CG351-551 Radiosity: Modelling the scene.

7.4. Modelling the scene

To compute the radiosity value of a given environment, first of all the scene must be modelled. Since the scene model is used in the radiosity computation, the model has to meet several requirements in order to get an accurate solution. Modelling algorithms are generally independent of the radiosity solution technique used for scene modelling.

7.4.1. Model geometry requirements

Before we model a given environment, first of all we have make sure that the model is built in a consistent manner. That is, not only the scene is represented in a geometrically consistent manner but that it also contains sufficient information to satisfy the radiosity algorithm requirements. The basic model geometry constraints are as follows :-

The model geometry database should contain the information equivalent to a real solid model.
There should not be ambiguous points lying inside of , outside of or on the object's surface.
Each surface should have a unique outward pointing normal and normals should also be derived in a consistent manner.
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                       Fig. 7.16 : Normals
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Each surface should have a unique front and back .
There should be no T-vertices : if two adjacent polygons do not share a vertex which lies along the common edge, that is called T-vertex. It should be removed, otherwise a shading discontinuity may occur.
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                     Fig. 7.17 : T Vertices
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Invalid face, one with both sides of the face involved in the illumination computation, should be handled carefully. It may lead to the computation of incorrect form factors.
Overlapping coplanar faces should not exist in a solid model( such as the bottom of box sitting on the desktop). They can cause difficulities for any rendering program because it is unclear which face should be seen or which face should be hidden. Thus, one of the coplanar surfaces should be removed.

7.4.2. Mesh requirements

When calculating the radiosity values, a given environment is broken down into a fixed number of small areas called patches (details explained in next section). To be able to get an accurate solution, meshes or patches have to meet certain requirements. The requirements are-

Mesh must be composed of primitive faces : triangle or convex quadrilaterals. By doing so, it will simplify the associated local interpolation.
No T vertices between adjacent faces are allowed in order to avoid discontinuity radiosity.
The faces should be well shaped : The aspect ratio of the radius of the inscribed circle of a surface to the radius of the circumscribed circle of a surface, is close to one [Frey,87].
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          Fig. 7.18 : Aspect ratio of inscribed circle
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Mesh should have sufficient receiver density( length of mesh ). If the density is inadequate, the radiosity solution will not be accurately evaluted especially at areas with high gradients. On the other hand, if the density is too small, it will lead to unnessary computation.
There should no be 'light leaks' : this occurs where the grid partitions along a surface do not coincide with light- occluding polygon adjoining the surface. The problem is based on the result of dividing the receiving polygons into fixed length grids.
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                     Fig. 7.19 : Light leaks
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7.4.3. Substructuring

In traditional radiosity, the environment is broken down into small areas called patches and each patch is assumed to have uniform radiosity value [Goral,84][Cohen,85]. This method gives a poor result when the patches are large relative to the area over which high gradients occur. Therefore, surfaces with high gradients such as shadow boundaries and penumbras should be subdivided into finer grids or patches [Cohen,86].

Cohen first introduced the substructuring method in 1986 to produce an accurate image of a given environment. In this approach, the objects are hierarchically subdivided into surfaces, patches and elements. Surfaces are composed of polygons and curved surfaces. Patches are obtained by subdividing the surfaces. Patches are convex polygons which consists of one or more elements and their intensity may vary over the patch area. Elements are planar polygons with a smallest geometric unit in which intensity is assumed to be constant( See the diagram below).


     

    
                 Fig. 7.20 : Structure Hierarchy

The advantages of this method over traditional patch dividing method are :

The intensity variations within a patch can be accurately defined.
More accurate patch-to-patch form factors (radiation exchange between patches) can be obtained and hence improve the global radiosity solution.
Share the information between levels of data hiearchy.
Surfaces are only subdivided when it is needed, thus, save storage space.
It also removes the restriction that patches must be small relative to the distances which seperate them.
Image quality is improved particularly areas with high gradients such as shadow boundaries and penumbras [Cohen,86][Kwok,92].

Unfortunately, there are some drawbacks in this method. Such as :

Since emitting surfaces are not subdivided, accurate soft shadowing can not be produced.
Division of polygons into regular grids can cause the 'light leaks'
Small objects casting shadows can be easily missed if the initial patch sizes are too large [Campell,90].

7.4.4. Mesh generation

Baum[91] presented an automatic mesh generation method which works with various modelling constraints. In order to create an initial patch mesh, fixed lengths of rectangular grids are superimposed on top of each surface by aligning them with edges of a surface (note that other grids such as an equilateral triangular grids may be used as well). Since the grids length are fixed for all the faces, output polygons are well shaped with no T-vertices.

The length of the grids is determined by uniformly subdividing the longest face edge. However, poorly shaped patches can occur when the edge length of the input face is small compared to the length of the grid edges. This problem can be solved by using a different radiator density (grid length) for different surfaces. Surfaces that have short edges can have small grid edge lengths, while those without short edges can have longer grid edge lengths.

Patches with high density variation will then be subdivided into smaller patches by using a bilinear subdivision method. The patches and elements of a surface are stored in a tri-quad tree, in which patches are at the top level and each points to a tri- quad tree whose root is an element identical to the patch. The resultant element mesh also has to meet certain constraints as described above(mesh requirements). Mesh elements are generated by four-to-one midpoint subdivision. Using that type of subdivision, if the parent patch is well shaped, the children elements also will be well shaped.

To maintain gradual mesh density changes, there should be at most one subdivision level difference between two neighbouring elements in the same face (see the diagram below).


     

    
                    Fig. 7.21 : Mesh density

However, problems arise when an element is subdivided without subdividing its neighbours. T-vertices can be created at the common boundaries. To eliminate these T-vertices, the neighbour elements of newly subdivided element are split by connecting corners of neighbouring polygons to the T-vertices. Hence, splitting is localized to prevent excessive meshing (see diagram below, notice there are no T-vertices).


     

    
                  Fig. 7.22 : Mesh subdivision

There are two different splitting arrangments for triangular and four for rectangular patches.


     

    
                Fig. 7.23 : Splitting of the Mesh

Like all other methods, Baum automatic mesh generation method has some drawbacks.

There can be a problem of over meshing when varying grid edge length on a surface by surface basis. For example, a single surface may have only one short edge but all the faces in that surface have to have small grids while a larger size would be sufficient for most of them.
When the surfaces are meshed, only the geometric information is used. Thus, appropriate mesh densities may not be computed where needed.
The initial element mesh is created by evaluting pixel-level visibility between all surfaces using a depth-buffer. Although this is computationally faster, it may produce considerable overmeshing and inaccurate splitting boundries.