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8/13/2019 L33_solidmother

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Solid Modeling Techniques

Sweep Representation

Analytical Solid Modeling (ASM)

AML710 CAD LECTURE 33

Sweep Representation Two and a half dimensional objects: The following two categories

of solids are considered of this kind.

Solid of uniform thickness Extruded solid

Axisymmetric solids Solids of revolution

The first kind is called Linear Sweep and the second kind is calledrotational sweep

Sweeping is used to create objects for B-rep and CSGrepresentations. Thus it becomes an input option in many types ofrepresentations.

There is no modeler entirely based on sweeping for the followingreasons:

Limited domain

No formal theory

Validation and regularisation schemes are unknown


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Types of Sweep Representation

Linear Sweep Circular sweep

(1)(OP)(2) set operations3. Hybrid

Higher order curves2. Nonlinear

Linear or circular1. Linear

PathClosed Profile

directrix

Profile

Types of Sweep Representation

Hybrid SweepNonlinear Sweep

A

Bb

c

d

d

directrix

Invalid Sweep

A-*B


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Basic Elements

Primitives: All 2-D contours are valid primitives. Lines,

arcs, circles and B-splines are widely used.The contour can be nested up to one level.

Building Operations: Generate the contour (profile) and apath curve (directrix). Sweep the profile along the pathcurve

Valid 2-D profile

for sweep, nestedup to one level Invalid 2-D profilefor sweep, nested

more than 1 level

Analytical Solid Modeling (ASM)

The method has its origin in FEM. The ASM followssimilar approach as three dimensional isoparametricformulation in FEM.

E.g. 8 noded hexahedron or 20 noded hexahedron

ASM is mainly for design applications and not suited formanufacturing.

It does not involve orientable surfaces as in B-rep andCSG

Applications: 1. Mass property calculation

2. Composite material modeling

3. Computer Animation

4. FEM mesh generation with hyperpatch concepts.

E.g. PATRAN-G is based on ASM and has interface to various FEApackages.


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Basic RepresentationASM is an extension of bi-parametric surface representation to three-

dimensional parametric space. Tensor product method is used asused in the case of surfaces. One can think of ASM solids astricubic, Bezier and B-spline solids analogous to bicubic, Bezier andB-spline surfaces in 2-D parametric space(u,v) and analogous tocorresponding types of curves in one-dimension (t).

u

w

v

x

z

y

Parametric spaceObject space

Hyperpatch

Parametric SolidsHyperpatch: The parametric solid is called hyperpatch as it is extension

of and bounded by surface patches. The points in the interior and onthe boundary of the parametric solid is given by

u

w

v

x

z

y


Hyperpatch

maxminmaxminmaxmin ;;

)],,(),,(),,([][),,(

wwwvvvuuu

wvuzwvuywvuxzyxwvuP

==


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Cubic HyperpatchBuilding Operation: The object is divided into hyperpatches. The

hyperpatches are represented using surfaces and curves.A cubic polynomial in each parameter is sufficient for most practical

applications

u

w

v

x

z

y


Hyperpatch

10;10;10),,(4

1

4

1

4

1

111=

= = =

wvuwvuCwvuP

i j k

kji

ijk

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