3.2.1 Photographs for Collage and Drawing
3.2.2 Paraline/Orthographic Drawings3.2.2.1 Planting Plans
3.2.2.2 Plan Symbols
3.2.2.3 Elevation and Section Symbols
3.3.1 Surfaces
3.3.1.1 Billboards
3.3.1.2 Silhouette
3.3.1.3 Layered Canopy3.3.2 Solid Representations
3.3.2.1 Simple Parametric Solids - Cones, Cylinders
3.3.2.2 Cylinder-based Hand-built Models3.3.3 Hybrid (3D and 2D) Plant Forms
3.3.3.1 Parametric 3D Models
3.3.3.2 Special Trees - Palms, Others3.3.4 Plant Structures: Groves and Allees
3.4.1 Maps on Solids
3.4.2 Simple Color
3.4.3 Bump Maps and Other Compound Textures
3.4.4 Photograph-based Textures
3.4.5 Procedural Textures
3.4.6 Grass and Groundcovers
3.5.1 Transparency
3.5.2 Lighting
3.5.3 Shadows
3.5.4 Levels of Detail3.5.4.1 Forest Models
3.6.1 Generation
3.6.1.1 Recursive Plant Forms
3.6.1.2 Other Plant-Generation Codes
3.6.1.3 Growth, Change, and Seasons3.6.2 Movement Through Vegetation
3.6.2.1 Vegetation Walk-throughs
3.6.3 Movement of Vegetation
3.6.3.1 Physics-based Kinetic Systems
3.6.3.1.1 Blowing in the Wind
3.6.3.2 Forest Growth Models
Figure 3.12 Parametric variations on palm tree form. Modeled in TreePro, rendered in 3DStudiomax.
Figure 3.13 Solid models of representative cacti. Modeled and rendered in 3DStudioMax.
Figure 3.26 Multiple images of a tree texture map, at 32, 64, 128, 256 and 1024 pixels.
Figure 3.31 The generation of branched form by succesive Y-shaped branches recursively applied.
Figure 3.37 Walkthrough of University Commons with Vegetation
Trees, and assorted other vegetation including shrubs and groundcovers, are perhaps the most visible elements of the usual landscape. They surround us at eye level with their trunks; they embrace us overhead with their canopies, their textures are underfoot. Leaves frame our views, grasses carpet the foreground. Foliage provides texture and color in the landscape - infinite varieties of green and brown, then, in temperate climates vibrant yellows, oranges, and reds. Trees with their verticality and shadows accentuate the terrain they stand upon; groundcovers, like grass, provide the texture and grain of the landform. For landscape painters, trees are sculptural things, majestic, comforting, or twisted, almost mystical, in the foreground, blanketing, shaping, framing in the background. For landscape architects, trees and vegetation are both armature and covering, forming spaces, rooms, allees, focal points, and framed views, at the same time providing color, texture, and mass to compositions.
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Figure 3.1 a. The precise geometry of the topiaries
seen at the Chelsea Flower Show recalls the form of the lollipop tree, generated
from solid geometric primitives. Chelsea Flower show 1999, Hope H Hasbrouck
b. The student exercise at the left clearly illustrates the use of solid geometric
primitives to represent a structured and maintained planting of trees. Student
Exercise 1999, Harvard University Graduate School of Design, Misty March.
For modelers, trees and vegetation present a variety of challenges. Fractally detailed, asymetrically branching and twisted, with corrugated bark and multiveined leaves, there are far too many surfaces and details to imagine modeling even one with accuracy or completely. And plants are also often numerous, with hundreds or thousands of trees in a scene, or millions of blades of grass. They are porous, light permeating unevenly to their interiors, casting ragged shadows over undulating earth below. And they blow in the wind, change colors with the seasons, and grow, transform, even die, over time. How far from the truth a simple "lollipop" tree seems to be!
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Two dimensional digital vegetation models are comprised of either vector or pixel/photographic entities. The choice of data type is dependent on the intent of the model or representation. Vector entities are easily combined to form symbols which suggest location and size while the photograph is more suggestive of character, density, and habit. Choices are not limited to one or the other, both data types can often be integrated into the same model.
Photography is an effective medium for the capture and representation of vegetative complexity. Modern digital technology allows for slides or photographs to be scanned at very high resolution for incorporation into digital media. Digital cameras create digital images directly on disk, RAM-chip or Website -ROM which can be shared across software applications and platforms. In addition to collecting or generating your own images, there are numerous published collections of images and textures on Website -ROM, as well as sources on the web. Compiling photographs in digital landscape models is invaluable, for the photograph captures the intangible complexity, variation, and textures that are integral to the suggestion of landscape space and experience.
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Figure 3.2 This image illustrates the combination of images with vector entities to produce an illustrative plan and section. Courtesy of Peter Walker and Partners.
When the two-dimensional image is too suggestive or detailed, design professionals rely on a vocabulary of simple shapes developed for representing trees in plan, section, or elevation. For plan representation the most obvious is a circle (representing the canopy) with a dot in the center (representing the trunk). This representation describes not only the exact location of the center of the trunk but the radius of the spread of the canopy. When several such tree symbols are overlapping, or many are, as in a grove or forest, graphical highlighting may emphasize just the outline of the joined circular forms. Sometimes these are even shown with a stylized shadow, to emphasize the 3D and spatial qualities of the trees represented.
Landscape architects and garden designers typically produce special working drawings or construction documents to guide the creation of a landscape or garden. Included among these, along with the dimensional plan and grading plan which defines the landform, is a planting plan, showing the locations and species of all plants. Usually this is given as an overlay on the grading plan, so that planting relationships to landform are evident. The location of each new or existing plant is indicated by a symbol, often a cross, indicating the approximate center of the stem, or bunch of stems, and a circle indicating the approximate size. These graphical symbols are highly simplified, and the sizes may be only general and relative to distinguish different larger and smaller species. When several similar plants are to be located in a clump, or other organized group, a connecting line is drawn between all the members of the group, to clarify that relationship. Finally, each plant or group is identified by name (or by a symbol) which can be looked up in an attached planting schedule, which identifies each plant, genus, species, and variety if indicated, as well as any special notes or other instructions to the planting crew.
Figure 3.3 Partial planting plan of the University
Commons Project at the University of Cincinnati, Hargreaves Associates. Using
vector entities the plan describes the location of trees and groundcover. When
describing the trees, note that the symbol describes both the trunk location
and the extent of the canopy. Digital data courtesy of Hargreaves Associates.
Elaborating on the simple circle, other symbols attempt to capture more specifically the branching structure and irregular outline of trees in plan, leading to the semirealistic, botanically derived tree stamp, sometimes even drawn with stylistic leaves, or clumps of foliage.
Figure 3.4 These tree symbols have been adapted from the tree stamps used by the landscape architect Dan Kiley.
In eye-level views (perspectives, sections, elevations, even axonometrics, and aerial oblique views) similar 2D representations can be used to present tree profiles. The characteristics of trees in side view - their proportion of height to width, shape of canopy, form of branching, and others - combine to form species-unique outlines, which can be used to identify and visualize specific tree forms, both in isolation and en masse. Some standard reference texts provide these profiles, sometimes derived from photographs of perfect specimens in winter conditions, for many kinds of trees, including deciduous, coniferous, and palms.
Figure 3.5 This image illustrates the combination of images with vector entities to produce an illustrative plan and section. Note the effectiveness of layering and transparency for conveying depth and spatial relationships within the project. Courtesy of Peter Walker and Partners.
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These 2D images of plant forms are useful for a variety of purposes, but to create a virtual landscape, which can be viewed from a variety of angles, or walked through, 3D is required. A full 3D model of any but the very simplest plant is a daunting prospect. The sheer number of polygons and solids required for even a small tree can be well in the millions. So the most common method for rendering plants is to use a very simple geometric figure, such as a flat plane, or billboard, and texture mapped-images.
Figure 3.6 Rendered plan and Perspective of the Miller Garden, by the Landscape Architect, Dan Kiley. Gary R. Hilderbrand, principal investigator; with Scot Carmen, Mami Hara, Pierre Belanger. Harvard University, Graduate School of Design, 1998. Courtesy of Gary R. Hilderbrand.
In general, 3D models may be classified as either solids or surfaces. For most purposes, models of plants are most readily made as surfaces, as these are easier to form and to manipulate in irregular ways. The simplest surfaces are just rectangular flat planes, or polygonal cut-outs; more complex ones are meshes or other combinations.
Side-view photographs of trees, shrubs, and flowerbeds can be easily be image-processed and used as a texture map on a transparent vertical plane in a 3D scene. This technique is often called "decals" or "billboards," and provides a direct way to introduce 2D images into the 3D scene. Photographs for this purpose need to be of high quality (resolution and clarity), and are most useful when made of single plant specimens against a solid color background (such as the sky) so that they can be isolated and then recombined in the final model. The solid color can be set to transparent in your rendering software, and so you can see through the trees in the final model, to give a more realistic, layered look.
Figure 3.7 a.Two intersecting vertical planes (billboards);
b. an image map; c. silhouette cut-out billboards including envelope; d. silhouette
cut-out of branching structure.
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[HOW-TO: BILLBOARD] <- Click here to see the Tutorial
Another potential problem with the billboard approach is that the billboard may cast a rectangular and most untreelike shadow. In modeling environments where shadow casting is supported, the image or texture map itself probably will not cast a shadow, but the object to which it is mapped will. In this case, it's necessary to further refine the billboard to become a cut-out, of an appropriate shape for - if not exactly the same as - the object mapped on it. In many cases, a simplified form, such as lollipop, will be satisfactory for the cut-out, if the shadow it casts will be further obscured by being on rolling or textured terrain, e.g., or mixed up with others. However, if the shadow cast by the tree cut-out will be plainly visible, or in the foreground, then it may be appropriate to strive for further realism by allowing some rays of light to pass through, as in nature, creating dappled sunlight in the shadow. See below for more on shadows.
[HOW-TO: SILHOUETTE] <- Click here to see the Tutorial
In between simple flat planes and more complex 3D representations, is a class of interesting models that are useful shorthand for plant materials. These are made by combinations of bent and curved surfaces, much like pieces of construction paper, sometimes impaled on a pole or stem. Useful at high levels of abstraction, like lollipop trees, these have the added advantage of being a bit more volumetric and slightly more realistic in that they have depth and layers of canopy, and can cast more interesting shadows, especially for conifers.
Figure 3.8 The strategy used to model trees in this student thesis can be adapted to create digital representation of trees by combining typical entities found in geometric modeling, most notably swept forms for trunks and branches with simple surfaces for the depiction of tree canopies. This photograph is from the landscape architect Garrett Eckbo's Master's thesis "Contempoville: Los Angeles World's Fair 1945". Mr. Eckbo completed his thesis in 1938 at the Harvard University Graduate School of Design. Courtesy of Special Collections, Frances Loeb Library, Graduate School of Design, Harvard University.
[HOW-TO: LAYERED CANOPY] <- Click here to see the Tutorial
To overcome the limitations of photographic textures on flat planes, true 3D models of plants may be used. In some cases, simple geometric forms such as cones and cylinders can be effective. Usually, though, these are limited to formal gardens with very specific characteristics. Plants in general need to be represented with more complexity and more variation in shape, and creating plantlike forms requires some very specific techniques.
The clipped hedges and pruned evergreen shrubs of some European gardens and many suburban ranch houses can be effectively modeled with geometric solids. These can even be simple, solid colors, and achieve a certain cartoonlike clarity of representation. For slightly more subtlety, try applying a few more complex textures, including transparency, eroded surfaces or bump maps. These combinations are endless.
Figure 3.9 The geometric forms seen at Hampton Court Palace in Richmond, England can best be represented with the parametric solid forms of cones and cylinders. Hope H. Hasbrouck, 1999.
Modeling branching forms can be constructed by hand, at least for a simplified structure. In this case, you can use a 3D modeling system to create tapered cylindrical forms, following a path in 3-space, which may be either straight or curved. Using some geometric snap operation to connect subsequent branches, you can draw a branching 3D form. Usually, attempting to draw in every small twig at the end is a losing proposition, so these forms are best when left slightly diagrammatic. They can be quite effective, especially for representing more angular, or sculptural tree forms.
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[HOW-TO: PARAMETRIC SOLIDS] <- Click here to see the Tutorial
For many purposes, a hybrid combination of 3D and 2D approaches may the best. Having a 3D solid skeletal framework is a great benefit for animations and virtual reality, since these can withstand close inspection from any angle. Having detailed foliage, bark, and flowers in 3D form is intractable for most systems, requiring far too much memory and rendering time. So the approach of combining texture-mapped foliage with a geometric solid tree trunk, or skeleton, makes sense for many applications.
Figure 3.10 Hybrid tree models combine a variety of
entity types. Selection of entity types is dependent upon the intention of the
visualization model and view composition in relation to the number of polygons
per tree structure. a.) This type of hybrid model combines the "Silhouette"
with the leaf structure of the "Parametric Model" generated by either Tree Professional
or Tree Storm by Onyx Computing. b.) This type of hybrid uses tapering swept
forms for the trunk and branch structure with simple surface wafers as the canopy.
[HOW-TO: HYBRID MODELS] <- Click here to see the Tutorial
Given the complexity of plant forms, and the repetitive nature of the branching structure, it's far more effective to use computer generating techniques to create 3D models of trees and other plants. Using rather simple basic branching and recursion algorithms, as explained below, modern software tools are capable of quite remarkable botanically-correct plant forms within a wide range of parameters of shape, size, and complexity.
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Figure 3.11 Parametric Trees: a. Blue Spruce (abies
concolor). b. Paper Birch (betula paperifera). Created in Onyx Tree Pro software.
Courtesy of Pjer Zanchi.
[HOW-TO: PROCEDURAL MODELS] <- Click here to see the Tutorial
Certain kinds of trees call for special modeling approaches. Palm trees, for example, which are widespread throughout warm climates, have a radically different structure and pattern of growth than the coniferous or deciduous plants of the more temperate climates. The simple technique of texture mapping photographs works equally well for any plant (or other object). But the palms, being in fact botanically simpler plants, are especially well suited to algorithmic generation methods for computationally growing the trunk and fronds. The fronds occur in a simple radial pattern, sprouting from the top of the tapered trunk, and have a clear, repetitive, geometric form. They are often arched in a curved form that can be modeled mathematically.
Figure 3.12 Parametric variations on palm tree form. Modeled in TreePro, rendered in 3DStudiomax.
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Figure 3.13 Solid models of representative cacti. Modeled and rendered in 3DStudioMax.
Often, in landscape and garden designs, plants are placed in geometric arrangements, creating lines and clumps, used to define space, such as paths and rooms, or just as a visual organizing technique. Most 3D modeling programs provide a range of tools for creating evenly spaced arrangements, in lines, or rectangular, or circular arrays with specified spacing and dimensions. When repetitive elements are used, some techniques to introduce some amount of variation, such as is found in nature, should be employed. Using two or three slightly different, but similar, tree images is a good technique; these should be randomly allocated to the array. Also, mirror flipping of a photographic image, or very slight stretching, horizontally or vertically, can be used to introduce some minor variation in repetitive groups. (But be sure that the resulting lighting model is not incongruous; images with a strong directional lighting and shadows in them should not be flipped horizontally and used together!)
Figure 3.14 Using image processing to create a row
of trees. a. A row of arborvitae, made by simply copying and repeating a single
image. b. Another row, made by first creating several variants of the image
(reversed, shortened, modified) and using them in a random mix.
Texture maps need not be limited in their application to planes. While effective especially at eye level, these models cannot capture other massing qualities of plants. Trees, for example, often form an overarching, intersecting canopy overhead. Using funnel-shaped solids to capture this characteristic can be effective, combined with texture maps applied for bark (on the trunk) and for branching and foliage overhead. With this method one can even look up and through the branches.
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Figure 3.15 Carefully trimmed and shaped hedges and evergreen shrubs in the ornamental garden at the Villa Lante in Italy.
"Plants are green" is a relatively safe assertion, but of course is not completely or always true. Plants come in many different shades of green, from almost yellow to nearly blue, thanks to their chlorophyll content; but they also come in deep purples, vibrant oranges and reds, and muted browns and tans as well. Choosing a good base color is a first step when creating a plant model. A solid simple green is a good choice with simple geometric forms and highly abstract models, but more detailed models need more subtlety and range of texture. When coloring plants in a scene, choosing very small variations in color by varying the amount of red and blue in the RGB values chosen can be helpful in adding variety; the amount to vary will depend greatly on the available color resolution of the display device. (A screen with only 1024 colors has far fewer greens possible than one with millions of colors, or 32-bit color.)
Figure 3.16 Simple solid shapes and simple color are used in this digital model of the Gropius House in Lincoln, Massachusetts. The model is a student project by Eric Kramer '98 at the Harvard University, Graduate School of Design. Modeled and rendered in FormZ.
For some purposes, using the built-in textures or bump maps available in a rendering system may be an adequate representation of vegetation, bark, or foliage. Exploring different settings is a useful way to start, since in many rendering systems small chanegs in settings can make distinct visual differences.
For many purposes, especially when plants or vegetation details are in the foreground, more realistic photographic-based textures are appropriate. Using basic image processing techniques, you can create a library of textures for bark, leaves, flowers, and foliage that can be used and reused in various combinations.
[HOW-TO: TEXTURED TREE BARK] <- Click here to see the Tutorial
Vegetative coverings, created by plants of all sizes, are more complex surfaces, characterized by depth and increased texture. Leaves of grass, or of other small plants, give a specific defining texture to an overall covering. This is best approximated, when needed, by procedural approaches or by embedded image maps in the texture. Simple plant forms, such as algae and moss, can be approximated with a combination of color and bump maps, and masks outlining the patches characteristic of their growth.
Grass - or more correctly, many different grasses - are plant materials common in all cultivated landscapes. While it is tempting to portray them as undifferentiated green, they are in fact characterized by ranges of coloration and texture. For many purposes, grasses have little form of their own, rather taking on the form of the underlying terrain, and so for modeling they can be dealt with as textures applied to to terrain.
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Figure 3.17 a. Tall grass rendered on berms of the
University Commons Project. The tall grass is procedurally generated with the
Digimation "Shag Fur" plug-in for 3DStudioMax. b. Detail of grass. c. Solid
model of grass blades in 3DStudioMax.
Bamboo, cattails and tall grasses offer a challenge in between fully branched trees and simple furry grass. Occurring in broad masses and clumps, the procedural generation approach is appropriate, and the results are simply more massive than with smaller grasses. Giant bamboo, of course, has color, form, and texture on every stalk, as well as branches and individual leaves, and so is best modeled as a special tree - all straight trunk, with lesser branches and spiky foliage.
Figure 3.18 Harima Science Garden City, Hyogo Prefecture,
Japan by landscape architects Peter Walker and Partners. Courtesy of Peter Walker
and Partners.
Figure 3.19 Detailed 3D model of a flowering plant (wild lily) witha photographic textured background. Modeled and rendered in 3DStudioMax.
Even with holes in the cut-outs for shadow purposes, trees painted on billboards may sometimes look just like that. An additional refinement can be to add some levels of transparency to the image. Many modeling environments provide a facility to enable you to specify a transparency map, as well as an image map. Typically, one 8-bit value (from 0 to 255) will be used to specify a level of transparency, with 0 (black) being completely transparent, and 255 (white) completely opaque (or the other way around - be sure to check the manual!) This can allow a kind of fuzziness around edges, and a speckled pattern of transparency, which may be desirable, or not. You will need to experiment with different settings for your individual task. This transparency mask may be either separate image, or embedded in the plant image in the "alpha channel."
Complex plant forms and their structure on the landscape are subject to great variation from lighting conditions. Plants can have both diffuse/matte (bark) and specular/reflective surfaces (leaves), and their open interiors may be in deep shade when their crowns are fully lit by sunlight. The shadows cast by large trees are important form-givers to any scene, and 3D plants will often cast shadows on themselves. Complex 3D shapes like trees and shrubs have subtle illumination and self-shadowing characteristics, and these need to be matched in the composite scene.
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Figure 3.21 A vegetated backyard scene in differing
light conditions: early morning, late afternoon, and cloudy. Note change in
sky color, shadows, outlines, color intensity, and apparent depth with different
lighting.
The dark shadows cast by plants, on the ground, on their neighbors, and on themselves, are visually important in anchoring them to the scene and to the terrain. The long shadows of tree trunks are often one of the most effective ways of illuminating the subtle shapes of landform, both in real life and in a landscape model. When using a complete 3D model and rendering software, the shadows can be cast by the rendering system. In this case, some parameters may be available to control the apparent fuzziness of the shadow (sometimes called soft shadows), and to set the maximum darkness of fully-shaded areas. There may also be controls required when setting up the lights, surfaces, and objects to specify them as shadow-casting. When a high-quality rendering system (with ray-tracing or equivalent methods for shadow-casting) is not being used, it is still possible to hand-place shadows on the ground. Simple dark smudges, elliptical or irregularly shaped patches placed underneath and slightly to the side of each tree or plant will add greatly to the illusion.
Figure 3.22 Hand-placed shadows, created as fuzzy,
black blobs, placed on terrain just below tree. Modeled and rendered in 3DstudioMax
Figure 3.23 Comparison of hard and soft shadows created
by: a. ray-tracing; b. "shdow map". Modeled and rendered in 3DstudioMax
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Figure 3.24 A projected shadow, using the black-and-white
bitmap image shown, assigned to a light in the lower left corner of the scene.
Modeled and rendered in 3DstudioMax
Plants in the landscape present one of the most daunting challenges to modeling and visualization because they encompass such a range of levels of detail. That is, a tree has branches, leaves, and flowers at the micro scale, but also exists within a continuous forest at the macro scale. And in between, the tree itself has a unique and recognizable form. When seen in the background, or at a distance, every leaf and flower cannot be seen; but when seen close up, they are the dominant visual features. Modeling every leaf in a forest is still an infeasible task.
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Figure 3.25 Tree images at three levels of detail: as a simplified 3D lollipop; as a volume with basic branching and transparent canopy; and as a detailed 3D model with full branching and fioliage. Modeled and rendered in 3DStudiomax.
In the VRML 2.0 language specification, there is a simple and powerful idea implemented for managing LOD. In this system, you can specify different representations altogether for a single object, to be applied at different distances. Thus, a tree can have a simple billboard with a low-res image at a great distance, a set of intersecting planes with high-resolution texture map at midrange, and a full 3D model with textures, branches, and leaves when viewed up close. The rendering system should handle the switch between levels automatically. Of course, it can be visually disturbing when the switch from one level to the next happens, especially when it is a dramatic change. This is one aspect of animation and visualization that is still evolving in technology. A good solution would be some kind of more finely graded intermediate steps, like a kind of morphing between representations. At the time of this writing (summer of the year 2000) there is no commercial modeling, rendering, or visualization system that handles this kind of transition well; but there are many research developments under way to improve the management of multi-resolution scenes, and no doubt new techniques for describing and controlling LOD will appear on the scene.
Figure 3.26 Multiple images of a tree texture map,
at 32, 64, 128, 256 and 1024 pixels.
Figure 3.27 Scene with different levels of detail in tree representation: a 3D solid model of pine tree in foreground (left); photographic texture-mapped billboards in mid-ground (center); and bump-mapped textured terrain in distant background. Modeled and rendered in 3DStudiomax.
In the foreground, forests are made up of a number of trees, typically, with some varying layers of lower, understory plants. Different forests in different regions and climates are quite different in structure and composition, but typically there are one or more large species which dominate the canopy and control most of the sunlight, then there are smaller, often big-leaved species which fill in below, right down to the ground level. Modeling this mix is a process of interplanting the various species and textures to achieve a desired blend.
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Figure 3.28 Forest model with considerable detail and botanical realism. Created by the Forest Simulation Lab at Texas A&M University with special research modeling and rendering software. Courtesy of Midori Kitagawa de Leon, Greg Schmidt and others.
Figure 3.29 Forested lake shore scene. Modeled and
rendered in Blueberry3D software. Courtesy of A. Ogren.
Figure 3.30 Forested hillside showing emergent tree
species (birch or poplar) and underestory vegetation over rocky terrain. Modelled
and rendered in Blueberry3D software. Courtesy of A. Ogren.
To overcome the obstacles to creating realistic, complex plant models by hand, a number of approaches have been developed for automatic, algorithmic plant generation. These techniques take advantage of the underlying mathematical structure found in most plants, and of codified botanical rules of growth, to generate plant forms automatically, from a number of mathematical parameters, or numbers which describe species characteristics, age, and so on.
Drawing these 2D tree symbols by hand, whether with pencil or computer mouse or stylus, one quickly realizes the repetitive and highly-structured nature of these forms. Basically, they are "branching:" each straight line, trunk, stem, or twig, leads to one or more branches, each of which is a straight line which leads to one or more branches, getting smaller and shorter at each repetition, until eventually they stop branching, and perhaps terminate in a leaf or a bud. This description, of a repeated action, each repetition somehow connected to its predecessor, making some change like getting smaller, until finally stopping, is called a recursive algorithm. Each successive branch from a previous branch is a recursion, and can basically use the same procedure each time, perhaps some minor variation in parameters such as length or thickness. Recursive algorithms can lead to repetitive structures, but are distinguished from simple repetition by using the result of a previous recursion as the starting point for the next. Also, recursive algorithms don't need to specify in advance the number of times that a repetition, or recursion, will be performed; rather some "stopping rule," such as a minimum size, or length being reached, is used to terminate the procedure.
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Figure 3.31 The generation of branched form by succesive
Y-shaped branches recursively applied.
Figure 3.32 Various parametric alternative forms using
the same recursive branching formula; from
the "java_tree" program on the attached Website .
This same algorithm is easily extended into three dimensions, where tapered cylinders instead of lines are generated (for trunk and branches), producing 3D treelike structures. The 2D angles of branching are replaced by 3D angles, and more branches around the trunk are generated, filling space instead of limited to a plane; otherwise, the algorithm is nearly identical.
Figure 3.33 Four frames from an animation showing
a 3D branching growth process. Note also that this displays phototropism; it
is growing towards, and has more leaves on the side of, the light source. Modeled
and rendered in special research software. Courtesy of Cyril Soler. (see
the "Plant Growth" animation on the attached Website ROM)
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Plants in the landscape grow, change and die. Too often, well-meaning designers place plants into environments which look great when they're young, but become much too large for the space; or, alternatively, would look great when mature, but grow so slowly that they look too small and out of place for years after planting. Computer models can help, by visualizing different ages and forms of plant material. Image processing, or parametric generation can be used to generate foliage colors and densities for different seasons.
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Figure 3.34 Parametrically generated Sugar Maple tree
(Acer saccharum) shown with a. fall foliage; b. in winter with no foliage. Modeled
and Rendered in Onyx TreePro . Courtesy of Pjer Zanchi, Onyx Software.
Figure 3.35 a. Illustration showing stages of growth
in a pine tree over multiple years. From plant growth simulation software by
AMAP; Courtesy of Stephane Gourgot.
Figure 3.36 Illustration of the effect of plant growth
over several years, as mature trees screen unattractive views of wires and poles,
also providing shade and greenery on residential street. Trees created in AMAP
plant simulation software, then inserted by image processing into existing photograph.
Courtesy of Andreas Muhar.
Plants provide vertical structure to the landscape, and in animation, when moved through, contribute visual effects, now obscuring, then revealing other parts of the landscape, covering overhead, providing shade, shadow, and filtered light. The biggest challenge to modelers creating animated virtual tours, walk--throughs and flyovers through landscapes with vegetation, is to use these characteristics of plants to enhance the visual and virtual experience.
Figure 3.37 Walkthrough of University Commons with
Vegetation
Click here to see the Animation.
In 3D models, especially those which the viewer can move through, whether interactively or along a pre-choreographed path, two complications arise from the simple billboard technique. The first problem is that billboards have only one or two good sides; when viewed end-on, they vanish to an infinitely thin line (cross section of a plane), and as viewing angle changes from head-on to more oblique, the flat plane shrinks in apparent size. These two combine to create the unnerving visual effect of trees shrinking and expanding as the viewer moves around, even disappearing and then winking back into partial view.
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Other than the phenomenon of their growth, change, and death over time, many plants are also in motion over short time spans, usually under the influence of the wind, rain, and sun. The rippling of blades of grass or rustling of leaves is an essential part of the natural landscape. Less perceptibly, many plants exhibit phototropism, the process by which they slowly turn to face the sun as its position changes over the course of the day. Naturally, static images can't show these, except indirectly by, for example, strongly leaning treetrunks and branches, such as are found in windswept landscapes like some mountains or coastlines. Animations are required to truly portray these dynamics.
While it is possible to generate some motion in 2D and 3D models purely "by eye," using the tricks of sprite animation, and frame-by-frame composition, often these effects can appear unnatural. And they are hard to sustain over time, in interaction with other elements and forces in the scene, or in the landscape. It's better to have these motions generated procedurally, based on simulations of real-world behavior. Although real simulations between thousands, or millions, of elements, are out of range for all but the most powerful computers, there are systems which enable some basic physics, such as gravity and collision, to be embedded in models and virtual worlds. Physical linkages between elements also provides a kind of realistic motion.
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Some modeling, rendering, and animation systems make provision for kinematic linkage between parts of a digital model, such that when one moves, other connected parts move also, but not as a single composition. That is, a leaf blowing in the wind may move its stem, which in turn may move a twig but to a lesser extent, and the twig move a branch but even less, to the point where the entire tree may sway slightly as a result. These inverse kinematics can be used to display the appearance of plants moving in the wind (or, when slower, more viscous movement is generated, such as underwater).
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Figure 3.38 Image of tree branches in the wind: a.
idle or gentle breezeon the left; b. gale-force wind conditions on the right.
Some visualization software has begun to introduce the notion of "ecosystems" as a way to model the development of plant communities in response to simple terrain variables, such as elevation, slope, and aspect. In these systems, you can specify which plants are to be found in which ranges of elevation, slope, and aspect, and then corresponding images textures are used to generate a rendering.
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Figure 3.39 Frames from an animation of trees growing
over several seasons in competition for space and light; notice how the center
tree iscrowded out by the two flanking it. Modeled with special research software.
Courtesy of Cyril Soler.
Click
here to see the "Forest Growth" Animation.
Whereas terrain is typically the foundation of any landscape model, it's usually vegetation that gives it texture, color, and much of its three-dimensionality. Photographic textures and images of plant materials - from tiny lichens to giant trees - are a necessary component of the landscape modeler's library. Fully developed 3D models are more time consuming and memory-intensive, but offer advantages in the foreground and in interaction with other architectural elements, or when navigating as in a VR model. Using procedural methods to generate vegetation, either textures or 3D models, is the most effective approach when photographs are not available, or when multiple different stages of growth are required. Similarly, adding dynamism in the form of animation, either of growth or motion, as of leaves blowing in the wind, can add realism to the final result.
(Note: This Website contains abbreviated text. For the
complete text,
click here to order the Landscape Modeling
book.)
Carpenter, Philip, Theodore Walker, and Frederick Lanphear. Plants in the Landscape. San Francisco, CA: W. H. Freeman and Company. 1975.
Prusinkiewicz, Premislaw and A. Lindenmayer. Algorithmic Beauty of Plants. New York, NY: Springer-Verlag, 1990.
Zion, Robert L. Trees for Architecture and the Landscape. New York, NY: Van Nostrand Reinhold Company. 1968.
Figure 3.40 a. View of forest in UK, created from
GIS data and forest stand information, modeled and rendered in Geomantics Courtesy
Genesis software. b. Forest scene in southwestern Alberta, Canada; the current
conditions of a subalpine forested landscape. c. The same scene as above illustrating
the impact of a very large fire event. Courtesy of Doug Olson, Olson + Olson
Planning and Design, Calgary Alberta. b. and c. modeled and rendered in World
Construction Set software. Client: Alberta Environment, Integrated Resource
Management.