2.2.1 Spot Elevations
2.2.2 Contours
2.2.3 Cross Sections
2.3.1 Surfaces
2.3.1.1 Simple Planes
2.3.1.2 Grid Mesh
2.3.1.3 Ruled Surface
2.3.1.4 TIN - Triangulated Irregular Network
2.3.1.5 Parametric Surfaces: Patches and NURB Surfaces2.3.2 Three-Dimensional Solid Terrain
2.3.2.1 Parametric Solids
2.3.2.2 Stepped Contours ("Pancake" Models)
2.3.2.3 Boolean 0perations
2.3.2.4 Rocks
2.5.1 Simple Color
2.5.2 Multichannel Textures, Including Photographic Based Textures
2.5.3 Draped 2D Image Maps
2.5.4 Geospecific Textures
2.5.5 Geotypical Textures
2.6.1 Tiling of Texture Maps
2.6.2 Levels of Detail
2.63 Lights and Shadows on Landform
2.7.1 Cut and Fill Volume Calculations
2.7.2 GIS-Based Elevation, Slope, and Aspect Analysis
2.8.1 Generation
2.8.1.1 Fractal Terrain
2.8.1.2 Terraforming2.8.2 Movement Through Terrain
2.8.3 Movement of Terrain
2.8.4 GIS-Based Erosion and Other Dynamic Models
Figure 2.4 The curvature of the earth, about 10 ft. in 30 miles (or about 1 meter in 15 kilometers).
Figure 2.7 Sinuous contours produced with smooth curves, and straight-line approximations of them.
Figure 2.11 Typical surface: a. From above. b. From below.
Figure 2.22 Triangulated surface without break lines. a. Plan view. b. Axonometric view.
Figure 2.23 Triangulated surface with breakline included. a. Plan view. b. Axonometric view.
Figure 2.26 NURB surface showing control points, curves and surface mesh. Modeled in Rhino3D.
Figure 2.30 Pancakes and layer cakes along with a wireframe and rendered stepped contour model.
Figure 2.37 a. Detail or draped map. b. A colored elevation map draped over terrain.
Figure 2.57 Walkthrough of University Commons Schematic Model
Figure 2.59 Morphing Terrain - The Eroding Pyramid
Landform, or terrain, is the basis of any landscape, forming the (roughly) horizontal foundation upon which all else is arrayed. Landform is made up of various underlying geological substrates, with diverse surface coverings: exposed rocks, sand, gravel, synthetic paving, grass, leaf litter, and so on. Usually, we don't see the constituent material directly, but rather the covering - often vegetation - that forms the surface. The underlying material, however, gives characteristic shape and texture to landform, influencing the way natural forms occur, and how built structures and surfaces will appear and behave.
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For landscape architects and others making 2D schematic drawings (plans), a stylized conventional form of representing landscapes by spot elevations and contour lines is used. These are often the base data from which a digital model is created. Surveyors capture spot elevations, and use mathematical formulae to interpolate the elevation, shape, and location of contour lines. These curved, closed, nonintersecting lines trace the imaginary beach line that would formed by water at various elevations (e.g., every foot, or every 10 meters) but are rarely ever seen in the real landscape (except at water bodies, of course, and in other special landscapes such as rice paddies).
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Most land surveyors produce data on landform by recording spot elevations at irregular intervals, attempting usually to capture important features in the landscape: high points, low points, centerlines of ridges and valleys, top and bottom elevations of walls, elevations at the base of notable trees and structures, etc. Often each such point is identified by a unique label. These spot elevations represent the basic data structure from which most other terrain data is constructed. Elevation data may be gathered by other methods as well, including remote sensing by aircraft and satellites, and ortho-photo interpretation from pairs of aerial photographs.
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Figure 2.1 Partial plan of the spiral landform as seen on previous page. The surface is expressed as spot elevations. Each point is labeled with a number that corresponds to the point table inset. University Commons, Hargreaves Associates (1998-1999).
Figure 2.2 Conic landform with spiral path, represented as a paraline drawing with contours and spot elevations. Screen capture of AutoCAD R14. University Commons, Hargreaves Associates (1998-1999).
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Technical Note: Projections
Geo-referencing information depends on both units of measurement (feet, meters, miles, etc.) and a projection system, which converts spherical coordinates on the earth's surface to rectangular (x,y) coordinates in a Cartesian system. Latitude and longitude are a spherical coordinate system, based on 360 degrees of longitude in the equatorial circle, with an arbitrary 0, located at the meridian passing through the royal observatory at Greenwich, England, and conventionally measured in degrees, minutes (1/60 of a degree), and seconds (1/60 of a minute). Because of the nature of the sphere, in which lines of longitude converge into a point at either pole, one degree of longitude represents a distance ranging from approximately 300 miles at the equator of the earth, to zero at the pole, and so is an inconvenient unit for measurement of distances. Consequently, most geographical x,y measurements are converted into some planar grid system, by means of a mathematical projection. ... (Note: This Website contains abbreviated text.
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Figure 2.3 Map showing differences in registration produced by two different projection systems - the UTM system, in meters, and the Massachusetts State Plane system in feet - over an area of about 30km x 40km. The misregistration can be as much as 1 kilometer near the edges of the study area.
Figure 2.4 The curvature of the earth, about 10 ft. in 30 miles (or about 1 meter in 15 kilometers).
The most common form of representation of terrain at the site scale by professionals is the contour plan: a series of curved lines, each with a specified elevation, set at a fixed vertical contour interval apart, representing lines of equal elevation (isolines). The contour interval may vary from a few inches, or fractions of a foot, for detailed construction plans or very flat areas, to tens of meters for larger scale maps and more mountainous terrain. Contour plans may also incorporate spot elevations, especially at high points and low points, whose elevation would not otherwise be conveyed by the contours. These data-sets are often derived from spot elevations for existing terrain, or produced by landscape architects and engineers for new proposed surfaces. Contours may also be obtained from USGS Topographic maps, and other data sources such as local or state highway engineering departments. Although they are a conventional 2D representation, contours can be hard to understand except by trained professionals, and when projected into three dimensions, tend to yield just so much "spaghetti."
Figure 2.5 Partial 2D contour plan at spiral mound and pyramid landform represented with both 2D and 3D contour lines (polylines). University Commons, Hargreaves Associates (1998-1999).
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Figure 2.6 Note the precise linear contours of the pyramid landform in contrast to the curvilinear forms of the freeform berms. University Commons, Hargreaves Associates (1998-1999).
Figure 2.7 Sinuous contours produced with smooth curves, and straight-line approximations of them.
Contour lines are limited to representing surfaces which are continuous in two dimensions, in which no vertical, overhanging, undercut, or multilayered conditions can be adequately represented (except by confusing graphic techniques such as dotted lines, etc.) Consequently, especially for site scale design, cross-sectional drawings of terrain conditions are also often used. Contours are in fact themselves cross sections, taken horizontally; most other cross sections are taken vertically, at specified locations, to reveal a side-cut view. (Terrain is rarely represented by real side views, or elevations, such as are used for the sides of buildings, etc, because terrain usually has few or no vertical faces).
Figure 2.8 Series of cross sections cutting through the variety of landform and plaza conditions. University Commons, Hargreaves Associates (1998-1999).
Cross-sectional drawings can be valuable for the generation of terrain surface and solid models by using a sweep operation, or by continuously joining up, or morphing between, a series of cross sections. This technique is especially useful for linear landform features, such as roadways, or drainage channels, in which cross sections are given at regular intervals along a path, or centerline.
Figure 2.9a. Section cuts of a free form berm with a centerline. b. The section cuts can be "swept" along the centerline to produce a three dimensional berm. The resulting geometric object can be either a ruled or NURB surface.
The various representations and tools described in the previous sections were designed to transform the sinuous, massive, and solid aspects of real terrain into 2D data structures for analog representations on paper. With a digital model, you can represent terrain in its three-dimensional complexity and then generate either 2D or 3D visual representations for analysis or presentation. The following section will reveal the variety of 3D data structures that can be employed for the creation of a three-dimensional digital terrain model. Although real terrain is massive and solid, with depth and volume, the starting point for most representation is to treat the ground as a surface.
Figure 2.10 Access to North Entrance, Plaza de la Constitucion de Girona. Giron, Spain, 1983-1993. The office of Elias Torres & Martinez LaPena.
A surface is a mathematical, infinitely thin object, with two sides, so that in a 3D view you can go beneath, and see the back-side. Mathematically, a surface can be characterized as a set of points (x,y,z) such that z = f(x,y); that is, at each location (x,y) seen from above, there is only a single z-value, or elevation. Terrain surfaces may be simple or complex, flat or rolling, shallow or steep. In the real landscape, landforms are constrained in their shapes and slopes by real-world physical criteria such as the geologic makeup of the soil, the climate, vegetative covering, and other ecological concerns. In most digital models, these constraints do not automatically apply, but should be considered if the terrain being represented is to be subject to real-world influences.
Figure 2.11 Typical surface: a. From above. b. From
below.
The simplest landform of all is just a flat plane; the next more complex is a tilted plane, representing a sloping hillside. At least this minimum landform is required for modeling a landscape, and provides a surface which can be used to locate other features, such as trees or buildings, and on which those features can cast shadows. Often, to make sure that surface objects appear to be sitting upon the terrain, they are created with their base elevation just below the elevation of the terrain surface, or plane, so that they are truly embedded in the surface.
Figure 2.12 a. Simple surface plane parallel to the construction plane. b. Simple surface plane sloped at 30 degrees from the construction plane.
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While contour lines have appealing graphic qualities in 2D, they are a somewhat complicated data structure to store digitally, as the data file must contain information about the connectivity of each point to its two neighbors, keep track of multiple lines, each with its own z-value, and so on. A far simpler, and therefore more common data structure for a digital elevation model - especially for large areas, such as the statewide and national coverage provided by the United States Geological Survey (USGS) - is a raster grid: a rectangular array of numbers, each representing the elevation (z) value of the land at each point (x,y) located on a regular grid. This form of digital elevation model (DEM, or DTM for digital terrain model) can be found at varying (coarse) resolutions for most areas of the world, from a variety of sources. (See the section on data sources on this Website -ROM.)
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Figure 2.13 a. The plan on the left shows a grid mesh surface with a resolution of 20' b. The plan on the right shows a grid mesh surface with a resolution of 5'. Consider what detail is maintained with the higher resolution at the cost of efficiency.
The most important variable decision to make for these models is the size of the grid cell. If the grid size is too small, the file size may get enormous, rendering time will increase, and the resulting image may be too dense with lines. If too large a cell size is used, the surface may appear too coarse.
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Figure 2.14 This set of images illustrates two of
the ways in which a surface generated through draped polylines can be represented.
a. M direction polylines b. N direction polylines. University Commons, Hargreaves
Associates (1998-1999).
Figure 2.15 This set of images illustrates in a three-dimensional
view the same surface represented with a 20 ' and a 5' polyface mesh grid. University
Commons, Hargreaves Associates (1998-1999).
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Technical Note: Grid Mesh
In grid mesh files, it is important to distinguish between numbers stored in Integer or Floating Point formats. Integer values, with no decimal point, are more compact in storage and quicker for computers to calculate with, but are inherently less precise (a value of 1.5 must be represented as either 1, or 2). In terrain with steep slopes and high variability (mountainous terrain, for example) integer data values may acceptable. Floating Point values, with a decimal point and some specified amount of precision (numbers to the right of the decimal point), consume more space, making larger data files (each value may have to be written out with all decimal places, as 1.000000, 1.500000 etc.), and are more complex and time consuming for computers to operate on. ... (Note: This Website contains abbreviated text.
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Figure 2.16 If the dots are at the center of the cell,
the grid is 4 x 3; if the dots are the corners, it is only 3 x 2.
Note that in a wire-frame representation, in areas where the slope of the terrain is viewed obliquely, and there is a greater density of lines (or pixels, on a computer screen), the greater density results in a darkening of the region, and in areas where the faces are viewed more head-on, and there is less density of lines (or pixels), there is an corresponding lightness. This gives a sense of shading to the image so produced, but this shading has nothing to do with lighting, or light or shade, and is in fact quite artificial and may be even be misleading.
Figure 2.17 In this wire frame plot, the density of white lines appears as if it is illumination on the surface of the mesa, but in fact there is no lighting at all, only density of lines and "false shading".
Another simple and direct method of generating a 3D surface model from contours is to create a ruled surface, generating 3D faces between adjacent pairs of contour lines. If each contour line is a 3D isoline (a polyline with a constant z-value), one simple approach consists of connecting each vertex point on the first line with an appropriate number of points on the second line, to form a series of quadrilaterals or triangles which together create a band of connected 3D faces. Since each point on each line is used in this method, there will be continuity across contour lines, and no gaps. The biggest trick to this method is determining, for each pair of lines, the appropriate number of points on the second line to connect to each point on the first. If the number of points on each line happens to be identical, then the choice is simple and a series of rectangular, trapezoidal, or lozenge-shaped quadrilateral faces will be created. If the numbers are unequal, especially if they are greatly unequal, then a series of triangles will be created.
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Figure 2.18 a. Simple isolines or contours (polylines)
from which the ruled surface will be derived. b. Ruled surface as derived from
the contours. This example makes explicit the risk involved with using the ruled
surface. Consider carefully the resolution and density of the surface before
generation. Note the gaps between the contour line and the ruled surface.
Figure 2.19 a,b a. Using a ruled surface to generate
a surface between the contours of a free form landform can produce unpredictable
results. b. One approach is to "break" the isolines at the ridges and breaklines,
and then use the landform-specific contours as input for the ruled surface.
Note the rectangular, trapezoidal, or lozenge shaped quadrilateral faces.
Figure 2.20 Ruled surfaces are suitable for representing either regular or geometric landforms. a. An axonometric view of the pyramid and cone landforms as isolines/contours. b. Those same landforms modeled with ruled surfaces. Note the differing density of the ruled surface and the crispness of the ridges. University Commons, Hargreaves Associates (1998-1999).
[HOW-TO : RULED SURFACE] <- Click to download PDF version of the Tutorial
Although regular rectangular gridded meshes (fishnets) and ruled surfaces are conceptually simple and computationally efficient, they suffer from several drawbacks. For one, regularly spaced grids may be inefficient: the regular spacing between cells cannot be varied, and in areas of low or no relief, many redundant and repetitive points must still be entered, and in areas of high variation, important features may be missed if they do not fall directly on the regular grid spacing. In terrain with a range of relief, the smallest grid required to pick up detail in the areas of greatest relief must be used for the entire area. If a larger grid is chosen for economy's sake, then detail may be missed in local areas; for example, a peak, or high point, maybe located in between grid points, and so not measured or stored. Second, as noted above, the non-planar surfaces of the quadrilateral faces in a rectangular mesh present a problem to simple rendering algorithms, as no single surface normal vector can be found.
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Figure 2.21 Illustration of Delaunay triangulation,
in black, and its inverse, or "dual," a Voronoi tesselation, in gray.
Figure 2.22 Triangulated surface without break lines.
a. Plan view. b. Axonometric view.
Figure 2.23 Triangulated surface with breakline included.
a. Plan view. b. Axonometric view.
Figure 2.24 Plan and axonometric view of a TIN surface
made from contours. a. Plan view. b. Axonometric view.
Figure 2.25 a. Contour plan of conical mound and path.
b. Plan of the same condition with contours generated from a TIN surface. The
original TIN surface is shown in gray.
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Technical Note: VRML Code for Triangular Irregular Network
The VRML language specification, at version 2.0, contains a clear specification and syntax for encoding the topology of TINs, and may be an attractive format for transferring between programs if the option is available. Using some other exchange formats, such as .DXF, often loses the topological connectivity, and represents every triangle separately, so many points are saved with all their 3 coordinates multiple times, which is grossly inefficient on a large TIN. In the VRML format, each point is entered only once, then a table of faces lists the three points used in each face just by its index number, which is much more efficient. ... (Note: This Website contains abbreviated text. For the complete text, |
[HOW-TO: TIN] <- Click to download PDF version of the Tutorial
The greatest disadvantage of TIN representations, other than their complex data structure, is their simple geometry and faceted nature. Truly smooth curves cannot be represented, except in approximation. In rendering, the sharp facets and plane faces of a TIN can be smoothed out, an important fact to remember. Smooth shaded renderings may be generated from faceted surfaces, by using interpolation in rendering to compute multiple intermediate angles between faceted surfaces, and generate an apparently smooth curve.
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Figure 2.26 NURB surface showing control points, curves and surface mesh. Modeled in Rhino3D.
[HOW-TO: NURBs] <- Click to download PDF version of the Tutorial
All of the previous section's representations are founded on a critical limiting assumption: that the terrain surface being modeled is a continuous surface, with no breaks, overhangs, holes, tunnels, bridges, etc. Mathematically, this means that for any x,y position, there is only one single z value. Such as surface is sometimes referred to as a 2.5D surface, because although there is a third dimension, it is severely constrained by the first two (this term is also used sometimes to refer to extruded forms, which have a similar characteristic). Plains, fields, mountains, planes, and the surfaces of cones all meet this criterion. But in the real world, this limitation doesn't hold, and many interesting and important landforms are in fact not continuous surfaces. Real terrain, of course, is not just a "skin," but has substance and mass. These characteristics can best be modeled using a different representation - a solid model. Solid models are in principle more complex than surfaces, and may offer more possibilities, including analytical ones such as the ability to slice cross sections, or compute mass or centroid, for example.
Figure 2.27 a. Herbert Bayer (1900-1987) Mill Creek
Canyon Earthworks, 1979-1982. Courtesy of City of Kent, Washington Parks, Recreation
and Community Services b. Harima Science Garden City, Hyogo Prefecture, Japan,
1993. Courtesy of Peter Walker and Partners.
The simplest building blocks for a solid digital terrain are the geometric primitives: slabs, wedges, cones, pyramids, spheres, etc. The primitives can be used alone and in combination to form a terrain model. Few natural landforms mimic these platonic shapes exactly, but they are often employed in designed landscapes, as evidenced in the work of Martha Schwatz, Herb Bayer, Jaques Wirtz, and the office of Peter Walker and Partners.
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Figure 2.28 This computer generated image, by Rick Casteel shows the hemispherical turf mounds encircled by undulating park benches. Martha Schwartz, Inc., General Services Administration, NY, NY. 1996. Courtesy Martha Schwartz, Inc.
Figure 2.29 These pyramids, considered as "land art," were used as a grand unifying device that march diagonally through a park surrounded by abundant vegetation. Jaques Wirts, Parc Cogels- Pyramids and Trees. Schoten, Belgium, 1976-1978.
[HOW-TO: PARAMETRIC SOLIDS] <- Click to download PDF version of the Tutorial
Most landforms are not simple planes or solids, and a more irregular modeling technique is required. Perhaps the simplest and most direct method of generating a 3D solid model from contours is to extrude contour lines, in a vertical direction, by an amount equal to the contour interval, creating a stack of polygonal solids, akin to a stack of pancakes, or a "layer cake."
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Figure 2.30 Pancakes and layer cakes along with a
wireframe and rendered stepped contour model.
Figure 2.31 Analog stepped contour model, produced by Letitia Tormay, is flanked by a wireframe and rendered view. The visual comparisons here clearly show the derivation of the digital form from the traditional analog model form. Both model forms share similar functionality, limitations and visual behaviors.
[HOW-TO: STEPPED CONTOURS] <- Click to download PDF version of the Tutorial
Surfaces, simple solids, and solids formed from surfaces, all share a similar characteristic: they represent continuous surfaces, without gaps, holes, or overhangs, and are sufficient for the majority of topographic models. But in more complex situations, especially as architectural buildings and other features (bridges, tunnels, et al.) come in to the model, an expanded range of 3D modeling tools will be required. These tools facilitate modeling the intersections between the continuous topographic surface and built structures as well as the anomalies of tunnels, caves, and retained walls.
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Figure 2.32 a. Circular pool structures in a field of turf and crushed stone. b. Detail of pool structure. Harima Science Garden City, Hyogo Prefecture, Japan, 1993. Courtesy of Peter Walker and Partners.
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Technical note: Boolean Operations
The solid resulting from some boolean operations (especially subtraction and intersection) sometimes can no longer be represented by simple contours or surface model, and may be represented internally in a unique format, so it may not be transportable between one software package and another. Also, some boolean operations may generate "ill-formed" solids in which all surface normal vectors have not been computed, or may be incorrect, etc. Often some cleanup operation must be applied to solids generated from boolean or other combinatorial operations to correct these defects before they can be reliably rendered. |
[HOW-TO: BOOLEANS] <- Click to download PDF version of the Tutorial
While the emphasis for most landform modeling is the surface characteristic required as a base for other landscape elements, sometimes the underlying geological base manifests as rocks visible on the surface, as objects. Whether giant glacial erratics (boulders left behind by ancient glacial processes), or small rounded stones found in a riverbed, rock objects offer some challenges for modeling, which reiterate in microscale the techniques presented so far for landform in general. That is, rocks may be modeled as geometric primitives (spheres, egg-shapes, crystalline forms); solids constructed by ruled surfaces; grid-meshed or triangulated solids.
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Figure 2.33 a. Individual rocks with photographic rock textures. Modeled after Peter Walker's Tanner Fountain at Harvard University in Cambridge, Massachusetts. Modeled in Rhino3D software; rendered in 3DStudioMax. b. Tanner Fountain, Harvard University. Courtesy of Peter Walker and Partners.
In the creation of space, architectural or landscape, landform may play several roles, ranging from subtle, supporting base to central, sculptural object. Landscape architects and earthworks artists have explored the use of earth as a sculptural material; these earthworks sculptures tend to be large in scale and undulating in form. Crisper, more vertical surfaces are possible at smaller scales by the addition of architectural reinforcing elements such as retaining walls. Compositional techniques such as repetition, variation, rhythm, juxtaposition, and layering can all be used with earth forms, and terrain objects including stones and boulders, just as painting or architecture manipulate other materials.
Figure 2.34 Harima Science Garden City Hyogo Prefecture, Japan, Peter Walker and Partners. Courtesy of Peter Walker and Partners.
For visualization purposes, after the underlying surface, or solid form, has been given dimension and shape, the surface texture must be applied. The variations that can be achieved with rendering effects only - color, textures, and lighting, and smoothing - are many, even on the same base form. The choice of color and lighting effects may be governed by the desired mood or atmosphere of the model or image being generated (See Chapter 5: Atmosphere for more discussion and examples,) or the colors may be governed by desire for some level of realism. Landform, or the groundplane, can be considered in two large categories: natural surfaces and built surfaces. Landform in nature tends to be either an exposed mineral substrate (rock, sand, gravel, clay, dirt), or to be textured by a vegetative cover (grass, lichen, moss, flowers, shrubs, trees, forest, forest, leaf litter, e.g.), and so colored in the earth tones (grays, tans, browns, or greens and olives). Built surfaces, including paving of all kinds, tend to be more flat, level, and regular, and in a different range of colors (white concrete, black asphalt, red brick, terra-cotta tiles, etc.).
The simplest texture that can be applied is just a solid color, and for some purposes this may be sufficient. For more realistic portrayals, earth-tone colors such as browns, tans, and greens are, of course, the best choice. In most cases a very bright color is inappropriate, but pastel shades and muted values are best. In more fantastic or other less-natural environments, any color at all may appear on the ground form.
Figure 2.35 This series of illustrations represent the types of materials that can be applied to a topographic surface. a. Simple color; b. Simple diffuse map; c. Procedural grass texture. The procedural grass texture was produced with the 'Shag:Fur' plug-in by Digimation for use with 3D Studio Max.
For realism, and other effects, more complex textures than simple color are required. Bump maps of various sorts are especially useful in terrain modeling, as the surface often has a grainy, or bumpy quality. Mineral, or geologic surfaces, can be best approximated by a combination of color and surface texture which consists mostly of particles (sand, granite) or facets (of smoother stones, e.g.) In these conditions, irregular tiling is important; no apparent repeating geometric pattern should be visible, for most realistic effects. Many of these surfaces also have a slightly reflective, or sparkling quality, due to mineral components (mica, silicates). Sometimes these highlights are dampened or obliterated by a fine layer of dust giving everything a matte finish. Other rocklike nonvegetative coverings in the landscape include snow and ice, which are most easily modeled simply as color and texture over terrain.
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Figure 2.36 a. Example of brick texture. b. Example
of a ceramic tile texture. c. Example of a grass texture.
If an ortho-rectified image is not available, some computer processing is required, usually called rectification, or rubber-sheeting, since the desired effect is to distort the image as if it were a rubber sheet, to fit to known positions, or coordinates. Some GIS and other image processing or remote sensing software offer this operation. In addition, the image needs to be registered, by determining the coordinates of the corners of the image.
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Figure 2.37 a. Detail or draped map. b. A colored
elevation map draped over terrain.
Figure 2.38 A synthesized view using GIS data as input, of an aerial view of Minute Man National Park, in Concord, Massachusetts. Courtesy of Carl Steinitz, Harvard Design School. Rendered in ERDAS.
When geo-referenced, scale-corrected imagery is available, you can use it as a surface texture over a digital elevation model to produce a landscape rendering with apparent features in the correct location on the terrain. This kind of image is sometimes called geospecific texture. Geospecific images are usually from either aerial photography (at scales from 1:500 down to 1:25000), or from satellite imagery (at resolutions from 30m/pixel down to 10 or even 1m/pixel). The geo-referencing information will either be included in the file format (as with a Geo-TIFF file), or in an associated header file. The USGS makes available digital ortho-photos and digital ortho-quads (DOQs) at the standard scale of 1:25000, to match the printed topographic quad sheets. Finer resolution (larger scale) images are increasingly available from governmental and private sources. Often 5m and 1m resolution ortho-photos are available.
Figure 2.39 a. Detail of Mt. St. Helens represented with a draped grid surface. b. Mt. St. Helens surface model with a draped ortho-rectified image. Courtesy of 3DNature.
Figure 2.40 a. Detail of an ortho-rectified image. b. Images of geo-specific texture Courtesy of Remote Sensing Laboratories, Dept. of Geography, University of Zurich. Satellite image (c) ESA/Eurimage, CNES/SPOT.
Figure 2.41 a. Detail of view. b. View of Beckenried, Switzerland, using SPOT satellite image draped on terrain Courtesy of Remote Sensing Laboratories, Dept of Geography, University of Zurich. Satellite image (c) ESA/Eurimage, SPOT.
Geospecific texture mapping as described above only results in a 2D image on a smooth 3D terrain surface - no 3D vertical elements are introduced. This looks moderately convincing from birds-eye perspective views, looking down on the terrain, but the more oblique the view, the less acceptable this approach. When side-views, as of trees or buildings are required, another technique must be used. Some landscape visualization software offers the capability of using a rectified image or landcover map as a key to guide the placement of 2D images (texture maps) and 3D objects into the rendered scene, using values from the landcover map to select appropriate textures and objects. These texture images are sometimes called Geotypical textures, since they are not the exact trees or buildings, but representative ones, used in the right place. (You can, of course, use actual photographs of actual trees, and actual 3D models of actual buildings, for accurate depiction of existing landscapes.) A registered and rectified landcover map is required, as well as optional data sources such as additional point files, or polygon files, which specify the locations of individual 3D objects or 2D texture/images to be inserted. Sometimes a random placing method may be specified for objects within polygons, at a specified density, for the rapid generation of forests, or even housing subdivisions.
Figure 2.42 A landscape synthesized using "ecosystem" rules. Courtesy of Karin Egger, Vienna Technical University. Modeled and rendered in World Construction Set.
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[HOW-TO: DRAPING AN IMAGE MAP] <- Click to download PDF version of the Tutorial
A common problem with visualizations of terrain is the artifacts that appear in textures applied to the ground surface. There are two most common ones: the appearance of a repetitive pattern in the surface, resulting from the regular tiling of a texture map, and the problem of textures which may look great in the midground, but when close-up, in the foreground, tend to be exaggerated, out-of-scale and blurry.
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Figure 2.43 a. Tiling of small texture map causes
visually disturbing repetitive pattern in surface; b. Larger map with fewer
repetitions appears distorted and blurry in foreground.
Figure 2.44 a. Diagram showing recursive subdivision yielding smaller rectangles in foreground. b. Surface texture generated procedurally (note the absence of tiling artifacts.)
Figure 2.45 TIN representation made of four separately created TINS, joined together. Note the gaps along the edges where the four tiles meet. Modeled and rendered in ArcInfo and ArcView.
In many modeling challenges, the extent of the scene calls for different conditions in foreground (close-ups), midground, and background (distance). It can be computationally expensive and inefficient to model all terrain at a similar level of resolution when the area is large. In visualizations where foreground and background area are known in advance, it is possible to use coarser information in the background, and finer in the foreground. For example, a very coarse grid mesh or TIN may be used to establish the base landscape for a large area, a finer TIN for midground areas, and carefully formed NURB surfaces in the very foreground, for maximum control of realism while keeping the overall polygon count (and thus rendering time) down to a manageable size. Often this is the case when specific site or project area is embedded in its larger context, and concentric rings of foreground, midground and background can be established in advance. When the furthest background is mountainous, or at least above eye level, then an additional panoramic photograph can be used to extend the terrain into the distance.
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Figure 2.46 TIN of the same terrain, created at three
different resolutions: a: 600 faces, b:10,000 faces, and c: 80,000 faces. Modeled
and rendered in ArcInfo and ArcView.
Figure 2.47 Representation of landform at three different levels of detail in VRML: a. as a flat plane and a cone; b. as a grid mesh; and c. as a TIN model.
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Technical Note:
The VRML2 language standard, and the newer "Active Worlds" and X3D specifications, provide an additional mechanism for LOD handling: Every object in a scene may be explicitly given multiple representations for rendering purposes, to be used at varying distances from the viewer. So, for example, a landform might be rendered as a single solid colored flat plane or cone in the far distance, a coarse grid with a texture map in the midground, and as a more detailed TIN model in the foreground. Careful design of these multiple representations can achieve real efficiencies in rendering animations. |
An important consideration in creating visualizations of terrain models is the establishment of lighting conditions. Since natural terrain often tends to be subtle in its variations, oblique lighting conditions, such as early morning or late afternoon sun's rays, are especially helpful in making vivid landforms. Choosing an illumination model, including both ambient and direct lights, is critical. (See Chapter 5, Atmosphere, for more on lighting techniques.) Also, making sure that shadows are cast, either by the landform itself, or perhaps by objects such as trees, etc., onto the landform, is extremely helpful in making landform visible. Since shadows on the ground are usually viewed obliquely, they need not be perfectly accurate; simple smudges and blurs of dark and light, correctly located with respect to shadow casting objects will suffice. Creating a shadow map as an image - in which black or gray shadows are painted on a ground surface - and applying this image to the texture of the landform is one way of achieving this.
Figure 2.48 The geometric base model of the University
Commons project rendered at two different times of day. Notice how the shadows
allow for the landforms to read in both plan or perspective view. The sun system
allows for the simulation of natural lighting conditions determined by the latitude,
longitude, and time of day. The lighting for the model was generated by the
3DStudioMax "Sun System".
In addition to rendering for visualization, or as an adjunct to the process, analysis of landform is enabled by many of the same data models presented so far. Typically embedded in Geographic Information Systems (GIS) software, some of these operations may be found in CAD or other engineering, modeling, or analysis software.
One common calculation required from digital terrain models, is some indication of volume of earth. Especially when two models are given, one from an existing condition and one for a proposed new terrain model, the calculation of cut (earth removed from the original) and fill (earth added to the original) is critical. In many cases, one goal is to achieve a balance, or net change of zero, so that soil cut from one place is filled in another on the same site. In addition to simple cut-and-fill, a more sophisticated analysis might indicate mass-haul requirements, showing what volume of soil is required to be moved over what distance (either within the site or to/from off-site.)
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Figure 2.49 Grid mesh surface representations illustrating
the existing and proposed site conditions, and the resulting volumes from the
cut and fill operation.
From a digital elevation model, or height field, two important and useful additional surfaces of information can be derived. The first is a slope analysis, which computes the steepness of the surface, in percent or in degrees; the second is an aspect, or orientation map, which computes which direction (north, east, southwest, etc.) the surface is facing. These two characteristics are especially valuable in design for functional purposes. (For example, a northwest facing steep slope is a bad place for a driveway in northern climates, as it may tend to be covered in ice in the winter. Fruit orchards are most desirably located on gently sloping southwest slopes, which encourage cold air drainage. Landscape architects use many slope criteria for different uses: a 2.5% slope is considered maximum for most playfields; 8% for access ramps to be used by wheelchairs, and so on.)
Figure 2.50 Slope map and aspect map created from
a terrain model. a. Shaded Relief Terrain Model ; b. Slope in ten classes; darker
reds are steeper slopes. c. Aspect in 9 classes (8 compass directions, from
N to NW, and None); orange colors face south, blues face north. Modeled and
rendered in ArcInfo and Arcview.
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Technical notes: The calculations of slope and aspect are typically made from a raster grid model, and although they yield a value at each grid cell, they must take into consideration the neighborhood of values around each cell. Slope, for example, is calculated by taking pairs of neighbors on either side of the cell in question, calculating the difference in elevation (rise) and the difference in horizontal difference (run); the slope is then the value of rise divided by run. For each cell, 4 different pairs of cells are used, and so 4 different slope values may be computed. Then it is a matter of choosing an appropriate mathematical function; the two most common are: the average of all the values, or the maximum. The maximum is the more intuitively correct approach. Aspect is computed by a more complex trigonometric formula, which essentially seeks to find the perpendicular (or surface normal) vector at each grid cell, then take the (x,y) component and represent that as an azimuth value ranging from 0¡ (due north) through 359.99 (where 180¡ is due south, 270¡ is due west, and so on). Perfectly flat horizontal surfaces have no aspect, which is usually represented by a special value such as -1. (Or zero may be used for no aspect, and north represented by 360¡.) Note that for both slope and aspect, neighboring cell values are required, and so both calculations may be either undefined, or potentially erroneous, at the very edges of a grid or raster. |
For terrain modeling and visualization purposes, dynamics can be thought of in three important ways: generative (and transformative) processes that create terrain representations; movement through the landscape, over terrain; and movement of the terrain, as in earthquakes and erosion processes. In all cases, there are mathematical, or algorithmic, models behind the dynamics, often derived from some underlying physical or natural system. In the special case of movement through, characterized by animations, walk-throughs and flyovers, considerations of human experience and perception is also important.
In the case of terrain models of real, existing, or proposed terrain, specific measurements and recordings of geometry, represented as contours, grids, or TINs, is usually required. But for more mathematically defined landforms, or for imaginary landscapes, it may be possible to achieve significant savings in memory and disk space by using procedural methods to generate, rather than record, the landform geometry.
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Figure 2.51 A "volcanic" form created by boolean subtraction of one inverted cone from another, then roughened and twisted using modeling tools. Red-colored "lava" textured interior added for visual effect. Modeled and rendered in 3DStudioMax.
<-
Click to see the "Volcano" Animation
Natural landforms are not geometrically regular, however, and some additional techniques must be used to introduce the irregularities which mark natural forms. Some interjection of randomness, or noise, is the first step, creating forms which are not perfectly smooth, but which nonetheless follow some basic formal structure.
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Figure 2.52 Synthetic terrain produced by "fractal terrain generation" software. Coloration is determined by elevation.
A simple form of this is the recursive subdivision, in which a single form is subdivided into smaller, identical forms, and these further subdivided, and so on. If slight variations are introduced at each subdivision, a kind of irregular detail within a larger structured whole results. For example, a landform may be described a starting with a triangular pyramid, then recursively subdividing each triangular face into smaller triangles, until some specified smallest size is reached (or else the procedure would go on forever, in an endless loop!) If at each step of the subdivision, triangle vertices are slightly randomly displaced, the result is an irregular surface conforming to the basic outline of the original pyramid.
Figure 2.53 Recursive triangle mountain, at several
levels of subdivision; produced by the"Java
Mountain" JAVA code, on the Website
<-
Click to run the Java Mountain code
Variations on these techniques for creating fractal terrain have been used extensively in the creation of synthetic landforms. For example, Lucas Films' seminal Pt Reyes illustration (right) features fractal mountains in both the foreground and background.
Figure 2.54 "Road to Pt. Reyes" This early synthetic landscape rendering has various procedurally produced elements, including rocks at left, vegetation at right, and landform in background. Also shows ray-tracing effects, including reflection and atmospheric haze. Created at Lucas Film Limited in 1983, by Rob Cook, Loren Carpenter, Tom Porter, Alvy Ray Smith, Bill Reeves, and David Salesin. Reprinted with permission of Pixar Animation Studios.
While the techniques of fractal terrain have elegance and efficiencies, they can not be used to produce precisely controlled surfaces. But the principle - of encoding rules for the generation of terrain, rather than the desired geometry - can be extended to achieve more controlled results. The basic idea behind such techniques is to specify a set of operations, such as cutting or filling terrain, with parametrically defined shape characteristics (such as angles of slope, depth of fill, etc.) usually to be performed along some path. This set of operations is then swept along the path, either over an existing base terrain, or on a blank surface, and the result is a terrain geometry which has the desired shape.
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Figure 2.55 Procedural landform produced by sweeping a simple cross-section ("U"-shape) along a specified path. Above, a sine-wave path; below, a spiral path ascending along Z-axis. Right, the inverse of these forms. From Terrain Sculpting Software (TSS) Courtesy of Caroline Westort.
Animated walk-throughs or flyover animations generated from three-dimensional models provide a time-based method for evaluating or communicating a design proposal's intent or anthropomorphic experience. Many times, digital models are made specifically for the purpose of creating an animated walk-through or flyover. Consideration of the final purpose(s) of the model (and animation) will help to make decisions such as level of detail, scale and resolution, color and texture of the terrain model.
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Figure 2.56 Plan showing camera and target paths for the animated walkthrough of the Unversity Commons Project. Paths were generated by drawing a spline curve over the terrain surface. Splines were then simplified for smooth movement.
Figure 2.57 Walkthrough of University Commons Schematic
Model
Movement through terrain depends on moving camera positions and viewpoints, through a fixed terrain model, but movement of terrain calls for a dynamic terrain model itself. Such a condition might be caused by attempting to model natural phenomena such as an earthquake, dune movement, or soil erosion, or might just be a desired effect in some model or animation. The algorithmic and procedural approaches described above are typically the most effective ways to achieve these effects, by creating procedures in which time (t) is a parameter. This may be explicit, or implicit as in the intervals implied by the steps between sequential applications of a recursive procedure or a GIS model.
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Figure 2.58 In this example and the associated animation
sequence the pyramid landform erodes over time. Two geometric models were generated
from two hypothetical grading conditions. The animation that corresponds to
the still frames is on the Website . Modeled and rendered in 3DStudioMax 3.1.
Figure 2.59 Morphing Terrain - The Eroding Pyramid
Click here to see the "Terrain-Morph" animation.
[HOW-TO: MORPHING TERRAIN] <- Click here for the Tutorial
Figure 2.60 a. Rippled landform produced by using parametric deformation of a NURB surface, specifying amplitude and frequency of wave form. b. More surface variation created by adding some random "noise". Modeled and rendered in 3DStudioMax.
The raster grid system of GIS terrain representation can be used to create time-varying models as well. Writing rules, or procedures, that transform each cell value a step at a time, as a function of similarly located cells in other layers, or neighboring cells in the same layer, can be used as a way to create dynamic models.
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Figure 2.61 Terrain representations. Modeled and rendered
using ArcInfo, ArcView, 3DStudioMax and Photoshop software.
Digital models of landscape almost always start with - and sometimes end with - a digital terrain model. Whether the landform is conceived of as regional context, site-scale field, or sculptural object, will help to determine an appropriate modeling and rendering approach. In many cases, data sources for terrain can be found from public sources or design professionals; some transformation from one format to another is almost always required. Digital terrain models can become cumbersomely large files, so often some simplifications, compromises and abstractions are necessary. Making the physical form, whether 2D surface or 3D solid, is just half of the necessary effort; the other half is choosing and applying a texture and lighting to create the desired image or effect. For the purposes of animations, either over, or of, terrain, the characteristics of the terrain should help inform the animation path and other parameters. Procedural methods, for generating, transforming, or animating terrain can be especially useful in cases where specific real landforms are not required.
Beardsley, John. Earthworks and Beyond: Contemporary Art in the Landscape. New York, NY: Abbeville Press, 1984.
Brunier, Yves. Yves Brunier: Landscape Architect Paysagiste. Basel, Switzerland: Birkhauser-Verlag fur Architektur, 1996.
Levy, Leah and Peter Walker. PeterWalker: Minimalist Gardens. Washington, DC:SpaceMaker Press, 1997.
Laurini, Robert and Derek Thompson. Fundamental of Spatial Information Systems. London, England: Academic Press, 1992.
Maguire, David, Michael Goodchild and David Rhind (Eds.) Geographical Information Systems: Principles and Applications. New York, NY: Wiley, 1991.
Mandelbrot, B.B. The Fractal Geometry of Nature. New York, NY: W. H. Freeman and Co., 1982.
Figure 2.62 Four views showing time-based simulation
of idealized stream channel erosion, using GIS software and the algorithm described
in the text. This sequence was modeled and rendered using ArcView and ArcInfo.