Unit-2-computer Aided Design

UNIT – II INTERACTIVE COMPTER GRAPHICS 1.0 INTRODUCTION Computer graphics may be defined as the process of creation, storage and manipulation of drawings and pictures with the aid of a computer. It is an extremely effective medium for communication between users and computers. There are two types of computer graphics. 1.

Passive computer graphics.

2.

Interactive computer graphics. v In passive computer graphics, the user has no control over the images occurred in display device. Just we can watch the graphic images. v In interactive computer graphics (ICG), the user may interact with the graphics and with the program generating them. The user can create, edit, and modify the images according to his needs. The images created by using computer can be modified, enlarged, reduced in size, moved to another location on the screen, rotated and transformed. The concept of interactive computer graphics is shown in fig. 1.1.

The user can communicate the data with computer through a keyboard and computer can communicate with user through CRT (Cathode Ray Tube) i.e., monitor of computer. The following are the functions of the IGC. (i) Modeling: It is the process of creating an object in computer by using basic primitives like points, lines, arc, circle, edges, areas, surfaces and volumes.

Fig. 1.1. Concepts of IGC (ii) Storage: It means that he process of storing the created data i.e., model in the memory of the computer. (iii) Manipulation: It is used in the construction of model from basic primitives in combination with Boolean algebra.

(iv) Viewing: It means that the looking of the model in various angles, zooming, orthographic and isometric views. 2.0 CREATION OF GRAPHIC FORMULATION FOR GRAPHICS

PREMITIES

OR

MATHEMATICAL

v The various primitives used in a typical CAD package are point, line, circle, ellipse, parabola, hyperbola, arc, polygon, rectangle, and spline. v Primitives can be described mathematically by non-parametric or parametric equations. Parametric representation of primitives contains many advantages over non-parametric representation. Creation of various such primitives are explained below. Creation of a point: v In parametric form, each point on a curve is expressed as a function of a parameter u. The parameter acts as a local co-ordinate for points on the curve. v A point is represented in two dimensions by its X and Y co-ordinates (i.e., Cartesian co-ordinate system). It is expressed as

Creation of straight lines: v Straight line form the basis for the display of all types of shapes in computer graphics. Suppose a straight line is to be drawn from point P (x1, yl) to point P (x2, Y2). v For drawing continuous line, the computer must be able to pick up a number of other pixels that should be illuminated in addition to the two end pixels. v A popular method uses an algorithm known as the “Symmetric digital differential analyzer” (DDA). The DDA generates lines from their differential equations. In DDA the equation of a line is expressed as a pair parametric equation. v For a like segment joining two points P1 & P2 a parametric representation is

Since P(u) is a position vector, each of the components of P(u) has a parametric representation x(u) and y(u) between P1 and P2 Therefore,

v Where the parameter u varies from 0 to1. If u is incremented by, say 0.2, then the DDA will generate 4 points in between the two ends of the line. v A pixel however can have only integer co-ordinates. Therefore, hardware is unusually provided that converts each fractional co-ordinate into the nearest integer. Thus 9.7 is rounded up to 10, and 9.2 is rounded down to 9. v Once the address of all the pixels is determined these are stored in a frame buffer. v The display driver reads the array of addresses and illuminates the corresponding pixels. In order to look a line continuous manner, it is necessary to increment the parameter u according to the resolution of the display device. If too large increment is selected, the line may appear to be discontinuous.

Fig. 1.2. Parametric representing of a straight line

Problem 1: Explain DDA algorithm for drawing a straight line connecting two points (4,9) and (18,15).

Creation of a Circle: v Circle is another important entity in computer graphics. An origin centred circle of radius r can be parametrically represented by

v Where e is the parameter which varies from 0 to 2pi. Although equal increment in 0 value produced excellent visual output as in case of St.line, it required repeated calculation of Fig. 1.3. Parametric representation of a trigonometric functions. This process is tedious.

Fig.1.3 Parametric representation origin centred circle. v Another method of generation of a circle is to represent it as a polygon inscribed within the desired circle. Hence the fixed numbers of uniformly spaced points on the circumference are calculated. The parameter & increment between points is a constant. v The Cartesian co-ordinates of any point on an origin-centred circle are then

Fig.1.4 Parametric representation non-origin centred circle. 3.0 DISPLAY TRANSFORMATION IN 2D: The various display control facilities in graphics are (i) Vector generation, (ii) Windowing and viewing transformation (iii) Clipping transformation (iv) Reflection transformation (v) Zooming (vi) Panning (vii) Transmitting information on a network and (viii) Graphics libraries. (i) Vector generation: v The aim of a vector display of a curve is to use sufficient display lines for the curve to appear smooth. v The number needed is controlled by the display tolerance, which is the maximum derivation of the vector representation from the true curve shape as shown in fig. 1.5. v In practice, lines are drawn between points on the normal curve shape, and therefore the permissible deviation is inside the curve.

Fig 1.5. Display tolerence (ii) The windowing and viewing transformation: v Sometimes it is necessary to view only a portion of the drawing in the full screen if the drawing is very large and too crowded in the screen. v Different part of the drawing can thus be selected for viewing by placing the windows. v The window is an imaginary rectangular frame or boundary through which the user looks onto the model. Portions inside the window can be enlarged, reduced or edited depending upon the requirements. v The viewpoint is the area on the screen in which the contents of the window are to be displayed as an image. Fig. 1.6. shows a window and a view port.

Fig 1.6. Window and viewport (iii) Clipping transformation: v Clipping is the process of determining the visible portion of a drawing lying within a window and discarding the rest. v In clipping each graphic element of the display is examined whether or not it is completely inside the window, completely outside the window or crosses a window boundary. Portions outside the boundary are not drawn. If the element of a drawing crosses the boundary, the point of intersection is determined and only portions which lie inside are drawn. v Many algorithms have been developed for clipping various graphical elements. A famous algorithm is developed by Dan Cohen and Ivan Sutherland.

Fig 1.7. Clipping transformation (iv) Reflection transformation: Reflection or mirror transformation is useful in constructing symmetric models. It allows a copy of the object to be displayed while the object is reflected about a line or a plane. Fig.1.8 shows typical examples, where

Fig.1.8 Reflection

(v) Zooming: v Zooming transformation is useful for getting magnified view or enlarged view of particular part of the drawing. v Zooming = Scaling + translation + Clipping

Fig.1.9 Zooming (iv) Panning: The panning transformation is used to move the screen across the work page. i.e. it is used to shift a drawing across the screen as if it were moving window. (vii) Transmitting information on a network: It is used to transfer the data from one device to another. For this purpose the data must be encoded using a protocol. Protocol is a set of rules that control the exchange of data between the communicating devices.

(viii) Graphics libraries: These graphic libraries are used to avoid unnecessary repeated programs when programming the operation described above. 4.0 THREE DIMENSIONAL INFORMATION IN 3D:

DISPLAY

FACILITIES

OR

DISPLAY

v The 3D transformation process is generally more complex than the 2D process. v The display devices are only 2D, therefore, it makes 3D viewing process as a complex one. The following are some of the visualization aid for the CAD system user to interpret static 2D projections of 3D objects. (i) Perspective transformation. (ii) Brightness modulation (iii) Hidden line removal (iv) Hidden surface removal (v) Shading (vi) Movement (i) Perspective projection: v Perspective projection is often used for pictorial projection of large objects. This enhances the realism of displayed image by providing the viewer with a sense of depth. v Perspective projection is used to represent an object that is so large. In perspective projection the projections converge to the eye. Therefore it may be generated by first transforming points to the eye co-ordinate system using a parallel viewing transformation. v The projecting each point onto the plane of the display screen by a projector passing through the eye co-ordinate system origin. Projected points may then be connected with lines to generate a vector display. (ii) Brightness modulation: v Generally parts of the picture near to the observer are bright while those far away are dim. During construction of drawing, the maximum and minimum z co-ordinates are noted. v The z region is the divided into n number of regions. There are n numbers of visible brightness levels available in the display system. v The picture is displayed with the appropriate intensity of brightness along zaxis. (iii) Hidden line removal:

(iv) Hidden surface removal: v It is also called visible surface determination. v It is more generally an image space process. In this process, an image of an object is generated at a particular resolution by manipulating pixels on a raster display, exploding the ability of raster devices to display shaded areas. v A wide variety of algorithms exists. They include the z-buffer algorithm, Watkin’ s algorithm, Wamock’ s algorithm and Painter’ s algorithm. (v) Shading: v This technique is used to display the images in a natural way. It is based on the recognition of distance and shape as a function of illumination. v The surface of the solid model is divided into patches. In regions of large curvature, the patches are reduced in size. v Then each patch is tested for visibility and the required degree of shading. The hidden lines must be removed before shading. (vi) Movement: v This leads to better recognition of displayed objects. When an object rotated or translated, ambiguities that arise due to the superposition of points are eliminated and clear picture are revealed. 4.1 Transformation: v During modeling of an object, many times it becomes necessary to transform the geometry. v The transformation actually converts the geometry from one co-ordinate system to the other. v The main types of 2D transformation which are often come across are as follows. •

Translation

•

Scaling

•

Reflection

•

Rotation

•

Shearing

(i) Translation: v It is one of the most important and easily understood transformations in CAD. v Translation is the movement of an object from one position to another. This is accomplished by adding to the co ordinates of each corner point the distance through which the drawing is to be moved. v Fig. 1.10. shows a square object in fig. (a) being moved to a new position fig. (b). Let us now consider a point on the object, represented by P which is translated along X and Y-axes by added dX and dY to a new position P’ .

v The new co-ordinate after transformation is given by the following equation.

Fig.1.10 Translation

(ii) Scaling: v Scaling is the transformation applied to change the scale of an entity. v This is done by increasing the distance between the points of the drawing. That means, this can be done by multiplying the co-ordinates of the drawing by an enlargement or reduction factor called scaling factor. v The size of the entity altered by the application of scaling factor is shown in fig. 1.11.

Fig.1.11 Scaling

Example:

Fig.1.12 Scaling a triangle (iv) Rotation: v Rotation is another important geometric transformation. Here the drawing is rotated about a pivot point. v The final position and orientation of geometry is decided by the angle of rotation and the base point about which the rotation is to be done. v Fig. 1.13. shows a rotation transformation of an object about origin 0. To develop the transformation matrix, consider a point P as the object in XY plane, being rotated in anticlockwise direction to the new position P’ by an angle 0. v The new position P’ is given by

Fig 1.13 Rotation

Fig 1.14 X shear

Fig.1.15 Y shear

4.2 Concatenation or Combination Transformation: v Many times it becomes necessary to combine the aforementioned transformations in order to achieve the required results. v In such cases the combined transformation matrix can be obtained by multiplying the respective transformation matrices. Sequence of transformations can be combined into a single transformation using the concatenation process. v For example, a line AB shown in fig. 1.16 is to be rotated through 45° in clockwise direction about point A. v This process can be achieved by the following three process. (i) Inverse translation of AB to A1B1 (ii) A is then rotated through an angle of 45° to A2B2 (iii) The line A2B2 is then translated to A3B3 The respective transformation matrices are

Fig1.16 Concatenation Process

4.3 Homogeneous Representation: v In previous cases, except translation, can be represented as a row vector X, Y and a 2x2 matrix. v For uniform representation of all transformations, these can be represented as a product of a 1 x3 row vector and an appropriate 3 x3 matrix. v The conversion of a 2D co-ordinate pair (X, Y) into a 3D vector can be achieved by representing point a [ X,Y, 1]. After multiplying this vector by a 3 x3 matrix another homogeneous row vector is obtained [ X,Y, 1]. v This three dimensional representation of a two dimensional plane is called homogeneous representation and the transformation using the homogeneous representation is called homogeneous transformation. v The matrix representation of four basic transformations is given below.

4.4 Three Dimensional (3d) Transformations: It is often necessary to display objects in 3D on the graphics screen. The 2D transformations as explained in earlier sections can be extended into 3D by adding the Z-axis parameter. The transformation matrix will now be 4x4. This section deals with the simple cases of 3D transformations.

5.0 VIEWING TRANFORMATION 5.1 CLIPPING Cohen sutherlan clipping algorithm: v In this method all the lines are classified to see if they are in, out or partially inside the window by doing an edge test. v The four digits binary code is used to identity the end points of the line with reference to the window. v The code is known as TBRL. v The code is identified as follows. If the point is above top of window T = 1 otherwise T= 0 If the point is above below of window B = 1 otherwise B = 0 If the point is above right of window R = 1 otherwise R = 0 If the point is above left of window L = 1 otherwise L = 0 Where, T= Top, B = Bottom, R = Right and L = Left. For example consider the object shown in fig. 1.17 within the window. The full 4 digit codes of the line end points with reference to the window are shown in fig. 1.17.

Fig.1.17 v After assigned the 4digit code, the system first examine whether the line is fully in or out of the window by the following conditions. v The line is inside the window if both the end points are equal to “0000”. v The line is outside the window if both the end points are not equal to “0000”. v For those lines which are partly inside the window, they are split at the window edge and discard the line segment outside the window. 5.2 HIDDEN LINE ELIMINATION v Since the early development of computer graphics, there is always a demand for clear and more realistic images by removing the hidden lines and surfaces. v The determination of hidden edges and surfaces is considered one of the most challenging problems in computer graphics. v The development of hidden line removal algorithm is influenced by the types of graphic display devices they support and by the type of data structure they operate on. v The hidden line elimination can be stated as, “For a given three dimensional scene, a given viewing point and a given direction, eliminate from an appropriate two dimensional projection of the edges and faces which the observer can not see”.

Fig.1.18 Algorithm for hidden line elimination

v The generic steps that can implement for a hidden line elimination process is shown in fig.1.18 v Three-dimensional data is a set of three-dimensional objects. Each object is defined by its geometry and topology. Example: Solid model of objects. These models have to be modified to be able to identify faces and the order of their edges. v The second step is to apply proper geometric transformations to the 3D data to obtain the two dimensional image data. At this stage, the image contains all visible and invisible edges. v Sorting is an operation that orders a given set of records according to the selected criterion. Various sorting techniques are available. v The visibility technique normally checks for overlapping of pairs of polygons in the viewing plane. If overlapping occurs, depth comparisons are used to determine if part or all of one polygon is hidden by another. The following techniques are available. Ø Minimax test Ø Containment test Ø Surface test Ø Edge intersections Ø Segment comparisons Ø Homogeneity test The surface test to eliminate the back faces is usually sufficient to solve hidden line if the image has no holes. Otherwise, a combination of techniques is required. In order to apply the visibility technique to the image data, the sorting of this data is required.

Fig 1.19. Hidden line elimination v With the completions of the sorting according to the visibility criteria set by the visibility techniques, the hidden edges have been identified and removed from the image data. The final step in this algorithm is to display the final images. v Fig. 1.19 shows an object with hidden lines and shows the same object after elimination of hidden lines.

The wide varieties of hidden line elimination algorithms exist. These algorithm are based on one of the following three approaches (i) Edge-oriented approach (ii) Silhouette (contour) originated approach or (iii) Area-Oriented approach. If the point is above top of window T= 1 otherwise T= 0 The various algorithms that utilize one or more of visibility techniques and follow one of the three approaches are as follows: (i) Priority algorithm (ii) Plane-sweep paradigm (iii) Algorithm for scenes of high complexities (iv) Algorithms for finite element models of planar elements. (v) Area-oriented algorithms. (vi) Overlay algorithm for surfaces defined by u-v grids. (vii) Algorithm for projected grid surfaces. 6.0 CURVE GENERATION TECHNIQUES v Three dimensional curves play an important role in the engineering, design and manufacture of a diverse range of products, v Example, automobiles, ship hulls, aircraft fuselages and wings, propeller blades, shoes etc. they also play an important role in the description and interpretation of physical phenomena, v Example in geology, physics and medical science. These products and science requires free form, or synthetic curves and surfaces. The need of synthetic curves in design arises on the following occasions. (i) When a curve is represented by a collection of measured data points and (ii) When an existing curve must change to meet new design requirements. v In the second case, the designer would need a curve representation that is directly related to the data points and is flexible enough to bend, twist or change the curve shape by changing one or more data points. v The synthetic or free form curves are required to pass through given data points. Therefore polynomials are the typical form of these curves. v Various continuity requirements can be specified at the data points to impose various degrees of smoothness of the resulting curve. v The order of continuity becomes important when a complex curve is modeled by joining several curve segments. Zero order continuity (C° ) yields a position continuous curve. v First (C and second (C order continuities imply slope and curvature continuous curves respectively.

Two approaches are available for modeling of synthetic curves (i) Interpolation (ii) Approximation. v The interpolation essentially tries to pass a curve on a surface called interpolent through all these points. v Approximation tries to fit a smoother curve on surface which may be close to thee points but may not actually pass through each of them. v One of the popular methods of interpolation is to use Lagrangian polynomial which is the unique polynomial of degree n passing through n+l points. But it is unsuitable in modeling of curves because they tend to oscillate about control points, are computationally inconvenient, and are uneconomical of storing curve in the computer. v A cubic polynomial is the minimum-order polynomial that can guarantee the generation of these curves. In addition, the cubic polynomial is the lowestdegree polynomial that permits inflection within a curve segment and that allows representation of nonlinear three-dimensional curves in space. v The various forms of synthetic curves are explained in detail in the following sections. 6.1 Cubic Spline: v Splines are functions that are used for fitting a curve through a number of data points. v In general, the mathematical spline is a piecewise polynomial of degree K with continuity of derivates of order K-1 at the common joints between segments. v The cubic spline has second order or C continuity at the joints. The cubic spline curve connects two data points and utilizes a cubic equation. v Therefore, four conditions are required to determine the coefficients of the equation. v The equation for a single parametric cubic spline segment is given by

v Equation (3) is for a single cubic spline segment which passes through the end points u = 0 and u = 1. It also shows that the curve’ s shape can be controlled by changing its end points or its tangent vectors. v The equation (3) can be generalized for any two adjacent spline segments of a spline curve that are to fit a given number of data points. 6.2 Bezier Curves: v Curves developed by this techniques pass through the number of given points. v There is an another alternative for creating the free-form curves which utilizes approximation technique. v Curves resulting from approximation techniques do not pass through the given data points. Instead, these points are used to control the shape of the resulting curves. v In the most of the cases approximation techniques are preferred over interpolant techniques curve design due to added flexibility and additional intuitive feed provided by this technique, Bezier and B-spline curves are examples for approximation technique. v Bezier curves, developed by P.Bezier of the French can company “Regrault” and used them in his software system called UNISURE to define the surface panel or outer panels of the cars.

Fig 1.20. Bezier curve v Bezier used a control polygon for curves, in place of points and tangent vectors as in case of cubic splines. v The Bezier curve is defined in terms of the locations of n+l points. These points are called control points. They form vertices of control polygon which uniquely defines the curves shape. v Fig.1.20. shows a Bezier curve which has tour control points. Only first and last control points or vertices of the polygon actually lie on the curve. v The other two vertices define the order derivates and shape of the curve. The curve is always tangent to first and last polygon segments. v Several four point Bazier polygon and the resulting cubic curves are shown in fig. 1.21.

Fig 1.21. Cubic bezier curve 6.21 Characteristics of the Bezier curves: 1. The curve interpolates the first and last control points. i.e. it passes through B and B if we substitute u = 0 and 1 in equation (7). 2. The curve is tangent to the first and last segments of the characteristic polygon. 3. The curve is symmetric with respect to u and (1—u ). Therefore, the sequence of control points defining the curve can be reversed without change of the curve shape. 4. Each control point is weighted by its blending function for each u value. 5. The curve shape can be modified by either changing one or more vertices of its polygon or by keeping the polygon fixed and specifying multiple coincident points at a vertex. 6. A closed Bezier curve can simply be generated by closing its characteristic polygon or choosing B0 and Bn to be coincident.

6.3 B-spline curve: The Bezier curve developed on the basis of Bernstein basis has the following limitations: 1. The number of specified polygon vertices fixes the order of the resulting polynomial which defines the curve. The only way to reduce the degree of the curve is to reduce the number of vertices and vice versa. 2. A change in one vertex is felt throughout the entire curve because of the global nature of the Berntein basis. This means that the value of blending function is nonzero for all parameter values over the entire curve. v B-Spline curves provide another effective method of generating curves defined by polygons. v In fact B-spline (Basis spline) curves are the proper and powerful generation of Bezier curves. B spline contains the Bernstein basis as a special case. Bspline basis is generally non global. v The non global behaviour of B-spline curves is due to the fact that each vertex B is associated with a unique basis function. v The B-spline basis allows the order of the basis function and hence the degree of the resulting curve to be changed without changing the number of defining polygon vertices. v B-spline curves have the ability to interpolate or approximate a set of given data points. v Let P(u) be the position vectors along the curve as a function of the parameter u then a B Spline curve is given by

Where the B, are the position vectors of the n+l defining polygon vertices and the N are the normalized B-spline basis functions. 6.3 Characteristics of the B-spline curves: 1. The local control of the curve can be achieved by changing the position of a control point or using multiple control points by placing several points at the same location.

Fig 1.22. Local control of B-spline curve

2. The B-spline curves do not pass through the first and last control points except when linear blending functions are used. 3. A non-periodic B-spline curve pass through the first and last control points and is tangent to the first and last segments of the control polygon. 4. A second-degree curve (k = 3) is always tangent to the midpoints of all the internal polygon segments as shown in fig. 1.23

Fig 1.23. Effect of degree of B-spline curve on its slope 5. If K equals the number of control points (n+l), then the resulting B-spline curve becomes a Bezier curve as shown in fig.1.24.

Fig 1.24. Identical B-spline and Bezier curve 6. Multiple control points induce regions of high curvature of a B-spline curve. Fig. 1.25 shows this property of the curve.

Fig 1.25. Multiple control point B-spline curve 6.4 Rational Curves: v Rational curves were first introduced in to the computer graphics by coons. v Rational curve is defined by the algebric ratio of two polynomials while a nonrational curve is defined by one polynomial. Rational Bezier curves; rational B-spline and 3-sp1ine curves, rational conic sections and rational cubics have been formulated. v The most widely used rational curves are non-uniform rational B-splines (NT.JRBS). NURBS is capable of representing in a single form non-rational B splines and Bezier curves as well as linear and quadratic analytic curves. v Rational B-splines provide a single precise mathematical form capable of representing the common analytical shapes like lines, planes, conic curves including circles, free form curves, quadric and sculptured surfaces etc. 7.0 MODEL STORAGE AND DATA STRUCTURE Data: v Data is a collection of numerical values, names, alphanumeric characters, codes, instructions etc. v The data are stored in the computer memory in the form of binary digits i.e. 0 and 1. Database: v Database can be defined as a collection of data in a single location designed to be used by different programmers for a variety of applications. v The term database denotes a common base of data collection designed to be used by different programmers. v More specifically, it is a collection of logically related data stored together in a set of files intended to serve on or more applications in an optimal fashion. v The amount of information in a database can vary from a handful to billions of entries. v A database must have a predetermined structure and organization suitable for access, interpretation or processing either manually or automatically.

Data structure: v Data structure is defined as a set of data items or elements that are related to each other by a set of relations. v It is a diagrammatic representation of the database. v From CAD point of view, a data structure is a scheme, logic or a sequence of steps developed to achieve a certain graphics. v The data structures are used in the interactive modeling purpose in the following way: 1. It allows interactive manipulation such as addition, modification and deletion of data. 2. It supports multiple types of data element like geometric, textual, dimensions, labels, tool paths, finite elements and so on. 3. It allows the property such as pen number, line style, colour and so on to be associated with geometric elements. 4. It provides facilities for the retrieval of parts of the data structural released by deletion or other modifications. 5. It should be compact to minimize disc storage and main memory requirements. 6. It allows models of various sizes and comprising various combinations of entities, to be defined. 7. It provides as efficient an access to the data as possible. The Advantage of having centralised control of database is as follows: 1. Eliminate redundancy. 2. Enforce standards that mean with central control of the database, both national and international standards are followed. Standards are most important for data interchange between systems. 3. Access to sensitive data and projects can be checked and controlled by assigning each used the proper access code to various parts of the database. 4. Maintain integrity which ensures its accuracy. Integrity proceeds consistency. 5. Balance conflicting requirements. Database Management System (DBMS): DBMS is defined as the software that allows access to use or modify data stored in a database. It consists of a collection of interrelated data and a set of programs to access that data. It acts as a intermediate source between database and the user of this database as shown in fig. 1.26.

Fig. 1.26. DBMS

The database management involves in the following activities: Organize a database v Add new data to the database v Sort the data in some meaningful order v Search the database for types of information v Print the data into formatted reports v Edit the data and delete the data Model Storage: v There are many ways in which the models called be stored. v Data structure is used to store the model in the CAD system. v Data structures are one in which the model creation and manipulation algorithms act. Simple Data Structure:

Fig 1.27. Entity table and entity data tables v A simple data structure consists of a list or table of entities with cross references (or pointers) from this list to separate arrays of floating point, integer and other data specific to the entities. v This is shown in fig. 1.27 In this figure we can see an entity table, a real data table for floating point data and an integer data table. v In the entity table, a series of slots are present. Each of these slots containing a number of elements of the array used for the table, are assigned one per entity. v It also contains pointers to connect the data with other data in the table. These are used to in such a way that data may be arbitrarily added, deleted and moved in the list.

General entity data table: v As already explained, the entity table has a series of slots, one for each entity. v These slots containing general data applicable to most entities. 8.0 CONCEPTS OF DATA PROCESSING AND INFORMATION SYSTEMS v In many places, the term ‘ data’ and ‘ information’ are often used interchangeably because their meanings are so closely related for most practical purposes. v If we define these two terms more precisely, ‘data’ usually means raw, unevaluated facts and figures and ‘ information’ refers to data that have been evaluated and recognized in more meaningful way. v The data are raw facts, may or may not be information but from which information is created. Information is data which provides meaning and relevance to some problem. v The information is useful for decision-making. Without information the system cannot survive. v Information flows are very much essential for any system as blood flow in human body. It applies to large system as well as small ones. v Fig. 1.28 shows information flow in a manufacturing company for different departments along with functional area. v This figure shows that the common information flow can be functionally divided into two types. (i) Geometry oriented data flow. (ii) Management or administration oriented dataflow. The control parameter for both data flows is exchanged between functional components of the company as shown in fig1.28. by dashed lines.

Fig. 1.28. Data flow in a manufacturing company

v Data processing should consist of a set of procedures (i.e. recording, classification and storing, storage and retrieval, summarization and analysis) used to process data to produce information for managers. v For understanding of management information system, a careful study of the nature of the data, the storage, processing and retrieval of data, the characteristics of information and communication is essential. 9.0 BANK CONCEPT v An important element for managing a situation is knowledge information about the grade and objectives, resources, operations and environment. v An individual personal knowledge is only what can be acquired and stored in his memory and then retrieved and manipulated as necessary. v However, many managers insist on operating with only the information stored in personal memory. v Now-a-days, it is necessary to store the information in other storage media. Books, magazines, journals, forms, records, data CD’ s and a wide variety of other media assist in storing information until it is needed. v However, now-a-days, due to complex managerial environment, it is necessary to use computers for storing, processing and retrieving information. v In developing an information system to serve the variety of needs of today, modem environment knowledge and information can be stored in the memory of the computer. v This knowledge can be described and called as a databank. Fig. 1.29 shows the transfer of information from human memory and other media to the memory of a computer.

Fig. 1.29. Data bank concept

10 A BANK INFORMATION STORAGE AND RETRIEVAL The data bank has the following two primary advantages over the manual system. 1. The accumulation of information in an information center where “One set of books” is maintained avoids the maintenance of separate record files. 2. It tends to integrate the separate functions and departments of the company/industry. v The databank or the central database is constructed to store and retrieve the information used in common by the various subsystems of the company. v By using recent trends in information processing techniques, a high speed, random access, mass storage device is used to store large volumes of data. v All relevant information about the company’ s operation is contained in one readily accessible file, arranged so that duplication and redundancy are avoided. v If we maintain one set of records, it will be easier to maintain their accuracy.

Fig. 1.30. Data bank concept v Fig. 1.30 shows the concept of data bank. It describes how a typical manufacturing firm’ s information files can be integrated into the central database. v In general data base system, the following major information sub systems are required to run the business. General accounting files Inventory file Customer and sales file Vendor file Personnel file

v The database should satisfy the requirements of the user, otherwise he will continue to maintain his own system. v The purpose of the central data base system may not be useful. The key element in this concept is that each subsystem utilizes the same database in the satisfaction of its information needs. This will yield an advantage of integration of departments and functions. v Each department/sections of an organization is integrated into a whole through its access and interface with central database of the organization and thereby, gains a greater understanding and application of how its actions and plans affect others throughout the organization. Important problems surrounding database are: 1. There is possibility of invalid input information by a unit wishing to maintain information security. 2. If anybody enters the ‘ error’ data, it affects other departments immediately and produces “multiplier effect”. 3. The interdepartmental agreement required concerning the degree of detail to be included in data elements of the database. v If there is no common ground for agreement and solution of these problems, organisational units tend to maintain their own system for their peculiar needs. This will also defeats the purpose of central database. v A good data base system should have the following features: Ø Satisfy current and future application needs. Ø Utilized in the best possible way according to the user requirement. Ø Validate data before storage. Ø Be easy to modify with changes. Ø Be expandable with the growth and changes. Ø Allows access for the data only to authorized persons. 11.0 DATA LIFE CYCLE Data within a system have their own life cycle. Fig. 1.31 shows three aspects of this life cycle which are particularly important in development, design and operation of systems. The three aspects are: (i) We need to know how data are generated i.e. how they are born. (ii) We need to know what manipulation or processing of data is carned out. (iii)We need to know how certain types of information processing are carried out, particularly the transmission of data and communication of information and storing/retrieving of data. The reproduction of data may occur at various stages in the life cycle.

Fig. 1.31. Data Life Cycle 12.0 INTEGRATED DATA PROCESSING The integrated data processing (IDP) has two fundamental objectives. 1. The recording of data at its point of origin in a machine communicable language in the form of punched tape, punched cards or optical characters. 2. The retrieved of data from which it is recorded for performing all subsequent processing. v The first objectives is met by adopting conventional devices such as adding machines, accounting machines, cash registers and typewriters so that they create punched tapes or cards as a by-product of a basic recording operation. v The second objective is met by carefully planning subsequent steps in the data processing cycle and using equipment that can accept or produce a language medium that has compatibility with other machines. v The concept of IDP is not new since it was demonstrated in the conference of American Management Association (AMA) in Feb.’ 1954 by U.S. Corporation. In that system, fire channel punched tape was the common language used. v Originally, integrated data processing involved the preparation of common language medium such as paper tape as a part of manual recording operation. However, the scope of IDP has been broadened by the development in source data automation such as optical character recognition and magnetic ink character recognition. v In addition, translating device such as tape-to-card converters has extended the range of IDP to include any machine that can use the output of another machine. v Effective integrated data processing represents a blending of the best techniques of systems analysis and design and data processing with those in the field of communications. v The broad objective is the treatment of data processing activities as a continuous integrated whole, rather than a variety of individual operations.

13.0 INFORMATION SYSTEM Model of general information system: v Fig. 1.31 shows a model of general information system. v The organization and its environment generate data which serves as input to data processing. v The function of data processing is to collect, transforms and stores the data and produces strategic, tactical and operational information’ s which are transferred to corresponding decision maker. v The various decision makers produces output according to the data which are received. These outcomes then stimulate organizational and environmental responses which forms the basis for new data.

Fig.1.31.A Model of general information system 13.1 Characteristics needed for good information system: 1. It must serve and support the managerial activities in the organization. 2. It should have components serving both the general direction of the organization and its internal regulation and control. 3. It should undertake the various activities of acquisition, processing, retention, transmission and reporting of information. 4. It should be designed to follow the pattern and structure of management at all levels of the organization. 5. It should be flexible enough to meet the changing need of the management. 6. It should not restrict the informal passage of information throughout the organization.

13.2 Operation of an information system: The following major steps which are applicable to all information systems. (i) Determination of information needs: First of all, an information system should determine the objectives of the system, such as what kind of information will be needed, when and in what form. (ii) Data collection: The data used for various activities is collected to provide the raw material (i.e. information) for the function of data processing. Data collection involves the element of sensing and recording. 14.0 ENGINEERING DATA MANAGEMENT SYSTEM (EDMS) v In large companies, hundreds of thousands of model files, drawing files and other CAD data files are stored. v It will be continuously reused for over a period of many years. They therefore need systems to index and manage these large data in a sort of electronic drawing vault. v These systems are used by the designers to enquire what data is available for particular project, where it is stored, when models were constructed and by whom so on. v Engineering data management system (EDMS) is a system to assist a design team in the indexing, browsing and searching of their design data. EDMS also provides the following facilities. 1. Data is available and easily accessible to all users who need access, but at the same time, it should be accessible only by authorized person for providing data security. 2. It checks that particular data items are unique i.e., for a given reference, only one data item may exist in the system. 3. Version control system that log changes and issues of drawings and other files. 15.0 DATA STRUCTURE ORGANISATION There are three ways in which data can be organized (i) Hierarchical (ii) Network and (iii) Relational Hierarchical Data Structure: v Fig. 1.31 shows a typical hierarchical data structure. In hierarchical data structure data files are arranged in a tree like structure. v At the top of the data tree the broadest possible description of the contents of the database is places. v As one moves downwards, the description become more specific. In fig. 1.31, the nodes in level 2 are the children of node at level 1. the nodes at level 2 in turn become parents of nodes in level 3 and so on.

v This type of data structure avoids repetition of the information and thus saves storage memory. v The search for specific information can be carried out by moving from top to bottom of the data tree. v A good example of such an organization might be a parts list, in which each product is composed of assemblies which are in turn composed of sub assemblies. v Fig. 1.33. shows an example of hierarchical data structure for the parts list of lathe assembly.

Fig.1.32. Hierarchical data structure

Fig. 1.33 Parts of a Lathe assembly v A major limitation of this model is the rigidity of the database structure. v It is very difficult to incorporate modification into the database; especially in cases where the new record involve substantial changes in the field data.

16.0 NETWORK DATA STRUCTURE: v The network data structure is a combination of several hierarchies in which child files can have more than one parent file, thereby establishing a many-tomany relationship among data. v Fig. 2.52 shows a network data structure. v As the network data structure is more compact than the hierarchical data structure, it is more efficient than previous one. v The difficulty associated with the modification of existing structure is just as great as compared to the hierarchical data structure.

Fig.1.34. Network data structure 17.0 RELATIONAL DATA STRUCTURE: v Relational data structure is simplest of all three types. v Relational data are stored in the form of table, where each row representing a record. v Each of these records consists of field under each column. v Table represents a bill of materials for a lathe in the form of a relational data structure.

17.1 Characteristics of relational data structure: 1. Each cell in the table holds only one field. 2. No two rows or records can be identical. In an atleast one of the columns there must be atleast one entry that is unique. 3. Records or rows need not be in any particular order. The user may add a new record at the bottom of the table or can insert in between two selected rows.

4. Since no two records are identical and fields are related by columns, the user may delete or modify any row without having to adjust any other part of the data structure. v The simplicity in the structure of this model made it very popular among the business people and there are number of commercial data base management systems are available. v The major limitation of this structure is the difficulty in searching and retrieval of particular data from the structure. v Any search has to be carried out sequentially in row-by-row manner until the desired information is located. 18.0 DATA STORAGE AND SEARCH METHODS The graphic data can be stored in a system by two forms (i) Sequential form and (ii) Random form v The major disadvantage in sequential form is that whenever we required to access certain data, it is not simple and one may not be retrieving the data in a sequential form. v From the graphical manipulation point of view, this method of storing the data is inefficient. v Random form alone can not provides better results in graphical manipulation due to inherent limitation within it. v The actual graphics systems use a combination of random and sequential form to get the best result out of both the forms. v In general, there are two data search methods exist. They are (i) Sequential search (ii) Binary search Fig. 1.35 (a) and (b) show these two methods. v In sequential search, the data is retrieved by reading each record sequentially. v In binary search, the first search is made in the middle of the file and then subsequent searches are made. Therefore it provides quicker retrieved than sequential search.

Fig. 1.35. Search methods

TWO MARK QUESTIONS 1. Define computer graphics. 2. What are the different types of computer graphics? 3. What are the functions of IGC? 4. What is meant by the term modeling? 5. What are the various primitives used in CAD package? 6. How is a point represented in two —dimensions? 7. Determine the parametric representation of the line segment between two points (4,5) 8. and (7,8). Also determine the slope of the line segment 9. Write the basic parametric equation of a non —origin —centered circle.\ 10. Write the basic parametric equation of a origin —centered ellipse. 11. Define a parabola. 12. Describe the hyperbola. 13. How can be the speed of input devices improved? 14. What is meant by viewpoint? 15. What is viewing transformation and windowing transformation? 16. What is meant by clipping? 17. State the use of reflection transformation. 18. How information is transmitted on a network? 19. Mention the use of graphic libraries. 20. List the some of visualization aids for the CAD system user to interpret static 2D projections of 3D objects. 21. Perspective projection enhances ______________________ 22. Hidden surface removal is also called as _________________ 23. What are the main types of 2 D transformations? 24. State hidden line elimination. 25. What are the various visibility techniques used for checking overlapping of pairs? 26. Name the various approaches used in hidden line elimination algorithm 27. At what situation synthetic curves are needed? 28. Give any four characteristics of Bezier curves. 29. Write any two differences between Bezier curve and Cubic spline curve 30. What are the limitations of B-spline curve on the basis of Bernstein ?

31. Give any two properties of B-spline 32. Define rational curve. 33. What is data? 34. Define database. 35. How can we define data structure? 36. Mention the various ways using data structure in interactive modeling. 37. Give any four advantages of centralized data structure 38. Define DBMS. 39. State the various activities of data base management 40. Mention any four characteristics of an effective data processing system 41. What are the elements of information system? 42. What are the advantages of data bank? 43. Give any problems surrounding database. 44. What are the special features for a good data base system? 45. What are the characteristics needed for a good information system? 46. List out the major steps involved in information system. 47. List the procedures involved in implementation of an information system. 48. What is network data structure? 49. What are the characteristics of relational data structure? 50. What are the two modes of data storage? 51. What are the types of data search methods? PART-B questions 1. Explain briefly the creation of graphic primitives both in 2D and 3D. 2. Determine the parametric representation of the line segment between two points (10.5) and (2,9). Determine the slope of the segment and explain DDA algorithm 3. Write short notes on the following terms: i.

Pointing

ii.

Clipping transformation

iii.

Transmitting information

iv.

Perspective projection

v.

Hidden surface removal

4. What is meant by concatenation? Explain. 5. Describe clearly hidden line elimination. 6. Explain curve generation techniques. 7. Differentiate Bezier curve and cubic spline curve 8. Write sort notes on “rational curves, model storage and data structure”. 9. Explain database management system, data bank information storage and data life cycle. 10. Describe information system. 11. Explain engineering data management system. 12. Explain the various types of data structure organization. 13. What are the 2 —D transformation? Explain each.