Data Representation Class 11 Notes Pdf Download
Zita Lifland
Listed below are lecture notes/slides saved as PDF files - there are 3 slides per page, with room for you to take notes. While the full set of lecture notes is still a work in progress, I will work to have lecture notes posted here at least two days before each class meeting, so that students who want to print these out to take notes on during class can do so.
This document provides an overview of different data representation techniques used in computer systems. It discusses decimal, binary, octal, and hexadecimal number systems. It describes how to convert between these different numbering systems using various methods like division and remainders. The document also covers topics like unsigned integers, binary addition, ASCII codes, ISCII codes, and Unicode encoding.Read less
In Chapter 4 - The Visualization Pipeline we developed a pragmatic definition of the visualization process: mapping information into graphics primitives. We saw how this mapping proceeds through one or more steps, each step transforming data from one form, or data representation, into another. In this chapter we examine common data forms for visualization. The goal is to familiarize you with these forms, so that you can visualize your own data using the tools and techniques provided in this text.
To design representational schemes for data we need to know something about the data we might encounter. We also need to keep in mind design goals, so that we can design efficient data structures and access methods. The next two sections address these issues.
Since our aim is to visualize data, clearly we need to know something about the character of the data. This knowledge will help us create useful data models and powerful visualization systems. Without a clear understanding of the data, we risk designing inflexible and limited visualization systems. In the following we describe important characteristics of data. These characteristics are the discrete nature of data, whether it is regular or irregular, and its topological dimension.
First, visualization data is discrete. This is because we use digital computers to acquire, analyze, and represent our data, and typically measure or sample information at a finite number of points. Hence, all information is necessarily represented in discrete form.
Because of the discrete character of the data we do not know anything about regions in between data values. In our previous example, we know that data is generated from the function \(y = x^2\), but, generally speaking, when we measure and even compute data, we cannot infer data values between points. This poses a serious problem, because an important visualization activity is to determine data values at arbitrary positions. For example, we might probe our data and desire data values even though the probe position does not fall on a known point.
There is an obvious solution to this problem: interpolation. We presume a relationship between neighboring data values. Often this is a linear function, but we can use quadratic, cubic, spline, or other interpolation functions. Chapter 8 - Advanced Data Representation discusses interpolation functions in greater detail, but for now suffice it to say that interpolation functions generate data values in between known points.
A second important characteristic of visualization data is that its structure may be regular or irregular (alternatively, structured or unstructured). Regular data has an inherent relationship between data points. For example, if we sample on an evenly spaced set of points, we do not need to store all the point coordinates, only the beginning position of the interval, the spacing between points, and the total number of points. The point positions are then known implicitly, which can be taken of advantage of to save computer memory.
Data that is not regular is irregular data. The advantage of irregular data is that we can represent information more densely where it changes quickly and less densely where the change is not so great. Thus, irregular data allows us to create adaptive representational forms, which can be beneficial given limited computing resources.
Characterizing data as regular or irregular allows us to make useful assumptions about the data. As we saw a moment ago, we can store regular data more compactly. Typically, we can also compute with regular data more efficiently relative to irregular data. On the other hand, irregular data gives us more freedom in representing data and can represent data that has no regular patterns.
Finally, data has a topological dimension. In our example \(y = x^2\), the dimension of the data is one, since we have the single independent variable x. Data is potentially of any dimension from 0D points, to 1D curves, 2D surfaces, 3D volumes, and even higher dimensional regions.
The dimension of the data is important because it implies appropriate methods for visualization and data representation. For example, in 1D we naturally use x-y plots, bar charts, or pie charts, and store the data as a 1D list of values. For 2D data we might store the data in a matrix, and visualize it with a deformed surface plot (i.e., a height field - see Exercise 4.2).
In this chapter and Chapter 8 - Advanced Data Representation, we show how these characteristics: discrete, regular/irregular, and data dimension, shape our model of visualization data. Keep these features in mind as you read these chapters.
Visualizing data involves interfacing to external data, mapping into internal form, processing the data, and generating images on a computer display device. We pose the question: What form or forms should we use to represent data? Certainly many choices are available to us. The choice of representation is important because it affects the ability to interface to external data and the performance of the overall visualization system. To decide this issue we use the following design criteria:
Efficient. Data must be computationally accessible. We want to retrieve and store data in constant time (i.e., independent of data size). This requirement offers us the opportunity to develop algorithms that are linear, or O(n), in time complexity.
Mappable. There are two types of mappings. First, data representations need to efficiently map into graphics primitives. This ensures fast, interactive display of our data. Second, we must be able to easily convert external data into internal visualization data structures. Otherwise, we suffer the burden of complex conversion processes or inflexible software
Minimal Coverage. A single data representation cannot efficiently describe all possible data types. Nor do we want different data representations for every data type we encounter. Therefore, we need a minimal set of data representations that balances efficiency against the number of data types.
Simple. A major lesson of applied computation is that simple designs are preferable to complex designs. Simple designs are easier to understand, and therefore, optimize. The value of simplicity cannot be overemphasized. Many of the algorithms and data representations in this text assign high priority to this design criterion.
The remainder of this chapter describes common visualization data forms based on these design criteria. Our basic abstraction is the data object, a general term for the various concrete visualization data types which are the subclasses of data object.
The most general form of data found in VTK is the data object. A data object can be thought of as a collection of data without any form. Data objects represent the data that is processed by the visualization pipeline (see the previous chapter and Figure 4-2). Taken by themselves, data objects carry little useful information. It is only when they are organized into some structure that they provide a form that we can operate on with visualization algorithms.
Data objects with an organizing structure and associated data attributes (Figure 5-11) form datasets. The dataset is an abstract form; we leave the representation and implementation of the structure to its concrete subclasses. Most algorithms (or process objects) in VTK operate on datasets.
Our model of a dataset assumes that the structure consists of cells and points. The cells specify the topology, while the points specify the geometry. Typical attributes include scalars, vectors, normals, texture coordinates, and tensors.
The definition of the structure of a dataset as a collection of cells and points is a direct consequence of the discrete nature of our data. Points are located where data is known and the cells allow us to interpolate between points. We give detailed descriptions of dataset structure and attributes in the following sections.
A dataset consists of one or more cells (Figure 5-2 and Figure 5-4). Cells are the fundamental building blocks of visualization systems. Cells are defined by specifying a type in combination with an ordered list of points. The ordered list, often referred to as the connectivity list, combined with the type specification, implicitly defines the topology of the cell. The x-y-z point coordinates define the cell geometry.
Although we define points in three dimensions, cells may vary in topological dimension. Vertices, lines, triangles, and tetrahedron are examples of topologically 0, 1, 2, and 3-D cells, respectively, embedded in three-dimensional geometric space. Cells can also be primary or composite. Composite cells consist of one or more primary cells, while primary cells cannot be decomposed into combinations of other primary cell types. A triangle strip, for example, consists of one or more triangles arranged in compact form. The triangle strip is a composite cell because it can be broken down into triangles, which are primary cells.
Certainly there are an infinite variety of possible cell types. In the Visualization Toolkit each cell type has been chosen based on application need. We have seen how some cell types: vertex, line, polygon, and triangle strip (Figure 3-19) are used to represent geometry to the graphics subsystem or library. Other cell types such as the tetrahedron and hexahedron are common in numerical simulation. The utility of each cell type will become evident through the practice of visualization throughout this book. A description of the cell types found in the Visualization Toolkit-including their classification as linear, nonlinear, or other-is given in the following sections.
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