UNIT-III
GEOMETRIC MODELING
INTRODUCTION
Geometric modeling is a branch of applied mathematical and computational geometry
that studies methods and algorithms for mathematical description of shapes
The shapes studied in Geometric modeling are mostly 2-Dimensional or 3-
Dimensional although many of its tools and principles can be applied to sets of any finite
dimension. Most Geometric modeling is done with computer and computer based
applications. 2-Dimensions models are important in computer typography (The art and
technique of arranging type in order to make language visible) and technical drawings. 3-
Dimensional models are central to CAD and CAD many applied technical fields. Such as
civil, mechanical, architecture, geology, medical image processing.
NEED OF GEOMETRIC MODELING
For manufacturing automobile engine it require around 10,000 drawings models in
various departments with different styles. Once models are prepared using any CAD
software, these models can be used in almost all departments of the organization which
includes-
1. Designing the parts and assemblies and then performing tolerance analysis of the
assemblies
2. Preparation of production drawings of individual parts, subassemblies, assemblies,
tooling and jig-fixtures
3. Making structural, thermal and kinetic analysis
4. Considering volume of parts and after extracting material properties from material
library, cost estimation can be easily done
,5. Process plans are also prepared for all the components
6. Using CAM software’s, we can model as input for CNC programming
7. Programming the movement of the components from one station to another is possible
using various material devices such as robots, conveyors, automated guided vehicles
8. Using coordinate measuring machine (CMM) dimensional and geometric accuracies are
checked by extracting various dimensions and parametric from the models only
9. Other supporting activities such as material requirement and procurement, preparation of
bill of materials, manufacturing resource requirement, planning and scheduling, analysis
With competitions products etc are also possible once geometric models are available
thus for all these activities, geometric models becomes the central that will be manipulate at
all these storages. While modeling, geometric models are prepared in such a way that the
other modules such as CAM, CAE, Mechanism systems are able to use this information in
the most optimal and efficient way.
REQUIREMENTS OF GEOMETRIC MODELING
The requirement of geometric modeling is manifold. The conceptual design is the
basis of the generation of geometric model. The choice of the geometric model depends on
the mechanical functions to be performed by it. A valid geometric model is created by CAD
system and its model database is stored. The database of geometric modeling is used for
engineering analysis and for design optimization. Design testing and evaluation may
necessitate changing the geometric model before finalizing it. When the final design is
achieved, it is documented and used for subsequent manufacturing applications, quality and
cost analysis.
Good geometric model is designed based in the following important guidelines-
1. Modeling method must be easy to use
2. Completeness of part representation
3. Representation should be able to represent a useful set of geometric objects
4. Model should not create any ambiguity (The ability to express more than one
interpretation) to users. A given representation should correspond to one and only one
solid
5. To represent the solid normally there should only unique way. With this one can compare
two identical solid representations
6. A geometric model must be very accurate. There should not be any approximation
7. Geometric modeling should not create any invalid or impossible models
, 8. The various transformations such as move, rotation, scale etc and manipulations such as
union, intersect, subtract etc should able to be performed on geometric model
9. A good representation should be compact enough for saving space and allow for efficient
algorithms to determine desired physical characteristics
10. Geometric model should have shading and rendering (Generation an image for a model
by means of a computer program) capability to give realistic effect to the model
GEOMETRIC MODELS
The geometric models are broadly classified on the basis of geometric construction
into the following categories
1. Two Dimensional (2D)
2. Three Dimensional (3D)
Two Dimensional (2D)
The 2D modeling includes the construction of geometrical faces, plane drawings, 2D
views (Top, Front, Right, and Light views) of objects. Presently, the application of 2D model
is limited to drafting, sheet metal manufacturing, Spot welding, Laser cutting etc.
Three dimensional (3D)
The 3D modeling is widely used for engineering applications. It provides all the
information required for animation, design analysis and manufacturing. The 3D objects are
shown in below figure.
GEOMETRIC MODELING
INTRODUCTION
Geometric modeling is a branch of applied mathematical and computational geometry
that studies methods and algorithms for mathematical description of shapes
The shapes studied in Geometric modeling are mostly 2-Dimensional or 3-
Dimensional although many of its tools and principles can be applied to sets of any finite
dimension. Most Geometric modeling is done with computer and computer based
applications. 2-Dimensions models are important in computer typography (The art and
technique of arranging type in order to make language visible) and technical drawings. 3-
Dimensional models are central to CAD and CAD many applied technical fields. Such as
civil, mechanical, architecture, geology, medical image processing.
NEED OF GEOMETRIC MODELING
For manufacturing automobile engine it require around 10,000 drawings models in
various departments with different styles. Once models are prepared using any CAD
software, these models can be used in almost all departments of the organization which
includes-
1. Designing the parts and assemblies and then performing tolerance analysis of the
assemblies
2. Preparation of production drawings of individual parts, subassemblies, assemblies,
tooling and jig-fixtures
3. Making structural, thermal and kinetic analysis
4. Considering volume of parts and after extracting material properties from material
library, cost estimation can be easily done
,5. Process plans are also prepared for all the components
6. Using CAM software’s, we can model as input for CNC programming
7. Programming the movement of the components from one station to another is possible
using various material devices such as robots, conveyors, automated guided vehicles
8. Using coordinate measuring machine (CMM) dimensional and geometric accuracies are
checked by extracting various dimensions and parametric from the models only
9. Other supporting activities such as material requirement and procurement, preparation of
bill of materials, manufacturing resource requirement, planning and scheduling, analysis
With competitions products etc are also possible once geometric models are available
thus for all these activities, geometric models becomes the central that will be manipulate at
all these storages. While modeling, geometric models are prepared in such a way that the
other modules such as CAM, CAE, Mechanism systems are able to use this information in
the most optimal and efficient way.
REQUIREMENTS OF GEOMETRIC MODELING
The requirement of geometric modeling is manifold. The conceptual design is the
basis of the generation of geometric model. The choice of the geometric model depends on
the mechanical functions to be performed by it. A valid geometric model is created by CAD
system and its model database is stored. The database of geometric modeling is used for
engineering analysis and for design optimization. Design testing and evaluation may
necessitate changing the geometric model before finalizing it. When the final design is
achieved, it is documented and used for subsequent manufacturing applications, quality and
cost analysis.
Good geometric model is designed based in the following important guidelines-
1. Modeling method must be easy to use
2. Completeness of part representation
3. Representation should be able to represent a useful set of geometric objects
4. Model should not create any ambiguity (The ability to express more than one
interpretation) to users. A given representation should correspond to one and only one
solid
5. To represent the solid normally there should only unique way. With this one can compare
two identical solid representations
6. A geometric model must be very accurate. There should not be any approximation
7. Geometric modeling should not create any invalid or impossible models
, 8. The various transformations such as move, rotation, scale etc and manipulations such as
union, intersect, subtract etc should able to be performed on geometric model
9. A good representation should be compact enough for saving space and allow for efficient
algorithms to determine desired physical characteristics
10. Geometric model should have shading and rendering (Generation an image for a model
by means of a computer program) capability to give realistic effect to the model
GEOMETRIC MODELS
The geometric models are broadly classified on the basis of geometric construction
into the following categories
1. Two Dimensional (2D)
2. Three Dimensional (3D)
Two Dimensional (2D)
The 2D modeling includes the construction of geometrical faces, plane drawings, 2D
views (Top, Front, Right, and Light views) of objects. Presently, the application of 2D model
is limited to drafting, sheet metal manufacturing, Spot welding, Laser cutting etc.
Three dimensional (3D)
The 3D modeling is widely used for engineering applications. It provides all the
information required for animation, design analysis and manufacturing. The 3D objects are
shown in below figure.
