Presentation On Exhaustive Enumeration in Solid Modeling

Ambrish Singh (CIM/15/R/)Kapil Verma (CIM/15/R/11)Rahul Modi (CIM/15/R/)Branch- CIM (IPE Dept.)

Computer Aided Design Computer Aided Design (CAD)- Use of computers to

assist with the design process NC Machining (‘50s) introduced a need for numerical part

models to drive the machines Drafting using computers became a reality when graphics

were added (CAD used to mean computer aided drafting) Finite Element Analysis (FEA) became popular in late

‘60s

Interactive Graphical User Interfaces (GUIs) made FEA programs much more productive and accessible

CAD has a wide variety of applications, including system modeling and synthesis, kinematic simulation and design, and optimization

Modeling MethodsI Geometric Modeling

A) Graphical Modeling (used for drafting)1) 2-D Graphical Modelers2) 3-D Graphical Modelers

B) Surface Modeling1) Parametric Surfaces2) Ruled Surfaces

C) Solid Modeling1) Decomposition2) Constructive3) Boundary

II Feature Based Modeling- Introduces features to betterstore and communicate design information

Solid Modeling Objects are defined as a solid mass.

May contain information about the density , mass, moment of inertia, volume and center of gravity of the object.

Solid Modeling features:

•Complete representation

•unambiguous description

•Appropriate for the world of engineering objects.

Solid models can be used for:-Volume calculations.

-Automatic Finite Element mesh generation.

-Collision determination in robotics or NC path generation.

Solid Modeling Entities

Construction Solid Geometry (CGS): Solid Primitives Boolean OperationBoundary Representation (B Rep): Geometric Entities Topological Entities

Sweep Representation: Translation sweep (Extrusion) Rotational sweep (Revolution)Decomposition Modelinga)Exhaustive Enumeration: All space is evenly blocked out & a 3D matrix stores information on the material (or lack of) in each block.

b) Cellular Decomposition: Irregular cells block out only the object. c) Space Subdivision: Recursively block out all space.

Exhaustive Enumeration

Special case of decomposition where primitives are cubical in shape

Uniformly-sized volume elements called voxels

Used extensively in computer graphics and medical graphics

Efficient but requires significant storage

Accuracy limited unless voxels are extremely small

Representation of Solid by Voxels

Use of Voxel Representation In Casting

Relatively Heavy Region Heaviest Region

Cellular Decomposition

• Represent solid as a combination of irregular cells that are pasted together over common faces

Ex: FEA

Representation of Space Subdivision

Each block has either one material type, no material, or is defined by smaller blocks

Figure AFigure B

Figure C Figure D

= exterior= interior= interior

Application of Exhaustive Enumeration

• Underwater environment representation.

• Finite elements meshing (first step in an algorithm to build such a mesh).

• Medical 3D data representation.

• Preprocessing representation for speeding up operations on other representations (eg. approximating integral properties such as volume, center of gravity, moments of inertia, distance transforms).

Summary of CAD/CAM

CAD

• Geometric based model

- Graphical Modeling

- Surface Modeling

- Solid Modeling

• Feature based model

CAM

• Tooling Operations/codes

Thanking You