Radiosity (computer graphics)
Radiosity or radiosity is a method of calculating the distribution of heat or light radiation within a virtual model. In the image synthesis radiosity is next based ray tracing algorithms of the two major methods for calculating the incidence of light within a scene. It is based on the energy conservation law: All the light that falls on a surface and is not absorbed by it is thrown back from her. In addition, can also be self-illuminating a surface.
The radiosity method is based on the assumption that all surfaces of ideal diffuse reflectors and all light sources are ideal diffuse reflector. Ideal diffuse means that light is evenly reflected or radiated in all directions.
In contrast to ray tracing radiosity is not from the viewpoint dependent; the illumination of the surface is thus calculated regardless of the position of the viewer for the entire scene. The viewpoint- dependent masking calculation shall be made in an independent step.
- 2.1 the first division of the surface
- 2.2 second definition of the basis functions
- 2.3 3 calculation of the form factors 2.3.1 Method according to Nusselt
- 2.3.2 hemi- cube method
- 2.3.3 Sillions improvement
Properties
Benefits
Disadvantages
Comparison with ray tracing
Historically radiosity was interesting, as it allowed the simulation of indirect diffuse illumination in a simple way, which was not possible with ray tracing long time. On the other hand, ray tracing was good for specular and transparent objects suitable form, a further radiosity was not capable. Therefore, it was initially proposed for the combination of radiosity rendered with ray tracing, who were, however, complex and ultimately did not succeed to a great extent.
With the advent of advanced global illumination methods such as path tracing and photon mapping, however, the capabilities of ray tracing have expanded considerably. Because such algorithms can simulate all supported radiosity effects with fewer errors and more elegant manner, radiosity is largely gone out of fashion in the field of high-quality realistic image synthesis. Commercial use is radiosity especially when rendering architecture models in which a time-consuming pre-calculation is acceptable. Also, such applications are only possible with ray tracing -based method (Particle tracing).
Other applications find radiosity method in the fields of air-conditioning or heat research because heat distribution is more diffuse than directed and radiosity is here practicable than radiation -based approaches.
Principle
With the adoption initially formulated the general rendering equation can be converted into the radiosity equation.
With
The desired radiosity at the point x is obtained from an integral in closed form, which can not be calculated directly. Remedy the discretization of the surface S: instead of considering all the infinitesimally small sub-areas DELTA.a ', divide the surface S into contiguous sub-areas ( or patches called facets ) Ai in (finite element method). For these sub- areas further assumptions are made: each Ai is planar; the respective radiosity Bi and the reflection coefficient ρi are constant over Ai. This then leads to the discrete radiosity equation.
With
The radiosity of patch is thus equal to the characteristic radiation of the patch plus the weighted with the diffuse reflection factor sum of the radiosity of all other faces. Where in this case, the form factor, which determines the proportion of the votes of surface j energy incident on surface i, is received. Thus the form factor of each other taken into consideration, the alignment and spacing of the sub-areas. Since you have this calculated for all sub-areas, a system of linear equations with as many equations and unknowns results as there are faces.
First subdivision of surfaces
In the first step the definition of the primitives is performed: how and in which part faces a given continuous surface to be decomposed? Are usual triangle and square. Even at this stage it is decided between quality and efficiency. The fine mesh the network, the more accurate the results, but the more complex the calculations.
In practice one usually uses adaptive methods. Based on a triangulated surface, for example, according to the scheme given here the corresponding radiosity values of all the facets are determined. With these data, then, take additional location-dependent mesh refinements. The main reason can be: a high radiosity gradient adjacent facets, discontinuities in the light curve ( eg light spot ) or a locally unfavorable net division ( eg T- node).
Second definition of the basis functions
Discrete radiosity equation provides a means of discretization; they based on the assumption that the radiosity of a given facet is constant, and therefore uses constant basis functions. The choice of basis functions higher degree is also possible, particularly with the Galerkin approach.
3 Calculation of the form factors
The most expensive step in radiosity is, regardless of the chosen algorithm, the calculation of the form factors. A form factor always applies between two patches and describes the amount of the exchanged radiation, that is between zero ( no radiation is exchanged) and one (all radiation is exchanged).
The form factor is purely geometric in nature, and is determined by the position of the patches to each other. In addition, the visibility of the patches is involved. The visibility calculation needs by far the most time in the calculation.
The formula for a form factor is:
With
Since the direct calculation of this double integral is very difficult approaches are generally used.
The simplest procedure is correct only for the areas that are relatively small and relatively far away and between which there is no partial blockage. It calculates distance and angle between two points only representative, the centers of the two surfaces.
With the center of the center and of is.
Method according to Nusselt
(also called " Nusselts analog" )
It is a representative point of the receiving surface, the center is selected. The visible parts of the channel area can be projected onto the hemispherical unit at this point. This is observed. Then, the projection on the unit sphere, in turn, projected onto the plane in which lies. The resulting surface is divided by (area of the unit circle ). By this step, the form factor is determined.
Hemi- cube method
Cohen et al. comes the so-called hemi- cube method. The unit hemisphere Nusselt is approximated by a half- unit cube whose side faces are divided into a discrete grid. Each grid area is a weighting factor, the delta form factor associated with which is a function of the position of the grating surface. A delta form factor so that the form factor of the grating surface by Nusselt. The sum of the delta form factors is 1
For each of the five half cube faces an item buffer is calculated with modified grid algorithms (usually Z- buffer). This includes the identity of the object surface (Item, red triangle in the picture), which was projected onto it for each grid area. For each item, the sum of the delta form factors of the covered grating surfaces calculated ( red grid areas in the image ). This sum is understood as a form factor between item and considered surface.
Sillions improvement
Instead of a half- die only a single surface is now used, which is positioned centered over the differentially small patch (dA). This area is also divided into small, discrete areas. These are then assigned to precisely the so-called delta form factors such as the hemicube process in dependence on the geometry dA. The advantage of this method is that a patch should be projected only onto this one surface, and not on five faces of a cube. Moreover, this method is legitimate, because patches, which are orthogonal to the surface of dA, do not have a large contribution to the total brightness. This observation can be made clear on the cosine between the normals of the two patches.
4 Calculation of the radiosity values
The discrete radiosity equation can be interpreted as a system of linear equations and can consequently after several forming steps described as follows in matrix form.
To determine all of the query radiosity values , the system of equations must be solved. The obvious is the inverse of the matrix ( IT) (matrix inversion by Gauss ), which is impractical but because of the enormous expense.
In general, there are two different iterative solution strategies that converge to the exact solution. Thus, an arbitrary compromise between image quality and computation time is possible.
- At the Gathering the radiosity Bi of a facet is formed by collecting all the main influencing Bj (depending on the form factor). The starting point is B0 = E and one sees only the self-luminous surfaces. After the first step B1 = E T • B0 all directly illuminated objects are also visible. In the next iteration step B2 = E T • B1 is the simple reflections are taken into account, is so striking that in each step, all form factors are needed. Based on this principle methods are Jacobi iteration and Gauss-Seidel iteration.
- When shooting the undistributed radiosity Bi is at all as a receiver shot (depending on the form factor ) in question facets. The starting point is again the self-luminous surfaces, thus B = E.
For each facet i Radiosity B = self-illumination E undistributed radiosity DELTA.B = self-illumination E repeat i = facet with maximum residual energy ΔBi • Ai for each facet j rad = ρj ΔBi • • Fji ( how much to be distributed radiosity gets facet j) ΔBj = ΔBj rad ( to be distributed radiosity of the facet j is increased by this amount ) Bj = Bj rad ( radiosity of the facet j is increased by this amount ) ΔBi = 0 ( to be distributed radiosity of the facet i has been distributed and is now 0) to ( termination criterion ) As termination criteria and the subjective impression can be used in addition to objective values as error metrics. Shooting methods are superior to the Gathering method in two aspects. On the one hand can be derived from the pseudo-code that for each iteration step only j form factors are needed. Secondly, in each run the radiosity of the facet is distributed with the largest residual energy, thereby shooting process much faster against " beautiful" pictures converge as Gathering process. On this principle based algorithms are Southwell iteration and progressive refinement. 5 rendering
The last step is the rendering of the final image. The value calculated at the selected points radiosity values are combined according to the selected basis functions. Were radiosity values is determined in the network nodes, for example, Gouraud shading possible. Is not that enough image so created the claim, as further iterations of ( 4) can follow. If unwanted graphical artifacts, it should be started with appropriate changes in the network structure of the algorithm from the beginning.
Historical Development
1984, the method first described by Goral et al. presented. It originates from thermodynamics, where it was used to calculate the exchange of heat radiation ( radiation calculation). At this time, the full- form-factor matrix method for solving the system of equations is used. Here the system of equations for all form factors between all patches ( = land) is situated in the world and then (usually the Gauss - Seidel method ) solved using a mathematical method. In principle, this approach corresponds to the collection of radiosity. For each patch is calculated how much light it receives from any other patch. This has the disadvantage that the calculation of the complete matrix required extremely much time and much space, which makes the process complex scenes unusable.
In 1988 was the progressive refinement method of Cohen et al. presented. Here, the process is reversed, and the light is not collected in each patch, but fired from each patch. So first you can even ship the light of the patches with the largest Radiositywert and then reach out to those with little radiosity. Here it is not necessary to compute the entire matrix, but, in each step just the form factor of a single patch to all other required. Hence, the memory required is reduced considerably, and, after each step, a useful image. The longer you wait, the better the image, as more indirect ions are calculated. To converge, this method needs, however, as long as the full - form-factor matrix method.
In principle, the method of series expansion of the matrix corresponds to. The system of linear equations that results from radiation equation, then, is the unit matrix, the matrix consisting of the form factor and the reflection coefficient and the self- radiation is described. If the equation is now to, so can be developed as a series of the form of the right part, and you get an incremental approximation of the actual radiation intensity:
1991 by Hanrahan et al. the Hierarchical Radiosity presented. In this method, a patch hierarchy is used. Few large patches consist of many small. The light exchange is now done at different levels. If the error is small, the light is at a high level in the hierarchy is replaced, when a large error is to be expected ( for example, when a lot of light is changed or the areas are very close to each other ), then the light is changed to a lower level. Thus, the number of calculated form factors is reduced substantially, and the calculation is much faster.
In addition to these methods, many extensions have been devised yet. For example, there is the method of clustering, which is an expansion of the hierarchical radiosity. Here is a further hierarchy is generated above the patch hierarchy, the cluster. Light can be exchanged between all cluster groups then also, depending on the expected error. Again, it saves the calculation of many form factors.