8/10/2019 Unit 4 CAD

1/45

Unit 43D Graphics:

1. Polygon surfaces-Polygon mesh representations,2. Quadric and Superquadric surfaces

3. Blobby objects;

4. Solid modeling-Solid entities, Fundamentals of Solid

modeling-Settheory, regularized set operations; Halfspaces,

5. Boundary representation,

6. Constructive solid geometry,

7. Sweep representation,

8. Color models9. Application commands for AutoCAD & ProE software

8/10/2019 Unit 4 CAD

2/45

8/10/2019 Unit 4 CAD

3/45

Geometric modeling

8/10/2019 Unit 4 CAD

4/45

8/10/2019 Unit 4 CAD

5/45

8/10/2019 Unit 4 CAD

6/45

8/10/2019 Unit 4 CAD

7/45

8/10/2019 Unit 4 CAD

8/45

Polygon mesh

A polygon mesh or unstructured grid is acollection of vertices, edges and faces thatdefines the shape of a polyhedral object in 3Dcomputer graphics and solid modeling. The

faces usually consistof triangles, quadrilaterals or othersimple convex polygons, since thissimplifies rendering, but may also becomposed of more general concave polygons,or polygons with holes

8/10/2019 Unit 4 CAD

9/45

Key points of Polygon Mesh

polygon meshes is a large sub-field of computer graphics andgeometric modeling.

Different representations of polygon meshes are used for differentapplications and goals.

The variety of operations performed on meshes may include

Boolean logic, smoothing, simplification, and many others. Networkrepresentations, "streaming" and "progressive" meshes, are used totransmit polygon meshes over a network.

meshes are distinct from polygon meshes in that they explicitlyrepresent both the surface and volume of a structure, whilepolygon meshes only explicitly represent the surface (the volume isimplicit).

As polygonal meshes are extensively used in computer graphics,algorithms also exist for Ray tracing, collision detection, and rigid-body dynamics of polygon meshes.

8/10/2019 Unit 4 CAD

10/45

8/10/2019 Unit 4 CAD

11/45

8/10/2019 Unit 4 CAD

12/45

8/10/2019 Unit 4 CAD

13/45

8/10/2019 Unit 4 CAD

14/45

Information table of mesh modeling:-

1. Geometrics Table

2. Attributes Table

1. Geometrics Table:- Its contains the information like vertexcoordinate ,and other parameter to define the shape and orientation of

the polygon surface.

Geometric table consist of:

Vertices

Edges

Faces

Edge

Face

Vertex

Polygon

8/10/2019 Unit 4 CAD

15/45

Elements of mesh modeling

Objects created with polygon meshes must store different types of elements.

These include vertices, edges, faces, polygons and surfaces. In many applications,

only vertices, edges and either faces or polygons are stored.

8/10/2019 Unit 4 CAD

16/45

A vertexis a position along with other information such ascolor, normal vector and texture coordinates.

An edgeis a connection between two vertices.

A faceis a closed set of edges, in which a triangle facehas

three edges, and a quad facehas four edges. A polygonis a set of faces. In systems that support multi-

sided faces, polygons and faces are equivalent. However,most rendering hardware supports only 3- or 4-sided faces,so polygons are represented as multiple faces.

Mathematically a polygonal mesh may be considered anunstructured grid, or undirected graph, with additionalproperties of geometry, shape and topology.

8/10/2019 Unit 4 CAD

17/45

.

Modelling the Elegant Teapot

8/10/2019 Unit 4 CAD

18/45

Polygon Meshes

VERTEX TABLE

V1: x

1, y

1,z

1

V2: x2, y2,z2

V3: x

3, y

3,z

3

V4: x

4, y

4,z

4

V5: x

5, y

5,z

5

EDGE TABLE

E1: V

1, V

2

E2: V2, V3E3: V

3, V

1

E4: V

3, V

4

E5: V

4, V

5

E6: V

5, V

1

POLYGON TABLE

P1: V

1, V

2, V

3

P2: V1 , V3 , V4 , V5

POLYGON TABLE

P1: E

1, E

2, E

3

P2: E

3, E

4, E

5, E

6

or

E1

E2

E3

E5E4

E6

V2

V3

V4

V5

V1

P1 P2

8/10/2019 Unit 4 CAD

19/45

Write down the Geometric table for

fig. given below:-

1

6 7

8

5

4

32

8/10/2019 Unit 4 CAD

20/45

2. Attributes table

Attributes table contains the information

regarding surface characteristics like surface

reflectivity, transparency, texture and other

such characteristics.

8/10/2019 Unit 4 CAD

21/45

8/10/2019 Unit 4 CAD

22/45

Quadric Surfaces

Quadric surfaces describes with the second degreeequation. These are the frequently used class of objectlike spheres, ellipsoids, paraboloids, hyperboloids, tori

etc. General Equation for Quadric surfaces:-

f(x,y,z) =a0x

2+a1y2+a2z

2+a3xy+a4yz+a5xy+a6x+a7y+a8z+a9(A)

U i h di t th

8/10/2019 Unit 4 CAD

23/45

Using homogeneous coordinate the

equation can be represented as:-

F( x, y, z)={x y z}

This 4x4 matrix called discriminant of quadricsurfaces.

Some common quadric surfaces:-

1. Sphere

2. Ellipsoid

3. torus

a0 a3 a5 a6

0 a1 a4 a7

0 0 a2 a8

0 0 0 a9

XY

Z

1

8/10/2019 Unit 4 CAD

24/45

Sphere

Sphere is generate by putting the constant a0, a1,a2=1

and rest of constant equal to zero in the generalequation(A) of quadric surfaces.

Now Equation of Sphere:-X2+ Y2+ Z2=1

or

X2+ Y2+ Z2=R2

X

Y

Z

8/10/2019 Unit 4 CAD

25/45

Ellipsoid

bb X

Y

Z

a

c

b

This is second type of quadric surface which define as theextension of sphere with different radius in three mutually

perpendicular direction.

Equation of Ellipsoid:-

(x/a)2

+ (y/b)2

+(z/c)2

= 1

8/10/2019 Unit 4 CAD

26/45

Torus

Torus can be generated by rotating a circle or some other

conic about certain specific axis.

Equation of Torus:-

+ (z/rc)2=1r-((x/rx)

2 + (y/ry)2)

8/10/2019 Unit 4 CAD

27/45

Super quadric Surfaces

It is the generalization of quadric surfaces and provide

greater flexibility in the generation of complicated

object shapes.

These are developed by adding additional parameterinto quadric surfaces.

Super quadric provided the concept of geometric

modeling .

SQS also provide the method for producing primitives

shapes useful in CSG modeling.

These are truly solid surface.

8/10/2019 Unit 4 CAD

28/45

Example of SQS

Super Ellipse:-

Equation for Super ellipse:-

[ (x/a)(2/1)+ (y/b)(2/1

)]=1

Here is a variable parameter that can be assigned any real

value.

Question:- Develop the shape of super ellipse for the = 1, 1.5,2, 2.5, 3.

Super Ellipsoid:-

Equation :-[(x/a)(2/2)+ (y/b)(2/1)](1/ 2) +(z/c)(2/1)=1Here 1 and 2any real number value.

If 1 = 2, designer get ordinary ellipsoid .

8/10/2019 Unit 4 CAD

29/45

Solid modeling

8/10/2019 Unit 4 CAD

30/45

8/10/2019 Unit 4 CAD

31/45

Solid entities Solid model of an object is created by using the three dimensional geometric entities known

as primitives of solid entities.

8/10/2019 Unit 4 CAD

32/45

In CAD Syll.

CSG(constructive solid geometry)

8/10/2019 Unit 4 CAD

33/45

CSG(constructive solid geometry)

or

C-rep

CSG also known as Building block approach ofsolid modeling

These primitives are connected by the Booleanoperations.

The commonly used Boolean operations areUnion, Difference, and Intersection.

8/10/2019 Unit 4 CAD

34/45

Boolean operations

8/10/2019 Unit 4 CAD

35/45

CSG Tree

1

2

8/10/2019 Unit 4 CAD

36/45

1

2

8/10/2019 Unit 4 CAD

37/45

8/10/2019 Unit 4 CAD

38/45

b

8/10/2019 Unit 4 CAD

39/45

Comparison of CSG and B-rep

8/10/2019 Unit 4 CAD

40/45

Sweep

a

a

a

8/10/2019 Unit 4 CAD

41/45

Extrude and Revolve

2

3

3

2

A li ti f S lid M d li

8/10/2019 Unit 4 CAD

42/45

Application of Solid Modeling

8/10/2019 Unit 4 CAD

43/45

Blobby Object

Some object do not consist a fixed shape, theytends to change their shape in differentcircumstances ,these circumstances may be

working environment, some action of anyexternal force etc.

These changes are occurs due to change in themolecule structure of the object, this behavior

of the object is known as Blobbiness andobject called Blobby Object.

8/10/2019 Unit 4 CAD

44/45

Example of Blobby objects

Freely fall water droplet.

Melting Substance.

Breaking and isolation of molecules.

When the person flexes his muscle, shape of

muscles change.

8/10/2019 Unit 4 CAD

45/45

Water

Drop

Isolation

ofMolecules

Example of Blobby Object