1. S.JOSEPHINE THERESA, DEPT OF CS, SJC, TRICHY-2
GEOMETRIC MODELS
S.JOSEPHINE THERESA,
DEPT OF CS,
SJC, TRICHY-2

2. CONTENT
A SIMPLE MODELING
GEOMETRIC MODELING
SYMBOLS AND INSTANCES

3. INTRODUCTION
Most popular and effective use of digtial computer is physical system
General term “Modeling”
Computer models can be built of both physical objects and physical processes

4. Examples Electric Circuit Building National and world Economies
Weather
All these examples use computer models to help them in their design work

5. Computer model is used as a basis for simulation
It is very important field of computing
Number of programming languages have been designed to help simulation by making it easier to build models
It is mainly used in Computer aided design
Solid objects are modeled by computer

6. Continuation….
Integrated circuits are modeled it can be checked automatically against design rule
CG is associated with modeling
It is very convenient way to observe the behaviour of computer models
Simulate weather patterns, we can plot pressure and temperature values on a displayed map instead of printing them in a tabular form

7. A simple data structure representing a circuit model
type x y
X y x1 y1 x2 y2
components
Wire segments

8. Each component is defined by an element
Data containing its type and coordinate position on the diagram and each line segment of a wire is defined by coordinates of its two endpoints
Relational information- Connection between components- is defined by procedures
We can write a procedure whether a wire and a component are connected by comparing coordinates

9. We can write another procedure to apply a similar connectivity test to any two wires
Then applying these two procedures iteratively to the contents of the data structure we can determine which components are connected together.

10. A SIMPLE MODELING
Many computer models consist of a mixture of data structure and procedures
In few cases models of a solid objects we find a lot of data and very few procedures
Circuit model is no exception to the rule
It consist of a simple data structure supplemented by some procedures
The data structure defines each of the components and connecting wires in the circuit diagram
It does not contain any relational information

11. Inclusion of component definition in the model1 2 3 X1 Y1 X2 y2 X1 Y1 X2 Y2
table
Component lines

12. Line segments are generated using the stored endpoints as parameters
The display of the components is slightly more complicated
This algorithm will scan the list of lines and components and display each at its apporpriate position

13. ALGORITHM Procedure showcomponents
Var I,j; integer; xt,yt;real;c:coponent
Begin
For i=1 to n components do begin
Xt=components[i].x
Yt=components[i].y
C=componenttable[component[i],comptyp];
With c do begin
For j=1 to n lines do begin
MoveTo(Lines[j].x1+xt,Linesj].y1yt);
LineTo(Lines[j].x2+xt,Linesj].y2yt)
End end end end
Procedure show wires
var I :integer
Begin
For i=1 to n wires do begin
MoveTo(Wires[i].x1, wires[1],y1);
LineTo(Wires[i].x2,wires[i],y2)
End end;

14. GEOMETRIC MODELING It is in the form of circuit diagram
The line segments representing each component and each connection in the circuit are fully defined by the coordinates stored in the data structure
Models which have this property are called geometric models
We can also construct physical model
Non geometric modeling is usually applied to physical processes rather than objects

15. Procedure to determine the coordinates of a sequence of lines connecting two components
Procedure LinkPoints(x1,y1,x2,y2:integer);
Begin
MoveTO((x1,y1);
LineTO((x1+x2)/2,y1);
LineTo((x1+x2)/2,y2);
LineTo(x2,y2)
end

16. A pair of components connected by lines generated with the LinkPoints Procedure

17. Displaying a Geometric Model
A model that defines the geometric form of an object
There are 3 different displayed representations of the same three dimensional object
Display model objects depends on hardware and software for their display
Methods are based on common features such as

18. Basic elements of data that typically appear as individual graphic entities on the screen
Structure
- Certain relationships between the basic data elements
- Many different kinds of relationship can be expressed in models
- Like lists, arrays, sets, rings and other kinds of structuring mechanisms

19. Transformation
- Define the position and orientation of each part of the modeled object
- When there is no repetitive use of the same component we use transformation to position the different parts of the modeled object

20. SYMBOLS AND INSTANCES
The use of graphical symbols is very common in charts and graphs
When we draw charts on a display we must be able to define symbols and multiple instances of each symbol in the chart itself
Define the symbol in a different coordinate system called master coordinate system
Functions are needed for the specification of instance transformations

21. There are three new instance transformation functions allow us to define the scaling, rotation, and translation to be applied to the symbol
Scale(sx,sy) – scale the symbol by factors sx and sy in the x and y directions relative to the origin
Rotate(teta) – Rotate the symbol through teta degrees clockwise about the origin
Translate(tx,ty)- Translate the symbol through distance tx and ty measured in x y directions

22. Master Coordinate Definition
Ori gin
Scale(0.3,0.3)
Translate(12,10)
Master Coordinate Definition
Rotate (45)

23. Steps in the transformation sequence
world
World coordinate
System
Apply viewing transformation
clip
Generate display code

24. Apply instance transformatiom Apply viewing transformation
master world
Master
Coordinate data
screen
Apply instance transformatiom
Apply viewing transformation
Generate display code
clip

25. PICTURE STRUCTURE
Geometric models and other forms of data has clear structure
Structure use certain symbols, in connections drawn linking the symbols
And overall organization of the displayed image

26. Techniques in picture Repetition - Inherent in many pictures
- Repeated instances of symbols
Connectivity
- Pictures show the relationship between elements by means of lines and arrows connecting them

27. Construction
- Use Transformation and symbols in constructing pictures
Interaction
- Dispplay file segments simplify the design of interactive programs and permit us to divide pictures .It is visible structure

28. DEFINING SYMBOLS BY PROCEDURES
Repetitive structure in pictures use symbols to represent these structures
Method of defining symbols and invoking instances of them that made use of sequences of primitive function calls