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CHAPTER 12 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 © 2005 by CRC Press DITM: “tf1732_c012” — 2004/10/26 — 10:02 — page 247 — #1 248 DIGITAL TERRAIN MODELING: PRINCIPLES AND METHODOLOGY Primary visual variables Graphic 1 Graphic 2 Hue (color) G B Saturation (intensity) G G1 Size Shape Orientation 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 Graphics 1 Graphics 2 Arrangement Texture Orientation 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 representation 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 information graphically — as a means of gaining understanding and insight into the data. © 2005 by CRC Press DITM: “tf1732_c012” — 2004/10/26 — 10:02 — page 248 — #2 VISUALIZATION OF DIGITAL TERRAIN MODELS 249 Zoom Drag Pan Exploratory acts Blink Click Highlight Figure 12.3 Exploratory acts for visual analysis (Reprinted from Jiang 1996 with permission). Table 12.1 Variables at the Different Stages of Visualization Stage Variables in Use Paper graphics Visual variables — — — — Computer graphics Visual variables Screen variables — — — Visualization Visual variables Screen variables Dynamic variables Exploratory acts — Web-based visualization Visual variables Screen variables Dynamic variables Exploratory acts Web variables 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 variables 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. © 2005 by CRC Press DITM: “tf1732_c012” — 2004/10/26 — 10:02 — page 249 — #3 250 DIGITAL TERRAIN MODELING: PRINCIPLES AND METHODOLOGY 2-D static 2-D Static 3-D static 2-D dynamic 3-D Dynamic 3-D dynamic Figure 12.4 12.1.2 Approaches for graphic representation of DTM surface. 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, in Chapter 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 illumination 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 12.5 summarize 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 © 2005 by CRC Press DITM: “tf1732_c012” — 2004/10/26 — 10:02 — page 250 — #4 VISUALIZATION OF DIGITAL TERRAIN MODELS 251 Reality Remote sensing images DTM and landscape visualization Low level symbolization Spot heights High level symbolization Shading and hypermetric tints Abstraction Figure 12.5 Figure 12.6 A comparison of various techniques for terrain visualization. (a) (b) (c) (d) 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. © 2005 by CRC Press DITM: “tf1732_c012” — 2004/10/26 — 10:02 — page 251 — #5 252 DIGITAL TERRAIN MODELING: PRINCIPLES AND METHODOLOGY 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 (a) Figure 12.7 (a) 255 (b) Interval-based coloring of terrain heights: (a) hypermetric tints (color layers) and (b) half toning (gray layers). The color plate can be viewed at http://www.crcpress.com/e_products/downloads/download.asp?cat_no=TF1732. (b) g 255 gmax gmax gi gi gmin gmin 0 zmin Figure 12.8 zi zmax z g 0 zmin zi zmax z Height value to gray level mapping: (a) linear mapping and (b) nonlinear mapping. © 2005 by CRC Press DITM: “tf1732_c012” — 2004/10/26 — 10:02 — page 252 — #6 VISUALIZATION OF DIGITAL TERRAIN MODELS 253 (b) (a) 1 Figure 12.9 0 1 Kilometers 1 0 1 Kilometers 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 (zi − zmin ) zmax − zmin (12.1) where gi is the gray value of height zi ; gmin is the desired minimum gray value, 0 ≤ gmin < gmax ; gmax is the designed maximum gray value, gmin < gmax ≤ 255; gmin is the lowest height in the area; and zmax is 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 thus zmin = 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 © 2005 by CRC Press DITM: “tf1732_c012” — 2004/10/26 — 10:02 — page 253 — #7 254 DIGITAL TERRAIN MODELING: PRINCIPLES AND METHODOLOGY (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 in Chapters 4 and 5, and the subdivision of triangles was discussed in Chapter 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 transformation of the terrain surface from the ground coordinate system (GCS) O–XYZ to the viewpoint-centered eye-coordinate system (ECS) Oe –Xe Ye Ze and then it projects the surface onto the display screen which is parallel to the Oe –Xe Ye plane. 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 axis Ze is 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 transformations 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 12.11 shows the relationship between the two coordinate systems. Given the coordinates of the viewpoint in the GCS as (XOe , YOe , ZOe ) and an observing direction (azimuth angle α and pitch angle β), the direction cosine of each © 2005 by CRC Press DITM: “tf1732_c012” — 2004/10/26 — 10:02 — page 254 — #8 VISUALIZATION OF DIGITAL TERRAIN MODELS Z 255 Xe Oe O Ye –Ze  Y
X Figure 12.11 The ground coordinate and eye-coordinate systems. eye-coordinate axis can be calculated. In order to simplify the calculation, the vector Oe O (from the viewpoint Oe to 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 distance DS from Oe to O are known, then the coordinates of the viewpoint can be derived as follows:     XOe DS × cos β × cos α YOe  = DS × cos β × sin α  DS × sin β ZOe (12.2) 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 PX , PY , and PZ (usually called l, m, and n). Let the direction cosines of Oe Xe , Oe Ye , Oe Ze be represented by (l1 l2 l3 ), (m1 m2 m3 ), and (n1 n2 n3 ). Suppose Oe Xe is the horizontal axis, then XOe , DS n2 l1 = − , r n1 = where r = YOe , DS n1 l2 = − , r n2 = n3 = ZOe DS (12.3) l3 = 0 (12.4)  n21 + n22 m1 = −n3 l2 = − n1 n3 , r m2 = n3 l1 = − n2 n3 , r m3 = r (12.5) And the relationship between the ground coordinate (X, Y , Z) and the eye-coordinate (Xe , Ye , Ze ) is:      l2 l3 l1 X − XOe Xe Ye  = m1 m2 m3   Y − YOe  (12.6) Ze n1 n2 n3 Z − ZOe © 2005 by CRC Press DITM: “tf1732_c012” — 2004/10/26 — 10:02 — page 255 — #9 256 DIGITAL TERRAIN MODELING: PRINCIPLES AND METHODOLOGY 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 –Xe Ye plane and with a distance f 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 ×f Ze (12.7) v= Ye ×f Ze (12.8) 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 when f 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 Invisible Partially visible Visible Culled Figure 12.12 Different surface facets, completely hidden, partially visible, and visible. © 2005 by CRC Press DITM: “tf1732_c012” — 2004/10/26 — 10:02 — page 256 — #10