Zz 
a 
  
  
Fig. 2 Sunlight (left) and ambient light (right). 
  
  
3.4 The Material Model and the Illumination Model 
  
The illumination model expresses the radiance L, of the light 
which leaves a point on the interface between two materials 
in a given direction. L; depends on the roughness of the ma- 
terial interface and the illumination and the materials on both 
sides of the material interface. The full illumination model (a 
slight modification of the model by Hall & Greenberg (Hall, 
1983) is used) will not be given in detail here. Instead, for an 
opaque, diffusely reflecting surface illuminated by natural 
daylight (section 3.3), the radiance L; of the reflected light is 
uniformly distributed in all directions and the illumination 
model reduces to 
L, = k;04; ( E; tE:;t E): (6) 
k, is the weight of the diffusely reflected component and 041 
[sr ^1] is the diffuse reflectance (directional hemispherical re- 
flectance) of the material. E,,, E,; and E,, are the irra- 
diances due to the incident sunlight, ambient light and sky- 
light according to (3), (4) and (5). 
3.5 The Camera Model 
World coordinates define locations in three-dimensional ob- 
ject space, image coordinates define locations in the two- 
dimensional image plane of a camera and bitmap coordi- 
nates define locations in the two-dimensional pixel raster of 
a digital image. 
The camera model represents a calibrated camera in three- 
dimensional object space. The interior orientation of the 
camera consists of the calibrated focal length, the image 
coordinates of a number of fiducial marks and the center and 
amount of the radial image distortion due to the non-ideal op- 
tics of the camera. The fiducial marks are not affected by the 
radial image distortion. Therefore, they define the image 
coordinate system in the image plane and allow to derive a 
linear mapping between the homogeneous image coordi- 
nates and the homogeneous bitmap coordinates of a digi- 
tized image. The exterior orientation of the camera consists 
of the three world coordinates of the camera position and the 
three angles of the camera orientation in object space. 
3.6 The Geometrical Object Model 
  
A geometrical object is either a planar convex or concave 
polygon, a polyhedron or a sphere. Each geometrical object 
has a material attribute which is a reference into the materi- 
       
  
  
436 
  
object zenith 
= = d, 
horizon 
  
Fig. 3 Skylight. 
  
  
  
al library (Fig. 4). 
4. INFORMATION FROM DIGITAL COLOR IMAGES 
The aim of this work is to produce realistic computer-gener- 
ated color images which aid to the judgement of aesthetic 
properties of planned buildings. These artificial objects are 
embedded into the existing environment by photomontage. 
The natural environment is represented by a number of 
digital site photographs. During an interactive preprocessing 
step which is supported by the program PREPARE (Fig. 4), a 
three-dimensional description of the natural environment is 
created by retrieving geometrical and non-geometrical in- 
formation from the site photographs. 
The models (section 3) are formulated in terms of the wave- 
length. Consequently, RGB triplets retrieved from input 
images have first to be converted to equivalent spectral dis- 
tribution functions. A simple and efficient conversion method 
is detailed in appendix A. 
In this section, a number of inversions are formulated. The 
term inversion stands for solving an equation or a system of 
equations given by one of the models (section 3) for one or 
more unknown model parameters. 
4.1 Inversion of the Camera Model 
  
Each of the digital color images which represent the natural 
environment is geometrically corrected to eliminate the effect 
of the radial image distortion. The geometrically corrected 
images are called the input images (Fig. 4). 
For each input image, the six unknowns of the exterior 
orientation are determined separately from the known world 
coordinates and the manually identified image coordinates of 
at least three control points. More control points help to re- 
fine the result. This is the resection in space or first inver- 
sion of the camera model. Each control point adds two 
equations to a system of non-linear equations which is itera- 
tively solved, starting from a user-specified estimation of the 
solution. The result of the resection in space is converted to 
a 4x4 matrix which expresses the linear mapping from homo- 
geneous world coordinates to homogeneous image coordi- 
nates. Since this mapping will be performed very often during 
rendering (section 6), its linearity is important for efficiency. 
The non-linearity introduced by the radial image distortion 
was previously eliminated by the geometrical correction. 
The geometry of relevant parts of the natural environment is