2. wire frame model
• A wire frame model is a visual presentation of
a three dimensional object used in 3D
computer graphics.
• The wire frame model representation contains
only vertex and edge information.
• Most of the solid modeling software such as
AutoCad, Proe etc. provided option for
wireframe representation of solid model.
3.
4. wire-frame representation
• A wire-frame representation of a three-
dimensional object consists of a finite set of
points and connecting edges, which define the
object.
• The term ‘edge’ does not necessarily imply
that it is a straight-line segment. An edge may
well be an arc of a circle or any other well-
defined space curve, which is required for a
‘good’ wire-frame representation.
5. • For complex models, a large number of lines
may overlap each other.
• If the model is complicated, it becomes
ambiguous and difficult to understand.
Figure: An ambiguous wire-frame object
6. Solid model
Solid modeling is based on complete, valid and
unambiguous geometric representation of physical
object.
•Complete :points in space can be classified.(inside/
outside)
•Valid :vertices, edges, faces are connected properly.
•Unambiguous : there can only be one interpretation of
object.
7. Euler-Poincaré Formula
• Euler-Poincaré Formula can be used for check the validness of a
solid.
A formula:
V -E + F -(L -F) -2(S -G) = 0
Where,
• V: the number of vertices
• E: the number of edges
• F: the number of faces
• G: the number of holes that penetrate the solid, Genus
• S: the number of shells
• L: the number of loops
8. For Example:
• A cube: eight vertices (V= 8), 12 edges (E= 12)
and six faces (F= 6), no holes and one shell
(S=1); L= F (each face has only one outer loop)
V-E+F-(L-F)-2(S-G) = 8-12+6-(6-6)-2(1-0) = 0
9. Solid model representation
Constructive solid geometry (CSG):
• Objects are represented as a combination of
simpler solid objects (primitives).
• The primitives are such as cube, cylinder,
cone, sphere etc.
• A complete solid model is constructed by
combining these “instances” using set specific,
logic operations (Boolean)
10. Constructive solid geometry (CSG)-
Boolean operation
• Union
• The sum of all points in each of two defined sets. (logical
“OR”). Also referred to as Add, Combine, Join, Merge.
11. Difference
• The points in a source set minus the points
common to a second set. (logical “NOT”)
• Set must share common volume
• Also referred to as subtraction, remove, cut.
12. Intersection
• Those points common to each of two defined
sets (logical “AND”)
• Set must share common volume
• Also referred to as common, conjoin
13. Hidden line or hidden surface
removal
• A common requirement of CAD package in
solid modeling is to hide the portion of a line
or -surface that lies behind another surface or
solid object. This process is called hidden line
or hidden surface removal.
• The lines are to be shown as dotted or dashed
lines.
16. • The conventional analytical methods for
solving stresses and strains becomes are very
complex and almost impossible when the part
geometry is intricate.
• In FEM becomes a very convenient means to
carry out the analysis.
17. Steps in FEM
• Identify the problem, sketch the structure.
• calculating various properties for each
element such as geometry, material
properties, constraints,loading and apply
Boundary condition.
• Interpreting the results.
