DATA VISUALIZATION

By

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V Sowjanya

Sr. Assistant Professor

Dept of Artificial Intelligence & Data Science

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LAKIREDDY BALI REDDY COLLEGE OF ENGINEERING

• Session Outcomes
• Screen Space
• Data Value Space
• Data Structure Space
• Attribute Space
• Object Space
• Visualization Structure Space
• A Unified Framework

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V Sowjanya

15/9/2025

Previously Discussed Topics

LBRCE

DATA VISUALIZATION

At the end of this session, Student will be able to:

• Understand the Visualization techniques for spatial data(Understand-L2)

V Sowjanya

15/9/2025

Session Outcomes

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Visualization of Spatial Data

• Spatial data visualization, under which the field of scientific visualization falls, assumes that the data has an implicit or explicit spatial or spatio-temporal attribute.
• This constraint facilitates both the creation and interpretation of the visualization, as there is an intuitive, and often straight forward, mapping of the data attributes to graphical attributes of the entities conveying the information in the visualization.
• The main differences are:

• In viewing the world surrounding us, we are not constrained by a two dimensional, discrete, low-resolution projection.

• On the screen, we can visually explore phenomena (real or simulated) at arbitrary scales.

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Visualization of Spatial Data

• On the screen, we can dynamically modify contrast, lighting, resolution, density, and other parameters and aspects of the data.

• On the screen, we can interactively navigate spaces that would be hard to enter in real life.

• On the screen, we can interactively add and remove parts of the data to get more context or remove clutter.

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Types of Spatial Data

• One dimensional
• Two dimensional
• Three dimensional

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LBRCE

DATA VISUALIZATION

• Given a one-dimensional sequence of univariate data (only one value per data item), we can map the spatial data to one of the screen dimensions and the data value itself to either the other screen dimensionor to the color of a mark or region along the spatial axis (to form a color bar).
• The data needs to be scaled to fit within the range of the display attribute (either number of pixels or number of colors).
• Parts of the display space or color range might be reserved for other aspects of the visualization, such as the axes, labels, and key, so the most general structure for an algorithm to generate such a visualization will use parameters for the bounds of both the data and display spaces.

V Sowjanya

15/9/2025

One Dimensional Data

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

One Dimensional Data

LBRCE

DATA VISUALIZATION

• Data with two spatial dimensions gets visualized predominantly by mapping the spatial attributes of the data to the spatial attributes of the screen.
• The result can be one of the following visualizations:
• 1. An image results if a single data value at each location is mapped to color and all intermediate pixels are colored via interpolation
• 2. A rubber sheet results if the data, whether regularly or irregularly spaced, is mapped to the height of a point in three dimensions, with the points triangulated so that a surface can be formed.
• 3. A cityscape is formed by drawing three-dimensional objects (generally boxes) at locations on a plane, where the data can control the at tributes of the graphical objects (i.e., height and color)

V Sowjanya

15/9/2025

Two Dimensional Data

LBRCE

DATA VISUALIZATION

• 4. A scatterplot results if, at each location on the plot, the data value(s) control the color, shape, or size of a marker. Note that unlike for images, no interpolation is performed.
• 5. A map results if the data contains linear and area features, as well as point objects. A linear feature, such as a road or stream, is represented as a sequence of connected coordinates, which are plotted as a series of line segments.
• 6. A contour or isovalue map conveys boundary information extracted from an image depicting a continuous phenomenon, such as elevation or temperature. The term isovalue means “single value,” and thus a contour on such a map indicates the boundary between points above this value and points below the value.

V Sowjanya

15/9/2025

Two Dimensional Data

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Two Dimensional Data

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Two Dimensional Data

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Two Dimensional Data

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Two Dimensional Data

LBRCE

DATA VISUALIZATION

• Besides the visualization techniques that display the entire data set, we can also choose to visualize one-dimensional subsets, projections, or summarizations of the data.
• Some probing techniques include
• Frequency Histograms
• Row and column aggregations.
• Linear probes.

V Sowjanya

15/9/2025

Probing two dimensional data

LBRCE

DATA VISUALIZATION

• We can summarize data sets of arbitrary dimensionality by computing the frequency at which values or subranges of values occur in the data, and then display this information as a bar graph.
• Important considerations when using subranges are how to decide the number of sub ranges to use, and where the breaks between subranges should be.
• Features of importance in the data might be lost if this is done incorrectly, and is best performed by someone extremely familiar with the data characteristics.
• Simply dividing the range into a fixed number of evenly sized subranges, while simple, is rarely an effective strategy

V Sowjanya

15/9/2025

Frequency Histograms

LBRCE

DATA VISUALIZATION

• Visually depicting summarizations of the rows and/or columns of an image is a useful mechanism for localizing the boundaries of features of interest and regions of low or high variability.
• Many descriptors can be used for this purpose, including the sum, average, median, standard deviation, maximum, or minimum values.
• The resulting one-dimensional visualization can be viewed separately or, as often the case, placed alongside the two-dimensional visualization as supplemental information.
• Color bars, line plots, and bar graphs have all been used with success in this type of visualization

V Sowjanya

15/9/2025

Row and Column Aggregations

LBRCE

DATA VISUALIZATION

• A line is passed through the data, and the values encountered are visualized.
• To accomplish this, we use two of the mathematical tools : parametric equations and bilinear interpolation.
• We start by creating a parametric equation of our probe using input from the user (either a pair of points or a point and a direction).
• If we assume that this line was specified as two sets of coordinates, P1 and P2, the parametric equation of the line segment joining the points is simply P(t)=P1 + t(P2 −P1), where 0 ≤ t ≤ 1.0.
• We can then get the coordinate of an arbitrary point along this line segment by choosing a value of t within this range

V Sowjanya

15/9/2025

Linear Probes

LBRCE

DATA VISUALIZATION

• Generally, these are evenly spaced, and the number of samples computed is proportional to the length of the line segment (so that probes that barely clip a corner of the data grid do not get represented by the same number of samples as a probe along the diagonal of the grid).

V Sowjanya

15/9/2025

Linear Probes

LBRCE

DATA VISUALIZATION

• As with two-dimensional data, three-dimensional spatial data may be either discrete samples of a continuous phenomenon or a structure best described via vertices, edges, and polygons.
• In reality, many visualizations of science and engineering data contain a combination of these data representations, such as air flow around a wing or stress attributes of a mechanical part.
• Three Dimensional Visualization techniques are
• Visualizing Explicit Surfaces
• Visualizing Volume Data
• Implicit Surfaces

V Sowjanya

15/9/2025

Three Dimensional Data

LBRCE

DATA VISUALIZATION

• An explicit surface is one that has been defined in one of two ways:
• a list of three-dimensional vertices, a list of connections between the edges (specified as a pair of indices into the vertex list), and a list of planar polygon patches (usually specified as a fixed or variable length list of indices into the edge list)
• a set of parametric equations for defining the x-, y-, and z-coordinates of points on the surface, along with an interconnection strategy (e.g., triangular or rectilinear grid) for computing the edges and patches. The step size of the parameters can be used to control the smoothness of the curved surface.

V Sowjanya

15/9/2025

Visualizing Explicit Surfaces

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Visualizing Explicit Surfaces

LBRCE

DATA VISUALIZATION

• Note that every edge is shared by exactly two faces, and that every vertex is a member of two or more edges.
• Also note that edge direction can be an issue; we often try to maintain a consistent orientation in traversing the edges of a face (either clockwise or counter-clockwise, from the outside of the face) to insure that we can compute surface normals correctly, e.g., pointing away from the inside of the object defined by the surface.

V Sowjanya

15/9/2025

Visualizing Explicit Surfaces

LBRCE

DATA VISUALIZATION

• Volume data is generally a sampling of a continuous phenomenon, and can be either acquired via sensors (e.g., tomographic data sets) or generated via simulations (e.g., computational fluid dynamics).
• In each case, we have one or more data dimensions with regular or irregular positions, and the goal is to convey to the viewer the structure, patterns, and anomalies within the data.

V Sowjanya

15/9/2025

Visualizing Volume Data

LBRCE

DATA VISUALIZATION

• Slicing Techniques
• Isosurface Techniques
• Direct Volume Rendering
• Slicing Volume Data with Cut planes
• Isosurface Extraction Using Marching Cubes.
• Direct Volume Visualization Techniques.

V Sowjanya

15/9/2025

Techniques to visualize volume Data

LBRCE

DATA VISUALIZATION

• Using a cut plane, either aligned with an axis or arbitrarily oriented, probe the data to extract a two-dimensional slice of the data, and then use one of the two-dimensional spatial data visualization methods.

V Sowjanya

15/9/2025

Slicing Techniques

LBRCE

DATA VISUALIZATION

• Given a user-specified value, generate a surface de scription and visualize it using one of the explicit surface visualization techniques

V Sowjanya

15/9/2025

Isosurface Techniques

LBRCE

DATA VISUALIZATION

• Either cast rays into the volume and compute a pixel value based on the data encountered by the ray, or project each voxel onto the projection plane using some method of accumulating effects on pixels

V Sowjanya

15/9/2025

Direct Volume Rendering

LBRCE

DATA VISUALIZATION

• A popular technique for volume data is the use of cut planes, where the data block is sliced by a plane with a given orientation and position, and the data that the plane intersects are mapped to the plane for display.
• The simplest implementation of this technique is to constrain the orientation of the cut plane so that its normal coincides with one of the data axes.
• The user then specifies a row, column, or depth in the data block, and the corresponding slice is displayed using one of the techniques described in the section on two-dimensional spatial data visualization.
• An effective strategy is to animate the slice selection so that the user can form associations between adjacent slices.

V Sowjanya

15/9/2025

Slicing Volume Data with Cut Planes

LBRCE

DATA VISUALIZATION

• Many variations on this technique exist, and each can provide significant details about the interior of the volume. Some of these include:

• nonplanar slices;

• consecutive slices in varying orientations to remove blocks of the data;

• stacked slices displayed simultaneously;

• orthogonal slices displayed simultaneously

V Sowjanya

15/9/2025

Slicing Volume Data with Cut Planes

LBRCE

DATA VISUALIZATION

• Many variations on this technique exist, and each can provide significant details about the interior of the volume. Some of these include:

• nonplanar slices;

• consecutive slices in varying orientations to remove blocks of the data;

• stacked slices displayed simultaneously;

• orthogonal slices displayed simultaneously

V Sowjanya

15/9/2025

Slicing Volume Data with Cut Planes

LBRCE

DATA VISUALIZATION

• Marching Cubes is an algorithm developed by Lorensen and Cline in 1987 for rendering isosurfaces in volumetric data (Wyvill et. al. developed a similar strategy a year earlier]).
• The basic notion is that we can define a voxel (cube) by the values at the eight corners of the cube.
• If one or more corners of a cube have values less than the user-specified isovalue, and one or more have values greater than this value, we know that the voxel must contribute some component of the isosurface.
• By determining which edges of the cube are intersected by the isosurface, we can create triangular patches that divide the cube between regions within the isosurface and regions outside.
• By connecting the patches from all cubes on the isosurface boundary, we get a surface representation

V Sowjanya

15/9/2025

Isosurface Extraction Using Marching Cubes

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Isosurface Extraction Using Marching Cubes

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Isosurface Extraction Using Marching Cubes

LBRCE

DATA VISUALIZATION

• Direct volume rendering means that no three-dimensional polygons are created for use with traditional graphics rendering techniques.
• Rather, pixels in the resulting image are computed on an individual basis, either by casting rays through the pixel through the volume, or by projecting voxels onto the plane of projection.

V Sowjanya

15/9/2025

Direct Volume Visualization Techniques

LBRCE

DATA VISUALIZATION

• The basic process of rendering a volumetric data set starts by transforming the positions of the voxels into the viewing coordinate system, following the same procedure used in the traditional three-dimensional graphics pipe line.
• The viewer must specify a view reference point (the origin of the plane of projection), a view direction (the normal to the plane of projection), the height and width of the image to be projected on the plane of projection, and, for a perspective projection, the distance from the camera to the plane of projection. Once the voxels have been positioned, we have the option of either:

• forward mapping—project each voxel onto the plane of projection and determine which pixels will be affected and in what way;

• inverse mapping—also called ray casting, send a ray from each pixel in the plane of projection through the volume, sampling values along the ray, and determining the resulting value for each pixel

V Sowjanya

15/9/2025

Direct Volume Visualization Techniques

LBRCE

DATA VISUALIZATION

• In forward mapping, we have a number of problems to be resolved (from [236]), including:
• how to deal with pixels that are influenced by multiple voxels
• how to handle pixels to which no voxel directly maps
• how to deal with the fact that voxels usually project to positions be tween pixels .
• For inverse mapping, we have similar problems:
• how to select the number of points to be sampled along the ray
• how to compute the value at these points, which usually fall between voxels
• how to combine the points encountered along each ray

V Sowjanya

15/9/2025

Direct Volume Visualization Techniques

LBRCE

DATA VISUALIZATION

V Sowjanya

15/9/2025

Direct Volume Visualization Techniques

LBRCE

DATA VISUALIZATION

• Session Outcomes
• Visualization of Spatial Data
• Types of Spatial Data
• One dimensional data
• Two dimensional data
• Probing two dimensional data
• Three dimensional data

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V Sowjanya

15/9/2025

Summary

LBRCE

DATA VISUALIZATION