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C. Neelima Devi
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UNIT - IComputers in industrial Manufacturing, Product cycle, CAD / CAM hardware, basic structure
CPU, Memory types, input devices, display devices, hard copy devices, storage devices.
UNIT ±II
Computer Graphics: R asterscan graphics coordinate system, database structure for graphics
modeling, transformation of geometry, 3D transformations, mathematics of projections, clipping,
hidden surface removal.
UNIT-III
Geometric Modeling: R equirements, geometric models, geometric construction models, curve
representation methods, surface representation methods, modeling facilities desired.
UNIT-IVDrafting and modeling systems: Basic geometric commands, layers, disply control commands,
editing, dimensioning, solid modeling, constraint based modeling
UNIT ± V
Numerical Control: NC, NC modes, NC elements, NC machine tools, structure of C NC machine
tools, features of Machining center, turning center, C NC part programming : fundamentals, part
programming methods, computer aided part programming.
UNIT ± VIGroup Tech: Part family, coding and classification, production flow analysis, advantages and
limitations, Computer Aided Processes planning, retrieval type and generative type.
UNIT ± VIIMaterial requirement planning, manufacturing resources planning, D NC, AGV, ASR S, Flexible
manufacturing systems ± FMS equipment, system layouts, FMS control.
UNIT ± VIIICIM: Integration, CIM implementation, major function in CIM, Benefits of CIM lean
manufacturing Just-in-time.
JNTU SYLLABUS:
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Geometric Modeling: Requirements, geometric models,
geometric construction models, curve representation methods,
surface representation methods, modeling facilities desired.
JNTU SYLLABUS: UNIT- 3
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LECTURE PLAN ± UNIT-3Lecture
NoTopic Slide No¶S
FROM ----TO
Lecture 1 INTRODUCTION TO GM,REQUIREMENTSOF GM, FUNCTIONS OF GM 6-14
Lecture 2 GEOMETRIC MODELS ± 2D, 2.5D, 3D, WIRE FRAME MODELING 15-22
Lecture 3 SURFACEMODLEING 23-32
Lecture 4 SOLID MODELING 33-41
Lecture 5 GEOMETRIC CONSTRUCTION METHODS 42-48
Lecture 6 GEOMETRIC MODELING APPLIC ATON 49-77
Lecture 7 CURVE REPRESENT ATION METHODS 78-88
Lecture 8 SURFACE REPRESENT ATION MTHODS, MODELING FACILITIESDESIRED.
89-96
SUBJECT TITLE:
UNIT -1
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Introduction to Geometric Modeling
Requirements of Geometric Modeling
Functions of Geometric Modeling
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Geometric modelling refers to a set of techniques
concerned mainly with developing efficient representations of geometric aspects of a design. Therefore, geometric modelling
is a fundamental part of all C AD tools.
Geometric modelling
Geometric modeling is the basic of many applicationssuch as:
Mass property calculations.
Mechanism analysis.
Finite-element modelling.
NC programming.
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R equirements of geometric modelling include:
Completeness of the part representation.
The modelling method should be easy to use by designers.
R endering capabilities (which means how fast the entities
can be accessed and displayed by the computer).
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Total product cycle in a manufacturing environment
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Functions of Geometric Modelling
Design analysis:
± Evaluation of areas and volumes.
± Evaluation of mass and inertia properties.
± Interference checking in assemblies. ± Analysis of tolerance build-up in
assemblies.
± Analysis of kinematics ² mechanics,
robotics. ± Automatic mesh generation for finite element
analysis.
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Functions of Geometric Modelling
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Functions of Geometric Modelling
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Functions of Geometric Modelling
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geometric models.
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3D geometric representation techniques
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Wire-frame ModelingWire-frame modelling uses points and curves (i.e. lines,
circles, arcs), and so forth to define objects.
The user uses edges and vertices of the part to form a
3-D object
Wire-frame model part
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Surface Modeling
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Surface Modeling
Surface modeling is more sophisticated than wireframe modeling
in that it defines not only the edges of a 3D object, but also its
surfaces.
In surface modeling, objects are defined by their bounding faces.
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SURFACE ENTITIES
Similar to wireframe entities, existing CAD/CAM
systems provide designers with both analytic andsynthetic surface entities.
Analytic entities include :
Plane surface,
R uled surface,Surface of revolution, and
Tabulated cylinder.
Synthetic entities include
The bicubic Hermite spline surface,B-spline surface,
R ectangular and triangular Bezier patches,
R ectangular and triangular Coons patches, and
Gordon surface.
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Plane surface. This is the simplest surface. It requires
three noncoincident points to define an infinite plane.
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Ruled (lofted) surface. This is a linear surface. It interpolates
linearly between two boundary curves that define the surface
(rails). R ails can be any wireframe entity. This entity is ideal torepresent surfaces that do not have any twists or kinks.
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S urface of revolution. This is an axisymmetric surface
that can model axisymmetric objects. It is generated by
rotating a planar wireframe entity in space about the axis
of symmetry a certain angle.
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T abulated cylinder . This is a surface generated by
translating a planar curve a certain distance along a
specified direction (axis of the cylinder).
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Bezier surface. This is a surface that approximates given
input data. It is different from the previous surfaces in
that it is a synthetic surface. Similarly to the Bezier curve,it does not pass through all given data points. It is a
general surface that permits, twists, and kinks . The
Bezier surface allows only global control of the surface.
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B-spline surface. This is a surface that can approximate
or interpolate given input data (Fig. 6-9). It is a synthetic
surface. It is a general surface like the Bezier surface but
with the advantage of permitting local control of the
surface.
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Solid Modeling
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Solid Modeling
Solid models give designers a completedescriptions of constructs, shape, surface, volume,
and density.
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In CAD systems there are a number of representation schemes for solid modeling
include:
Primitive creation functions.Constructive Solid Geometry (CSG)
Sweeping
Boundary R epresentation (BREP)
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Primitive creation functions:
These functions retrieve a
solid of a simple shape from
among the primitive solidsstored in the program in
advance and create a solid of
the same shape but of the
size specified by the user.
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Constructive Solid Geometry (CSG)
CSG uses primitive shapesas building blocks and
Boolean set operators (U
union, difference, and intersection) to constructan object.
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Sweeping
Sweeping Sweeping isa modeling function in
which a planar closed
domain is translated or
revolved to form a
solid. When the planar domain is translated,
the modeling activity is
called translational
sweeping; when the
planar region isrevolved, it is called
swinging, or rotational
sweeping .
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Boundary R epresentation
Objects are represented by their bounded faces.
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B-R ep Data Structure
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Component model produced using translational (linear) sweep
(extrusion)
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Component model produced using translational (linear) sweep with taper in
sweep direction
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Component model produced using linear sweep with the sweep
direction along a 3D cur ve
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Component model produced using translational (linear) sweep with an
overhanging edge
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Component produced by the rotational sweep technique
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geometric construction models, curve
representation methods, surface
representation methods, modeling facilities
desired
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Rendering:
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Rendering: Rasterization
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Rendering: Raycasting
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Rendering: Radiosity
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Rendering: Raytracing
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Reverse Engineering of a computer mouse
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Reverse Engineering of a computer mouse
Step 1: Point Cloud Data in Sub Regions
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Step 2: Point Cloud Data after applying Maximum Error Method
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Step 3: Surface fitting to Point Cloud Data
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Step 4: Surface after Cleaning
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Step 5: Computer mouse after Prototyping
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Curve Representation
P t i C R t ti
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Parametric Curve Representation
The x, y, and z coordinate of a point on the
curve are represented respectively as a
single valued function of a same parameter u
of real value:
I = [u0, u1] is called the domain interval of
P(u).
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Examples of Parametric Curves
x = 3u2
y = u3 ±u + 1
z = 2u + 3
f C
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Examples of Parametric Curves
Diff i l G f C
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Differential Geometry of Curves
Scalar and vector functions
- Scalar function: A single valued real
number function of a real number parameter, e.g.
f(u) = u3 ±u + 1 + sin(u)
- Vector function: A vector or a point in 3Dwhose x, y, and z coordinates are scalar
functions of a same parameter, e.g.
Diff ti l G t f C
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Differential Geometry of Curves
Functions of class Cm
- A scalar function f(u) belongs to class Cm
on an
interval I if the mth order derivative of f exists and is
continuous on I. (³Exist´ means the mth order derivativeis defined and not a constantly zero.)
- A vector function f (u) belongs to class Cm
on an
interval I if the mth order derivative of f exists and iscontinuous on I. (³Exist´ means the mth order derivative
is defined and not a constantly zero vector.)
- Examples
Y
Diff ti l G t f C
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Differential Geometry of Curves
Regular curves
- f (u) (uI) is a regular curve if
1. f (u) is of class C1 in I
2. f ¶(u) { 0 for all u in I.
- Example (the circular helix curve)
f (u) = [x(u), y(u), z(u)] = [acos(u), asin(u), bu]
f ¶(u) = [-asin(u), acos(u), b] is a non-zero
vector in -g<u<+g.
Diff ti l G t f C
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Differential Geometry of Curves
What¶s so special with regular curves?- A cusp (³kink´) on a curve
- If f (u) is of class C1, can it have a ³kink´?
- Impossible if it is regular
f·(u)
x
y
f(u)x
y
Diff ti l G t f C
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Differential Geometry of Curves
Definition of arc lengthLet f (u) be defined on interval a e u e b.
a = u0 < u1 < « < un
= b
f 0=f (u0), f 1=f (u1), «,
f n=f (un)
s(Pn) = §|f i ± f i-1|f 0
f 1
f 2 f n-1
f n
Diff ti l G t f C
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Differential Geometry of Curves
How to calculate arc length
- If f (u)=[x(u), y(u), z(u)] is a regular curve on interval
aeueb, its arc length between a and b is:
- Example
f (u) = [x(u), y(u), z(u)] = [acos(u), asin(u), bu],
0eue2T
Diff ti l G t f C
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Differential Geometry of Curves
Arc length as a parameter
- Let f = f (u) be a regular curve on interval aeueb
Define:
Note:
Same curve f, but defined as a function of its arc
length s:
f = g(s).
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Surface Representation
Parametric Surface Representation
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Parametric Surface Representation
The x, y, and z coordinate of a point on the
surface are represented respectively as a
single valued continuous function of two
parameters u and w in a range and.
P(u, w): also called a patch.
[u0, u1]v[w0, w1]: the parameter domain of
P(u, w).
10 uuu ee
10 wuw ee
±±À
±±¿
¾
±±°
±±¯
®
!
),(
),(
),(
,P
wu z
wu y
wu x
wu )(
Component Parametric Patches
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Component Parametric Patches
[u0, u1]v[w0, w1] = [0,1]v[0, 1]
Each of x(u,w), y(u,w),
and
z(u,w) is a continuoussingle-
value function of u and w,
a
component parametric
patch.
They together form a
continuous patch in the
3D
Euclidean space.
Terms of Parametric Patches
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Terms of Parametric Patches
Four corners:
p00=P(0,0), p01=P(0,1), p10=P(1,0), p11=P(1,1)
Four parametric boundary curves:
P(u,0), P(u,1), P(0,w), P(1,w)
Isoparametric curves:
u-constant curve: P(ui,w)
w-constant curve: P(u,w j)
Partial derivatives:
Pu(u, w) = ; Pw(u, w) =
Normal vector:
(u, v) = Pu(u, w) v P
w(u, w)
u
wu
xx ),P(
w
wu
xx ),P(
nÖ
Example of Parametric Patches
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Example of Parametric Patches
A planar patch
x = (c ± a)u + a y = (d ± b)w + b z = 2u + w
Four corners:
p00 = (a,b,0), p01=(a,d,1), p10=(c,b,2), p11=(c,d,3)
Four boundary curves:
P(0,w ) = (a, (d-b)w + b, w ); P(1,w ) = (c, (d-b)w + b, 2 + w );
P(u,0) = ((c ± a)u + a, b, 2u); P(u,1) = ((c ± a)u + a, d, 2u +1) Isoparametric curves:
u-constant curve: ((c ± a)ui + a, (d ± b)w + b, 2ui + w )
w-constant curve: ((c ± a)u + a, (d ± b)w j+ b, 2u + w j)
Normal vector at (u, w ):
(u, w ) = Pu(u, w) v P
w(u, w) = (c-a, 0, 2) v (0, d-b, 1)
nÖ
Example of Parametric Patches
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Example of Parametric Patches
A sphere
nÖ
,, ¼½»¬-
«22TTu ? AT 20,w
x = a + r cosu cosw
y = b + r cosu sinw
z = c + r sinu
(u, w) = ???
(T/2, w) = ???nÖ
Example of Parametric Patches
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Example of Parametric Patches
An ellipsoid
nÖ
,, ¼½»¬-
«22TTu ? AT 20,w
x = x0 + a cosu cosw
y = y0 + b cosu sinw
z = z0 + c sinu
(u, w) = ???
(T/2, w) = ???nÖ
Example of Parametric Patches
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Example of Parametric Patches
A revolution
? A,,10u ? AT 20,w
x = x(u) cosw
y = x(u) sinw
z = z(u)
u = constant curve?
v = constant curve?
(u, w) = ???
(, w) = ???z
nÖ
nÖ(x(u), 0, z(u))
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