Introduction to virtual engineering

Introduction to virtual engineering

Óbuda UniversityJohn von Neumann Faculty of Informatics

Institute of Intelligent Engineering Systems

Lecture 2.

Description of shapes in model space

László Horváth university professor

http://nik.uni-obuda.hu/lhorvath/

Definition of shape by its boundary

Basic groups of shapes to be described

Problem of boundary representation of shape

Topological and geometrical entities

Shape independence of topology

Topological consistency

Geometry: creating a curve

Geometry: creating a surface

Contents

László Horváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

Definition of shape by its boundary


Linear Curved

Free formAnalitical Generated according to predefined rule

F1

F2

G1

Complex surface

Basic groups of shapes to be described


F1

F2

F1

F2

G12

G1G2

L1

L2

F1

Connections of surfaces at intersection curves are to be described.

Method:Topology(Euler)

Problem of boundary representation of shape


V

E F

V = vertex

L = loop, ring

E = edge,

P = point

G12

C = curve

F = face S = Surface

coedgeShell

Consistent(complete)

Shell + material = body

Topological and geometrical entities (1)


Prism – box = four prismatic segment

Combination of solids Topology

Body = four lumps

Topological and geometrical entities (2)


Same topology for three different shapes

Same structure

Shape independence of topology


Euler ruleLeonhard Euler (1707-1783) swiss mathematican.

Euler number for boundary of body: V - E + F

Euler number is a constant V - E + F = C.

For simple bodies ( no through holes or separated bodies (lumps) V - E + F = 2

Topological consistencyComplete topology. Check by using of topological rules.

Three or more edges must run into a vertex.

Face must be enclosed by a closed chain of edges.

Edge is included always in two loops for adjacent faces.

Topological consistency (1)


V-E+F=8-12+6=2 V-E+F=10-15+7=2 V-E+F=2-3+3=2

Topological consistency (2)


Task Method

Through specified points Interpolation

Controlled by specified points Approximation

P0

P1

P2

P3

According to specified rule Analitical

Geometry: creating a curve


Contour

Generator

Meridian curve

Axis

Direction ofrotation

Extension angle= 360o

Tabulated surface Rotational surface

Geometry: creating a surface (1)


Generator curvePath curve

Spine

JointProfil curves

Boundary curves

Control of shape at the creation of a swept surface

Geometry: creating a surface (2)


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Introduction to virtual engineering