Digital Terrain Modeling: Principles and Methodology - Chapter 12 pps

Visualization of Digital Terrain ModelsIt has been estimated that over 80% of information one obtains is through our visual systems and thus our visual systems are overloaded.. 12.1.1 Va

Visualization of Digital Terrain Models

It has been estimated that over 80% of information one obtains is through our visual systems and thus our visual systems are overloaded From an other point

of view, visualization is an important issue in all disciplines, including digital terrain modeling

12.1 VISUALIZATION OF DIGITAL TERRAIN MODELS: AN OVERVIEW

DTM visualization is a natural extension of contour representation, which has been discussed in Chapter 11 In order to understand this, the basic concepts, that is, variables used at different stages, approaches, and basic principles, will be discussed here

12.1.1 Variables for Visualization

Visual representation is an ancient communication tool and contouring is a graphic representation for visual communication Here, communication means to present information (results) in graphic or other visual forms that are already understood Six primary visual variables are available for such a presentation:

1 three geometric variables

• shape

• size

• orientation

2 three color variables

• hue

• value or brightness

• saturation or intensity

247

Primary visual variables Graphic 1 Graphic 2

Size

Shape

Orientation

Hue (color)

Saturation (intensity)

Value (brightness)

Figure 12.1 Six primary variables for visual communication The color plate can be viewed at

http://www.crcpress.com/e_products/downloads/download.asp?cat_no = TF1732.

Secondary visual variables

Arrangement

Texture

Orientation

Graphics 1 Graphics 2

Figure 12.2 Three secondary variables for visual communication.

Figure 12.1 shows these six variables graphically In addition, three secondary visual variables (Figure 12.2) are available:

1 Arrangement: shape and configuration of components that make up the pattern.

2 Texture: size and spacing of components that make up a pattern.

3 Orientation: directional arrangement of parallel rows of marks.

Visualization is a natural extension of communication and goes into a domain called visual thinking (DiBiase 1990) Visualization emphasizes an intuitive repre-sentation of data to enable people to understand the nature of phenomena represented

by the data In other words, visualization is concerned with exploring data and infor-mation graphically — as a means of gaining understanding and insight into the data

Blink

Highlight

Click

Exploratory acts

Figure 12.3 Exploratory acts for visual analysis (Reprinted from Jiang 1996 with permission).

Table 12.1 Variables at the Different Stages of Visualization

variables

graphics variables variables Visualization Visual Screen Dynamic Exploratory —

variables variables variables acts Web-based Visual Screen Dynamic Exploratory Web variables visualization variables variables variables acts

Thus, visualization has been compared to visual analysis, with an analogy to numerical analysis

Visualization is a fusion of a number of scientific disciplines, such as computer graphics, user-interface methodology, image processing, system design, cognitive science, and so on The major components are rendering and animation techniques

In visualization, in additional to the traditional visual variables, some other sets of vari-ables are in use One set, related to analysis, is called exploratory acts (Figure 12.3), which consists of drag, click, zoom, pan, blink, and highlight and so on (Jiang 1996) Theoretically, some variables particular to screen display such as blur, focus, and transparency (Kraak and Brown 2001) are also in use In the era of Web-based visualization, more exploratory acts are in use, particularly the browse and plug-in Table 12.1 lists the sets of variables in use at different stages

The dynamic variables (DiBiase et al 1992) are related to animation, including duration, rate of change, and order These variables will be discussed in Section 12.5

3-D

Static

Dynamic

2-D static

3-D static

2-D dynamic

3-D dynamic

Figure 12.4 Approaches for graphic representation of DTM surface.

12.1.2 Approaches for the Visualization of DTM Data

Visualization of DTM data means to make use of these variables for visual presentation

of the data so that the nature of the terrain surface could be better understood In fact,

inChapter 1,a brief discussion on the representation of terrain surface was conducted and it was pointed out that terrain surfaces could be represented by either graphics or mathematical functions(Figure 1.4).This chapter focuses on graphic representations

It is understandable that there are 2-D and 3-D representations, both in static and dynamic modes Figure 12.4 shows a classification of these visualization approaches This chapter gives a brief discussion of 2-D representation techniques and a few new developments in 3-D representations, as follows:

1 Texture mapping: This is to produce virtually real landscapes by mapping aerial

photographs or satellite images onto the digital terrain model This method can show the color and texture of all kinds of ground objects and artificial constructions, but the geometric texture of terrain relief cannot be clearly represented Therefore, the method is often used to represent smooth areas where there are many ground objects and human activities, such as towns and traffic lines

2 Rendering: This is like shading, but in 3-D representations It makes use of

illumi-nation models to simulate the visual effect produced when lights shine on the terrain This method can be used to simulate micro ground relief (geometric texture) and color using pure mathematical models Terrain simulation based on fractal models

is considered to be the most promising method

3 Animation: This can be used to produce dynamic and interactive representations.

If all these techniques are compared, one would find that some are more abstract than others and some are more symbolic than others.Figure 12.5summarize this

12.2 IMAGE-BASED 2-D DTM VISUALIZATION

In two dimensions, contouring is the most popular technique A detailed description

of contouring was given in Chapter 11 This section presents some image-based

Shading and hypermetric tints

DTM and landscape visualization

Remote sensing images

Spot heights

High level symbolization

Low level symbolization

Reality

Abstraction

Figure 12.5 A comparison of various techniques for terrain visualization.

Figure 12.6 Shading of terrain surface: (a) a pyramid-like object; (b) the orthogonal view;

(c) hill shading; and (d) slope shading.

techniques It is possible to make the 2-D representation dynamic through animation; however, it is not common to do so, therefore 2-D dynamic representation will not be discussed here

12.2.1 Slope Shading and Hill Shading

Among these image-based techniques, shading is still widely used Two types are available, hill (or oblique) and slope (or vertical) shading

Slope shading assigns a gray value to each pixel according to its slope value The steeper the slope, the darker the image Figure 12.6(a) is pyramid consisting of four triangular facets and a base Figure 12.6(b) is the orthogonal view of Figure 12.6(a) Figure 12.6(d) is the result of slope shading It can be found that the two facets with identical slope angles are assigned the same gray shade

Figure 12.6(c) is the result of hill shading The idea is to portray the terrain variations with different brightness by illuminating the pyramid so that shadow effects are produced, thus leading to the stereoscopic sense, which is produced by the readers’ experience (but not by perception on a physical level) In hill shading, a light source

is assumed, normally from the northwest The facet facing the light is brightest and the facet facing away the darkest

12.2.2 Height-Based Coloring

Here, the term height-based coloring means to assign a color to each image pixel

based on the heights of the DTM data Two approaches are in use, interval-based and continuous coloring

Hypermetric tinting (color layers) is an interval-based coloring widely used The basic principle is to use different colors for areas with different altitudes Theoretically, one could use an infinite number of colors to represent heights However, in practice, terrain surface is classified into a few intervals according to height and one color is assigned to each class The commonly used colors are blue for water, green for lower altitude, yellow for medium, and brown or red for higher altitude Figure 12.7(a) is

an example

Gray can also be used to produce an image similar to Figure 12.7(a) Figure 12.7(b)

is an example It is possible to use a continuous variation of gray tones to illustrate the variations of the terrain surface (instead of height ranges) In other words, gray levels from 0 to 255 are used to represent the heights of the terrain surface A mapping process is needed to fit the terrain height variations into the gray range of [0,255] Figure 12.8 shows some possible mappings The simplest is linear stretching (if the range of heights is much smaller than 256) or linear depression (if the variation is

Figure 12.7 Interval-based coloring of terrain heights: (a) hypermetric tints (color

lay-ers) and (b) half toning (gray laylay-ers) The color plate can be viewed at http://www.crcpress.com/e_products/downloads/download.asp?cat_no = TF1732.

g

z

255

0

gmax

gmin

zmax

gi

255

0

gmax

gmin

gi

g

(b) (a)

Figure 12.8 Height value to gray level mapping: (a) linear mapping and (b) nonlinear mapping.

(a) (b)

Figure 12.9 Representation of DTM by continuous gray image: (a) a contour map and (b) the

gray image of the contour map.

outside the range of [0,255]) Equation (12.1) is the formula for a linear mapping

gi= gmin+gmax− gmin

zmax− zmin(zi− zmin) (12.1) wheregi is the gray value of height zi; gmin is the desired minimum gray value,

0 ≤ gmin < gmax;gmaxis the designed maximum gray value,gmin < gmax≤ 255;

gminis the lowest height in the area; andzmaxis the largest height value in the area

In this way, the height range[zmin,zmax] is mapped into a gray range [zmin,zmax]

Usually, the full gray range [0,255] is used and thuszmin = 0 and zmax = 255

Figure 12.9 is an example of the continuous gray image of a DTM, which clearly shows the shape of the landscape

12.3 RENDERING TECHNIQUE FOR THREE-DIMENSIONAL

DTM VISUALIZATION

With the development of computer graphics, 3-D visualization has become the mainstream of DTM visualization The 3-D wire frame (Figure 12.10) is widely used, especially in computer-aided design However, rendering, which employs some illumination models to produce a vivid representation of 3-D objects, has become a more popular technique for DTM visualization

12.3.1 Basic Principles of Rendering

The basic idea of rendering is to produce vivid representations of 3-D objects

A surface is split into a finite number of polygons (or triangles in the case of TIN); all these polygons are projected onto the view plane of a given viewpoint; each visible pixel is assigned a gray value, which is computed based on an illumination model

(a) (b)

Figure 12.10 Three-dimensional wire frame of a surface: (a) hidden lines not removed and

(b) hidden lines removed.

and the viewpoint In other words, rendering of DTM is to transform a DTM surface from a 3-D to a 2-D plane The rendering process follows these steps:

1 to divide the surface to be rendered into a set of contiguous triangular facets

2 to set a viewpoint, determine the observing direction, and transform the terrain surface into an image coordinate system

3 to identify the visible surfaces

4 to calculate the brightness (and color) of the visible surface according to an illumination model

5 to shade all the visible triangular pieces

The first step is omitted here because triangulation was discussed inChapters 4 and 5, and the subdivision of triangles was discussed inChapter 9

12.3.2 Graphic Transformations

What can be displayed on the screen is determined by the position of the observer (or viewpoint) and the direction of the sight line Rendering begins with the

trans-formation of the terrain surface from the ground coordinate system (GCS) O–XYZ to

the viewpoint-centered eye-coordinate system (ECS) Oe–XeYeZeand then it projects the surface onto the display screen which is parallel to the Oe–XeYeplane This series

of transformations is called graphical transformations, which consists of shifting, rotating, scaling, and projection

Both the GCS and the ECS are right-hand 3-D Cartesian coordinate systems For the ECS, its origin is fixed on the viewpoint, and its axisZeis opposite the observing direction Based on the characteristics of digital computation with a computer, a vector

in 3-D space is described by three direction cosines This simplifies the relationships between two 3-D coordinate systems and makes the computation of coordinate trans-formations more efficient All subsequent processes, such as recognition of visible facets, projective transformation, and the shading process, will be carried out in the ECS.Figure 12.11shows the relationship between the two coordinate systems Given the coordinates of the viewpoint in the GCS as(XO e,YO e,ZO e) and an

observing direction (azimuth angleα and pitch angle β), the direction cosine of each

Z

Y

X

Ye

Xe

–Ze

Oe



Figure 12.11 The ground coordinate and eye-coordinate systems.

eye-coordinate axis can be calculated In order to simplify the calculation, the vector

OeO (from the viewpoint Oeto the origin of the GCS O) and the direction of the sight line are merged here This joint direction will be considered as the future projection direction This simplifies the problem That is, when the direction of the sight line and the viewing distanceDS from Oe to O are known, then the coordinates of the viewpoint can be derived as follows:



X YOOee

ZOe



 =



D DSS× cos β × cos α × cos β × sin α

DS× sin β



The three direction cosines are the cosines of the angles between the vector from the origin to a point P and each of the coordinate axes (in the plane including the vector and the axis) If vector−→OP is of unit length, these direction cosines reduce to

P X,P Y, andP Z(usually calledl, m, and n).

Let the direction cosines of OeXe, OeYe, OeZe be represented by (l1 l2 l3), (m1m2m3), and (n1n2n3) Suppose OeXeis the horizontal axis, then

n1=XO e

DS

, n2= YO e

DS

, n3=ZO e

DS

(12.3)

l1= −n2

r , l2= −

n1

wherer =n2

1+ n2 2

m1= −n3l2= −n1n3

r , m2= n3l1= −n2n3

r , m3= r (12.5) And the relationship between the ground coordinate(X, Y , Z) and the eye-coordinate (Xe,Ye,Ze) is: 

X Yee

Ze



 =



m l11 m l22 m l33

n1 n2 n3







X − X Y − YOOee

Z − ZO e



To project the 3-D terrain surface onto the 2-D screen, either parallel or central (perspective) projection can be used To obtain the visual effects consistent to the human eye and to produce perspective views with strong stereo sense and realism, the perspective projection is used in the field of computer graphics Suppose a plane parallel to the Oe–XeYe plane and with a distancef to the viewpoint is used as a

projection plane (screen), then the coordinates of a point in the ECS can be transformed into the coordinates(u, v) on the display screen by using the following formula:

u = Xe

v = Ye

In these formulae, f is similar to the focus of the camera, expressing the distance

between the projection plane (screen) and the observer Experience shows that optimal visual effects can be obtained whenf is three times the size of the screen.

12.3.3 Visible Surfaces Identification

The challenge in generating graphic images with a stereo sense is the removal of hidden surface, which is similar to the hidden line removal in the 3-D wire frame This means that those facets that can be seen from the position of the current viewpoint need to be identified Surface facets outside the view field are cut out, and those facets that are in the view field but are partially blocked by others have to be identified This process is also called the recognition of the visible surface facets in the literature Figure 12.12 shows these different surface facets

All algorithms for visible surface recognition make use of a form of geometric classification to identify the visible and hidden surfaces Visible surface recognition

Partially visible

Culled

Figure 12.12 Different surface facets, completely hidden, partially visible, and visible.