The growth simulator SIBYLA uses the central projection to visualise 3D perspective (Figure 1). A stand is placed in the coordinate system (x,y,z) starting from the point P(0,0). Figure 1 presents the forest stand in the shape of a cube. Apart from the main coordinate system, a secondary coordinate system (x',y',z') starting from the point R is defined. The point R is the centroid of the forest stand (cube), around which the rotation in direction of axis y' is performed. At the same time, the secondary coordinate system also serves for shifting operations in direction of all axes. The observer is located in the point P. The point is remote from the front cube wall (ab) 200 m in direction of axis z', and from the rotation point R(bP) 50 m in direction of axis  y'. The coordinates of the secondary coordinate system are convetred to the main coordinate system using transformation functions:

x = x'

y = y' + 50

z = z' - 200

The central projection is defined by the point Z°. The point Z° specifies the projection depth and its distance from the rotation point R is called a projection factor (f_P). Its value is 1,500 m. The basis of the visualisation algorithm is the transformation of 3D coordinates (x_3D,y_3D,z_3D) into 2D coordinates (x_2D,z_2D) using the functions:

The growth simulator SIBYLA has the possibility to shift the forest in the direction of secondary axes, in Figure 1 shown by letters A, B and C. The shift is performed as follows:

x_shifted = x_original + shift_vector_of_x

y_shifted = y_original + shift_vector_of_y

z_shifted = z_original + shift_vector_of_z

Apart from the shift, the rotation around the rotation point R in direction of the vertical axis can also be performed in the model.  In Figure 1, letter D stands for the rotation. The change of coordinates depends on the value of the rotation angle Alfa. New coordinates (x^R,y^R,z^R) are calculated from the original coordinates (x,y,z) as:

The visualisation is performed in the following steps (example of the result is presented in Figure 2):

1. Terrain visualisation: Terrain is displayed in the form of a sheet model defined by a regular grid (lattices). The coordinates x, y, and  z of the points in the grid are known. The points are marked, and when they are linked together with lines, they create the grid of the terrain.

2. Visualisation of trees: Trees are visualised schematically. A stem is displayed as a vertical black line with the length equal to the tree height, and a crown is displayed as a unicolour picture with the shape of crown form of a particular tree species (Table 1). The size of the crown results from its height and its width. The trees are displayed in sequence beginning with the tree farthest to the observer up to the closest tree using the so called Maliar´s algorithm.(Žára et al. 1992). Among the trees, the snap points from which spherical photographs were taken can be added as small targets. 

3. Visualisation of crown projections: Crowns are displayed as circles of the same colour as tree crowns in point 2 and the diameter equal to the widest crown diameter. The crowns are visualised sequentially starting from the smallest up to the highest tree.  

The computer execution is based on the technology DirectX and enables an interactive change of the observer´s standpoint to the displayed forest stand (shift and rotation).

Figure 1 The principle of the central projection of a forest stand in the growth simulator SIBYLA

Figure 2 Example of schematic 3D visualisation of a simulation plot 

Table 1 Crown forms of individual tree species:

• 1 ... Norway spruce 

• 2 ... Blue spruce

• 3 ... Silver fir

• 4 ... Grand fir

• 5 ... Scots and European black pine 

• 6 ... Weymouth pine

• 7 ... Cembra pine

• 8 ... larch

• 9 ... Douglas fir

• 10 ... yew

• 11 ... beech

• 12 ... oak

• 13 ... hornbeam

• 14 ... maple

• 15 ... ash

• 16 ... elm

• 17 ... lime

• 18 ... robinia

• 19 ... birch

• 20 ... poplar

• 21 ... aspen

• 22 ... willow

• 23 ... alder

• 24 ... cherry

• 25 ... rowan 

• 26 ... walnut

• 27 ... chestnut

• 28 ... plane

• 29 ... dead coniferous

• 30 ... dead broadleaved

In the growth model SIBYLA, a forest can be visualised also in the form of virtual reality (Fabrika 2003), while for this purpose VRML 97 language is utilised.

What is virtual reality ?

Specific procedures of computer graphics represent the basis of virtual reality. It concerns the development of spatial models and scenes, their manipulation, the movement in three-dimensional space and displaying in real time. These methods are intensified using specific peripherals that ensure visual, acoustic, and touch (positional) interactions. Virtual reality is characterised by following features (Žára 1999):

• all actions are performed in real time, i.e. if possible with instant response on input activity of the user, 

• the artificial world and objects in it have a three-dimensional nature or at least they give such an illusion, 

• the user examines the virtual world not only from outside, but he also enters the world and can move in it on various trajectories (he can walk, fly, jump, and move in a moment, i.e. he can teleport),

• the world is not static, the user can manipulate its parts. Virtual bodies often act as active objects - they can move on animation curves, they interact with the user and between themselves.  

What is VRML ?

VRML (Virtual Reality Modeling Language) is a language intented for the description of the content and the behaviour of virtual worlds. It is standardised with ISO standard labeled as ISO/IEC 14772-1:1997.

Figure 3 Principle of visualising an individual tree 

For the purposes of tree visualisation, the principle originating from computer games was used (Figure 3). A tree is divided into three parts: stem, crown, and tree foot (buttress). The stem and the tree foot are represented by interlocked cones. The crown is formed by four planes that are rotated about an axis through 45 degrees. Both the stem and the tree foot are covered with the bark texture of a particular tree species. The illusion of the real crown is created by texturing the crown habit into the rotated planes. The background of the crown texture is transparent. Table 2 presents the list of all visualised tree species with their crown and bark textures. 

Table 2 Visualisation of individual tree species:

Individual trees are visualised in real dimensions, and using their coordinates they are placed in terrain. Terrain has the texture of forest litter. The forest established in this way is situated in the background with clouds. Illumination and reduced visibility (mist) effects are also included. At the same time, suitable forest sounds are added. It is also possible to place plants, mushrooms, and shrubs in the forest in the form of small textures with transparent background. These are projected into small upright planes coming out of the ground with the height equal to plant height that always rotate towards the user (so called "billboard"). The user can move in the forest without any limits, while 3D illusion is ensured by object perception "with own eyes" - the principle of "first-person game". The perception of real tree dimensions (diameters and heights) is achieved by inserting a 3D person (so called Avatara) into the model of a forest stand, which "moves in the forest instead of the user" - the principle of "third person game". The user will get the real idea of tree dimensions by comparing the person "Avatara" and the surrounding trees. In addition, information about the tree is automatically displayed in the text window called "console" as the cursor points at it. Prompt interaction between the user and the stand also includes the possibility to mark a tree by repeated clicking on the stem. Trees are marked by a colour ring at the height of 1.3 m. In the model of the virtual stand, a tree can also be felled by clicking on their tree foot. The transfer between the stands in particular development phases is enabled by clicking on a crystal sphere situated on a stone stand. Most of the above mentioned features are shown in Figure 4. 

Figure 4 Interaction with forest environment 

 What are spherical photographs of a forest?

 A spherical photograph is the result of spherical projection of an image (Figure 5). For this purpose, a special lense of "fish eye" type, which can scan an image in the range of more than 180° in all directions, is used. In this way, a so called hemisherical photograph is formed. By merging two hemispherical photographs taken from two opposite directions one spherical photograph is created. If this photograph is projected onto the inside wall of the sphere, a true image of the reality is formed. If the observer is inside of such a fictitious sphere and looks around in any directions (to the right, left, up, down), he gets an impression that he stands exactly in the place, of which the photographs were taken. This method is suitable for taking photographs of the real points inside the forest that are interesting or important from the point of their structure. It is mainly used in permanent research plots, where all real tree coordinates and tree dimensions are known. At some points, hemispherical photographs are taken to enrich the virtual reality. The photographs represent the actual reality very well, and can serve for the comparison with the virtual reality.        

The growth simulator SIBYLA utilises iPIX (internet PIcture eXtension) technology. On the schematic forest picture, the photographed points are located by iPIX target. In the virtual reality, they are visualised by a virtual read-and-white range rod.     

Figure 5 Principle of a forest spherical photograph using iPIX technology