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# KP3213 CAD/CAM - PowerPoint PPT Presentation

KP3213 CAD/CAM. Lecture 3 snap shot Objective of Lecture 4 Lecture 4: Curve representation and solid modelling Book review of week 2 & 3. Curve Representation. Curve Representation. Curve Representation. Coordinates are given by continuous parameter single valued

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Presentation Transcript
• Lecture 3 snap shot
• Objective of Lecture 4
• Lecture 4: Curve representation and solid modelling
• Book review of week 2 & 3

### Curve Representation

Curve Representation

Coordinates are given by continuous parameter single valued

polynomial X=x(u), Y=y(u) and Z=z(u). Variable u is constraint

By Closed interval such as [0,1]

Rapid Prototyping (RP)
• Physical model that directly represents component.
• Based upon layered manufacturing concept
• 3D CAD decomposed into cross-sectional representations of small thickness
• Sequence
• A CAD model constructed and converted to STL (standard triangular language)
• Model sliced.
• First layer created, model lowered by one layer until completion
• Model and supports removed. Surface is cleaned.

Technologies Involved

• Stereolithography / photolithography
• Selective Laser Sintering
• 3-D Printing
• Laminated Object Manufactruing (LOM)
• Fused Deposition Model

### Solid Modelling

3-D SOLID MODEL

3-D solid model captured complete geometry of an object

-inside and outside of the object

-volume and intersection of the object can be calculated

-Hidden-surface/line removal and a shaded image can be produced

Internal representation vs external representation

Internal representation is how computer stores the model.

External representation is how picture or image is displayed

Approaches
• Constructive Solid Geometry (CSG)
• Boundary Representation (B-rep)
• Pure Primitive Instancing - Parametric model
• Spatial Occupancy Enumeration - model of fixed size spatial cells
• Cell Decomposition - model of variable spatial cells
• Hybrid (feature-based modellers)
Constructive Solid Geometry (CSG)
• Based on simple geometric primitives
• boxes, cones, spheres, etc.
• Primitives are positioned and combined using boolean operations
• difference (subtraction)
• intersection
• Represented as a boolean tree

C

A

(A-B)  C

B

A-B

CSG Example
Boundary Representation (B-Rep)
• Solids represented by faces, edges and vertices
• Topological rules must be satisfied to ensure valid objects
• faces bounded by loop of edges
• each edge shared by exactly two faces
• each edge has a vertex at each end
• at least 3 edges meet at each vertex
• Euler’s rule applies: V-E+F=2
• Surface must be closed

Edges

Vertices

Faces

B-Rep Example

BOUNDARY MODEL

12

Geometry and Topology

8

13

6

7

1

2

4

object

9

5

3

10

11

14

Face

F1

F2

F3

F4

F5

F6

F7

F8

F9

F10

F11

F12

F13

F14

face

equation

Loop

L1

L3 L4

. . .

E5 E6 E7 E8 E10

E1 E2 E3 E4

. . .

Edge

V5 V6 V7 V8 V10

V1 V2 V3 V4

Vertices

. . .

CSG

Simple representation

Limited to simple objects

Stored as binary tree

Difficult to calculate

Rarely used anymore

B-Rep

Flexible and powerful representation

Stored explicitly

Can be generated from CSG representation

CSG vs. B-Rep
Feature-Based Modelling
• Parts modelled by adding features to a base part
• Features represent manufacturing “operations”
• holes, ribs, fillets, chamfers, slots, pockets, etc.
• Material can be added or subtracted, similar to CSG
• Features are not limited to simple primitives, and can be created by extrusion, sweeping, revolving, etc.
• A history tree is created, similar to a CSG boolean tree
Example

Slot

Fillets

Shell

Hole

History Tree

Final Part

Increasing

part

complexity

Part3

Shell

Part2

Hole

Part1

Fillets

Features

Base

Slot

Modifying Parts
• The part is created from the history tree
• Features can be added, deleted and re-ordered
• Feature dimensions can be changed
• Feature parameters can be changed
• eg. From protrusion to cutout
Book Review for Week 2