology. One example of a data structure is seen below.

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Vertex Points Vertex

• A common data focus uses the edges of an object to define the shape (vertices and faces can also be used)

Winged-edge data structure

E F2

F1

successor 2

predecessor 1

•Euler operations can be used to build an object.

•We can check to see if the solid model is valid using the basic Euler equation, or the more involved Euler-Poincare tologoical equation. These equations must be satisfied for the models to be valid.