Post on 07-Dec-2015
description
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
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
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
wireframe modelling:
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
wireframe modelling:
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
wireframe modelling:
advantages:
• low cost requirement
• less time required
• less memory requirement
• easy to make
geometric modelling
tanveer ahmed
wireframe modelling:
limitations:
• ambiguity
o example that consists of 16 vertices and 32 edges
geometric modelling
tanveer ahmed
wireframe modelling:
limitations:
• ambiguity
• inability to recognize curved profiles
o example: we cannot tell the direction of the opening of the cube
geometric modelling
tanveer ahmed
wireframe modelling:
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
solid modelling – modelling functions:
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
solid modelling – modelling functions:
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
solid modelling – modelling functions:
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
solid modelling – modelling functions:
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
solid modelling – modelling functions:
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
solid modelling – modelling functions:
primitive creative functions
block pyramid
wedge cone
cylinder torus
hemisphere sphere
geometric modelling
tanveer ahmed
solid modelling – modelling functions:
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
solid modelling – modelling functions:
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
solid modelling – modelling functions:
limitations:
• most complex
• computer memory
• require reasonable time