lec4.1

geometric modelling

by

Assistant Professor Tanveer Ahmed

geometric modelling

tanveer ahmed

the process of constructing a complete mathematical description (geometric database)

to model a physical entity or system

geometric modelling

tanveer ahmed

traditional approach:

traditionally prototypes were used for information

geometric modelling

tanveer ahmed

traditional approach:

traditionally prototypes were used for information

engineering drawings

geometric modelling

tanveer ahmed

current approach:

presently design concepts are simply (digitally) fed into software

which subsequently displayed either in 2D or 3D forms

a general term applied for 3D

Computer-Aided Design (CAD) techniques

geometric modelling

tanveer ahmed

current approach:

presently design concepts are simply (digitally) fed into software

which subsequently displayed either in 2D or 3D forms

a general term applied for 3D

Computer-Aided Design (CAD) techniques

geometric models are computational (symbol) structures that capture the spatial aspects of

the objects of interest for an application

geometric modelling

tanveer ahmed

need to represent:

shape

appearance (color, shininess etc)

material properties (density, stiffness etc)

geometric modelling

tanveer ahmed

creating symbolic models of the physical world has long been a goal of mathematicians,

scientists and engineers

recently technology has advanced sufficiently to make computer modelling of physical

geometry feasible

engineering modelling:

modelling for engineering applications require higher accuracy of representation

engineering models are used in computer-based design, manufacturing and analysis

geometric modelling

tanveer ahmed

ideas

design

analysis

production

geometric

modelling

geometric modelling

tanveer ahmed

geometric modelling is a basic engineering tool

geometric modelling

tanveer ahmed

geometric modelling is a basic engineering tool

serves as the backbone of design shadows the design process

geometric modelling

tanveer ahmed

engineering modelling:

feature model =

geometric model + design intent

geometric model =

geometry + topology

design intent =

constraints + rules

geometric modelling

tanveer ahmed

requirements:

evaluation of geometrical properties:

• centroid

• cross-sectional area

• surface area

• volume

evaluation of mass properties:

• mass

• density

• inertia

geometric modelling

tanveer ahmed

requirements:

finite element analysis and optimization:

• complex shapes or geometries

• materials

• loads

volume visualization

animation of graphics:

• obstacle avoidance in robotics

• verification of NC tool paths

• car crash analysis

geometric modelling

tanveer ahmed

requirements:

automatic assembly:

• modelling of assemblies

• assembly sequence

• inference checking

tolerance analysis:

• process planning

• assembly operations

• part inspection

• interchangeable manufacturing

geometric modelling

tanveer ahmed

requirements:

manufacturing:

• generation of part families

• NC code generation

• inventory control

computer-aided inspection and control

geometric modelling

tanveer ahmed

CAD/CAM:

stages

• conceptual design

• mechanical design

• simulation

• production

geometric data need to be shared

geometric modelling

tanveer ahmed

CAD/CAM:

conceptual design

geometric modelling

tanveer ahmed

CAD/CAM:

mechanical design

geometric modelling

tanveer ahmed

CAD/CAM:

simulation

geometric modelling

tanveer ahmed

basic categories of geometric modelling:

2 dimensional

3 dimensional

geometric modelling

tanveer ahmed

coordinate systems:

the coordinate systems and orientation can be

understood using the right-hand convention as

shown in figure

in most CAD packages, there are two coordinate

system notations are used

the fixed or global coordinate system (GCS) used for

overall definition of model, which cannot be re-

orientated

work coordinate system (WCS) which is used to

assist construction of model. it can be redefined as

per requirement i.e. moving individual parts in an

assembly

geometric modelling

tanveer ahmed

categories of 3D geometric modelling:

wireframe modelling

surface modelling

solid modelling

geometric modelling

tanveer ahmed

wireframe modelling:

it is a part of 3D schemes

computationally most simplified approach

the wireframe model is perhaps the oldest way of representing solids

the name arises from wire like appearance of the models when viewed on the

computer screen

it can be referred to as extension of draughting in 3D visualization

the entities used for wireframe model generation are same as used in draughting

geometric modelling

tanveer ahmed


geometric modelling

tanveer ahmed


wireframe model consists of two tables:

• the vertex table

o the vertex table records a vertex and its coordinate values

• the edge table

o the edge table has two components giving the two incident vertices of that

edge

geometric modelling

tanveer ahmed


a wireframe model is created with ordinary lines, circles, arcs, etc., to represent

edges

• only vertex and edge data is stored

• no shading, hidden line removal

geometric modelling

tanveer ahmed


advantages:

• low cost requirement

• less time required

• less memory requirement

• easy to make

geometric modelling

tanveer ahmed


limitations:

• ambiguity

o example that consists of 16 vertices and 32 edges

geometric modelling

tanveer ahmed


limitations:

• ambiguity

• inability to recognize curved profiles

o example: we cannot tell the direction of the opening of the cube

geometric modelling

tanveer ahmed


limitations:

• ambiguity

• inability to recognize curved profiles

• inability to detect interference between components

• difficulty in calculating physical properties

• no facility for automatic shading

geometric modelling

tanveer ahmed

surface modelling:

description corresponding to the visual model includes surface information in

addition to information about characteristic lines and their end points contained in

the wireframe description

model description includes information regarding how adjacent surfaces are

connected at which points (this information is critical for machining operations)

geometric modelling

tanveer ahmed

surface modelling:

model with surface objects

meshes frequently used to represent surfaces

surface, edge & vertex information stored

shading, hidden line removal

useful for modelling shapes with complex

curvature (e.g., hull forms, airfoils,

automobiles)

(10,100,100)

(0,0,0)

Z

Surface Model

6 meshed surfaces

X

Y

geometric modelling

tanveer ahmed

surface modelling:

surface models may be:

• planar

• cylindrical/conic

• sculptured or freeform in shape

geometric modelling

tanveer ahmed

surface modelling:

two major uses of surface modeling systems include:

• visual model: used to evaluate the model aesthetically

• mathematical description: used to generate NC tool paths to machine its surfaces

geometric modelling

tanveer ahmed

surface modelling:

advantages over wireframe modeling:

• ability to recognize and display complex curved profiles

• ability to recognize faces and thus provide the facility of shaded surfaces in 3D

• ability to display very good tool path simulation

• improved robot simulation

geometric modelling

tanveer ahmed

surface modelling:

limitations:

• does not represent internal features of the model, no sense of volume

• models of limited value for volumetric and mass property analysis

geometric modelling

tanveer ahmed

solid modelling:

solid modeling is used to model a shape having closed volume called a solid

main difference from wireframe modeling and surface modeling includes:

• simplified characteristic lines of surfaces are not allowed unless they make a closed

volume

• mathematical information additionally includes information that determines

weather any location is inside, outside or on the closed volume

• consequently machining information is more elaborate

geometric modelling

tanveer ahmed

solid modelling:

model with solid objects (e.g., primitives,

sweeps)

database contains information about

vertices, edges, surfaces and the space

enclosed by the surfaces:

• mass and material properties

• interference checking

shading and hidden line removal

(100,100,100)

(0,0,0)

Z

Solid Model

1 primitive

X

Y

geometric modelling

tanveer ahmed

solid modelling – modelling functions:

the modeling functions (MFs) supported by most solid modeling systems can

generally be classified into five groups:

• primitive creative functions

• moving surface MFs

• modifying shape MFs

• boundary / lower level entities MFs

• customization using familiar shapes

geometric modelling

tanveer ahmed


primitive creative functions

• these include primitive functions that help the designer to get a general shape that

is close to what he finally aims to achieve

• example: we want to make a table. this is the primitive model of the table

geometric modelling

tanveer ahmed


moving surface MFs:

• these include functions such as sweeping and skinning. the surfaces are created by

defining some parameters and revolving the model functions to obtain the

defined surface

• example: the next step of creating the table would include defining the top

through sweeping

geometric modelling

tanveer ahmed


modifying shape MFs:

• these are used to modify some existing shape to get closer to the original design.

these include functions such as rounding, bending, lifting and more

• example: the top would be more clearly defined through rounding or bending

geometric modelling

tanveer ahmed


boundary/ lower level entities MFs:

• lower level entities include vertices edges and faces. manipulating these forms the

4th

type of modeling functions

• example:

geometric modelling

tanveer ahmed


customization using familiar shapes:

• the last step involves customization of the model to achieve the final form.

customization includes using familiar shapes such as chamfer and holes of certain

sizes at certain places

• example: this is considered to be the last stage of solid modeling functions

geometric modelling

tanveer ahmed


primitive creative functions

block pyramid

wedge cone

cylinder torus

hemisphere sphere

geometric modelling

tanveer ahmed


advantages:

• full description of the object, unambiguous

• volumetric shape

• able to distinguish between the interior and exterior of the object

• able to detect unwanted interference between objects

• help to appreciate in the design of:

o 3D kinematic mechanisms

o robot simulations

o complex piping systems

geometric modelling

tanveer ahmed


advantages:

• ability for automatic 3D sections

• ability to use an extensive colour palette and shadow effects, giving improved

visualization of the components

• in addition such modellers can be used in combination with other computer

programs which are specialized on models presentation and thus provide the

image of an object as this will exist in real life

geometric modelling

tanveer ahmed


limitations:

• most complex

• computer memory

• require reasonable time

geometric modelling

tanveer ahmed

overview:

with hidden lines without hidden lines

geometric modelling

tanveer ahmed

overview:

lec4.1

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