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CNC Technology and Programming seminar

Solid modeling

Presented by: VIPIN

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Solid modeling• For many engineering purposes wire-frame and

surface models are satisfactory.• The increasing application of computers in

engineering analysis, or generation of various engineering information, means that representation of an object should be as complete as possible.

• Solid model representations have been developed and become a predominate form of design representation

• Unlike wire frame and surface models, which contain only geometric data, solid models contain both geometric data and topological information of the corresponding objects.

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Use of solid modeling in design and manufacturing is rapidly increasing because of ,

reduced computing costfast computing hardwareImproved user interfacesSoftware improvementproduces accurate designprovides complete 3‐dimensional definitionimproves quality of designimprove visualizationhas potential for functional automation and

integration.

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MethodsSolid modeling is the most powerful 3D

modeling technique.There are more number of methods

available to generate solid models. Out of which two basic approaches are

important.They are

(1) Constructive solid geometry (CSG).(2) Boundary representation (B-rep.)

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Constructive solid geometry (CSG)

Constructive solid geometry allows a modeller to create a complex surface or object by using Boolean operators to combine objects. The common Boolean operators include set-theoretic intersection (∩), set-theoretic union (∪), and difference (-).

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Constructive Solid GeometryA solid modeler has a library of set of basic element shapes known as primitives like cuboid, cylinder, sphere, cone, wedge, torus etc as shown

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Boolean Operations

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Different ways of constructing the same part using CSG

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Boundary Representation (B-Rep)• Boundary representation models contain

two pieces of critical information, geometry and topology

• B-rep model represents objects by describing the bounding entities.

• It is comprised of faces, edges and vertices of the object are identified.

• These topological items are defined using a Connectivity data structure

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Baumgart’s Winged-edge data structure

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Validation of a B-rep model Euler’s law states that a polyhedron is

topologically valid if the following equation is satisfied,

F-E+V=2

which means that for a polyhedron to be

valid, the number of faces (F), edges (E), and vertices (V) must satisfy this equation

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Advantages of B-Rep over CSG• The B-rep scheme is more widely used

because In CSG the number of basic primitives available are limited.

• The performance of B-rep scheme is very much superior to that of CSG scheme for complex engineering models.

• Conversion of CSG to B-rep is possible, but conversion from B-rep to CSG is not possible.

• Combining the wire frame and surface model is possible only through B-rep solid representation.

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Comparison

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THANK YOU!!!