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Render zone university

Render principles

Albumen print, also called albumen silver print. Gift of Alden Scott Boyer. 'Wah Lum Chu, Canton" from ca. 1868. John Thomson, Scottish (1837-1921).



Radiosity methods were developed in 1950, not for rendering purposes but for calculating heat transfer. Of course heat is also a form of lightwave on the lower site of the spectrum. In 1984 researches at the famous Cornell University in the UK the methods were refined with the focus on rendering.

Some known render brands that uses Radiosity:

3ds Max
LightWave 3D

If we compare the way direct Illumination and Radiosity is working on the render then the choice is made fast. One sees a render picture that resambles more the actual realism of the scene.

On the left (example from Wikipedia) the direct illumination with several different lightsources: spot light, ambient light and omnidirectional light.

The spot light brings out the shadow part.

On the right the Radiosity algorithm with only one lightsource with an HDRI image that is placed outside the window. We see all kind of shadows from dark going to the lighter parts. Notice that the color of the red on the floor is also chaning because of the light source. Look at the walls, they were grey on the left and colored red on the right.

The way Radiosity methods works is iteratively. After each iteration we can look at the scene how it is building up the softer parts in the shadow part and the coloring of surfaces.

Radiosity method is asking a lot of time to render and in theory there is an increase in computation time with added geometry quadratically. Because of the time problem there are lots of other methods that uses a sort of false Radiosity, semi Radiosity or a combination of Direct Illumination and Radiosity.

In theory the Radiosity algorithm with global illumination is 'relative simple' to explain in math. So it is a useful algorithm for theaching students render programs.

One can tell that in the current computer graphics Radiosity is most of the time refered to heat transfer, where a certain number of flux (re-radiated and reflected) is leaving the surfaces (radiant eexitance).

Here we see a common heater and the energy (Farenheid) on different distances in foot.

One of this methods is Ambient Occlusion, which is a crude approximation Global Method because each point is a function of other geometry in the 3D scene. One looks at the scene as if we have a overcast day in our secne of looking at objects.

A house that is emmitting heat (energy) out of the windows: What you can't see is costing you money.


The Radiosity Algorithm: Basic Implementations



Hugo Elias 2000

The Radiosity Algorithm: Basic Implementations
by Bruce Makoto Arnold
Basic implementation of the radiosity algorithm.
More Info: Hopefully someone can get some use out of this since I spent so much time working on the figures and formulae!
Research Interests: Radiosity

What is Radiosity?


book Radiosity


Background - The Phong Model

The Phong lighting model [PHO75] is very commonly used in computer graphics today. In the Phong model, the light at any given point is made up of three components:


These three additive components are combined to determine the illumination or color of a point or polygon.


The diffuse component of the Phong model represents reflections that are not directional in nature. Each surface has a diffuse reflectance characteristic that determines how much light is reflected off the surface. The amount of light reflected is independent of the direction that the surface is being viewed from since surfaces that reflect diffusely reflect in all directions equally. The intensity of the diffuse reflection varies only with the cosine of the angle between the surface normal and light source.

The diffuse component of the Phong model is used to characterize reflections that are highly directional. Examples of this would be bright highlights on a shiny object. Similar to diffuse reflections, each surface has a specular reflection coefficient that determines how much light is reflected off the surface. The intensity of a specular reflection is also proportional to the cosine of the angle between the view direction and the direction the light is reflected in. In addition, there is a specular exponent that determines how quickly the specular highlight drops off as the view angle moves away from the reflection angle.


The ambient component of the Phong model is added to take into account light generated from inter-object reflections. In real environments surfaces that are not directly lit are not completely dark. Light generated by reflections off other diffuse and specular surfaces serves to illuminate these areas. To model this, Phong uses a constant ambient illumination term that when multiplied by the ambient reflectivity of the surface, gives the ambient component of illumination.

We have direct illumination, with one or more bright lightsources and a rather harsh shadow casting. And a global illumination, where it is hard to guess where the light is coming from. Of course this one with global illumination is the perfered one with quality photo like renders.

Light coming from one lightsource, like the sun is bright and brings strong contrast in the renders. More natural is that the light (of the sun, in clouds) or the artificial light is spread out because the available light sources all have small light sources alongside from the surfaces. It is as if they all react as individually light sources themselves.

Radiosity is computer graphics is the way a finite method is used to solve the rendering equation in scenes. Each surface is reflecting the available light individually and diffusely.

The number of times (it is finite method) that a ray is causing new light sources (reflection and defraction) has be restricted and must be adjusted by the user of the render software. More rays causes more lightsources and will be quality wise better, but the rendering time will be much longer as well. If we look at the surface with Shaders and materials, then light will not only comming from lightsources, but also from the illumination of other sources that act like new light sources.

Radiosity is not depenable on the Viewpoint (the way we look at the 3D scene) so that many viewpoints are possible. But the con is that this Radiosity is timeconsuming to render. The intensity of surfaces in the model are computed before any View calculations are being made.

It is the difference between demand-driven (with z-buffer, raytrace, the location of the polygon is computes_ or data-driven (radiosity the lighting is beforehand computed, certain surfaces are given initial intesities and they are computed in an iterative manner) lighting computation.

The precense of these lit surfaces in the model is what drives the computation of the system.


A Radiosity render proces

1. generate the model

2. compute the form factors

3. solve Radiosity Matrix eq.

4. Render

We see those things elements back into Maxwell Render, where a change in paramaters does not require a restart from step 1. Only if the geometry of the scene is changed then you have to go back to step 1.

During the render proces one can change the lighting or reflectance parameters, then a new start from step 3 is possible. And if you change the View parameters then you have to re-render from step 4 onwards.




An Empirical Comparison of Radiosity Algorithms

(3.1 MB)


Raytracing is a technique for generating images by tracing rays of light through pixels in an image plane out into a scene and following the way the rays of light bounce and interact with objects in the scene. More information:

Or in other words: Scenes are being rendered by firing out rays and letting them bounce around a scene to form Ray Paths. Different render modes control the way Ray Paths are constructed. Then have different strengths and weaknesses for different scenes.

One could speak from 'backwards ray tracing' due to the fact that the rays do not orrigin from the light source, but quite the opposite: from the eye or camera. There could be some confusion, because in the history of rendering where James Arvo uses the term backwards ray tracing in the past. One could speak of 'eye-based' rendering or 'light-based' rendering. Then it is clear where the start of the rays begins.

Caustics always is difficult to implement, because bright patterns are focused into narrow area of surfaces. A change in startpoint of the ray to the lightsource is better to see that this phenomenon is handled well.

BiDirectional Path tracing is considered to be the 'best' all-round solution. With tricky scenes MLT could hep a lot, for instance with glass, polished surfaces.


Very high degree of visual realism, better then scanline, ray casting rendering methods, but at certain level of computational cost. Where it is possible (not for Games) to render for stills, film, animation, visual effects, TV etc.

Ray Tracing comes with shadows (not simple with other rendering methods) optical effects like: reflection, refraction, scattering, dispersion, chromatic aberration etc.

Each ray is more or less independable against other rays, but the rays need some sort of sorting and adding and saving, so for parallel processing (with GPU) it is a lot of work to put all those individual processes in the right box for outputing the wanted stills.

It is possible to shoot more rays then needed to perform anti-alisaing or improve image quality where needed.


The disadvantage of Ray Tracing is performance. Where Scanline algorithms and Ray Casting algortihms are fast by using data coherence and sharing computations between pixels.


Although Ray Tracing is using the optical laws and ability to perform Shadows and reflection. It is in no way automatically Photorealistic. Strange because all the algorithms to work like fysics and nature is working with light should give automatically a photorealistic look.

One problem here: if one is using the rendering equation as close to nature as possible, one could and should render 'for ever' to fullfill even the slightest reflection and refraction. Every surface and material is not only the source of interacting with light, but at the same time all those points acts themselves as new light sources in the scene.


Ray tracing Wikipedia

Ray Tracing as close as possible (computational wise) to the Physics is bound to Whitted's algorithm. But again not necessarily the most realistic or photo like representation.

Ray Tracing

To come close to Whitted's algorithm (and realism) one can combine some rays according to their direction to gain a better performance.

Path tracing

In path tracing, a collection of paths is sampled backward, starting at the eye.

They are fired from the camera, bouncing around the scene until they hit a light.

Path tracing

Shows a single path tracing sample from the thesis PDF of Van Antwerpen TUDelft.

"While print exposure may appear at first glance to be one of the more simple and straightforward aspects of Albumen and Salted paper printing, in reality it is one of the most complex. The biggest difficulty arises from the fact that the color and intensity of the exposing light affect the color and ultimate contrast of the print. "

This shows that Albumen prints in the past has a lot of common with modern way of making 3D renderings as good as possible and in a way comparable / resembling reality as much as possible.

Albumen print. An indoor printing studio ca. 1890.
South facing orientation was the best for printing (best possible sun light intensity).

BiDirectional Path Tracing (BDPT)

BiDirectional Path Tracing was independently developed by Veach and Lafortune.

It samples an eye path and a light path and connects these to form complete light transport paths. The eye path starts at the eye and is traced backwards into the scene, like in the PT sampler. The light path starts at a light source and is traced forward into the scene. Connecting the endpoints of any eye and light path using an explicit connection results in a complete light transport path from light source to eye.


BiDirectional path tracing sample from the thesis PDF of Van Antwerpen TUDelft.

In the PT sampler, all but the last path vertex are sampled by tracing a path backwards from the eye into the scene. This is not always the most effective sampling strategy. In scenes with mostly indirect light, it is often hard to find valid paths by sampling backwards from the eye. Sampling a part of the path forward, starting at a light source and tracing forward into the scene, can solve this problem.


BiDirectional Path tracing

Here the Rays are fired from both the camera AND the light sources. They are joined together to create many complete light paths.



Eric P. Lafortune and Yves D.Willems. Bi-directional path tracing. In Proceedings of
third international conference on computational graphics and visualization techniques
(COMPUGRAPHICS 93), pages 145&endash;153, 1993.
Eric Veach. Robust monte carlo methods for light transport simulation. 1998. Adviser-
Guibas, Leonidas J.

All sort of combinations are developed.

Path tracing with MLT

Rays are fired from the camera, bouncing around the scene until they hit a light. When a successful light-carrying path is found, another is fired off on a similar direction. Gives good results for caustics.



Bidirectional path tracing with MLT

Rays are fired from both the camera and the lights, then connected to create many paths. When a successful light-carrying path is found, another is fired off on a similar direction. Gives good results in general for caustics and "difficult" scenes.

Photon Mapping

A very fine way of making rendering is Photon Mapping. There eye-based and light-based ray tracing is performed. In 3-dimensional space (photon map) one follow the photns along the lines originating from the light. In subsequent passes rays are traced from the eye to determine the visible surfaces. The sometimes big photon map is used to estimate the illumination at all visible surface points. The other points (not visible) are not computed.


One can 'reuse' some photons in the calculation, thereby gaining rendering speed. That's not possible with Bidirectional Path Tracing (BPT).


If light is coming from a limited space into the scene then only a small subset of paths will be the transport of light energy.

Infrared house rendering

Metropolis Light Transport (MLT)

Nicholas Metropolis &endash; The physicist after whom the algorithm is named

Nicholas Metropolis

The man behind the used algorithm for optimalisation the render proces.


Metroplis Light Transport and the introduction of the Monte Carlo method
at Stanford august 1997.

See the PDF ( 3.446 MB)

Bidirectional path tracing with 40 samples per pixel.

Far better noise content.
Metropolis light transport with an average of 250 mutations per pixel. The same computation time as image a above.

Enlargement of both pictures / renderings.
Below the BiDirectional path tracing (noisy) and above the proposed MLT version.


Bidirectional path tracing with 40 samples per pixel

Metroplis Light Transport with average of 250 mutations per pixel, with the same computation time as above picture.

The light is coming from behind the door and has bounced several times in order to lighten the scene. With caustics in a pool of water the gain of MLT is far greater then in this example. Within 100 mutations per pixel there is a clear view, against noisy ptah tracing with 210 samples per pixel, all in the same time limit. At that time they 'worked' with a very slow computer with 190 MHz MIPS R10000 processor, so the render times were ranging from 15 minutes to 2.5 hours and 4 hours.

Method that explores the random search of path space. A variant of the Monte Carlo or Russian roulette methods. It is a statistical approach to solve many-body problems. The Monte Carlo method uses random sampling to estimate an integral. Monte Carlo methods rely on repeated random sampling to compute the final results of the rendering. But for 'Unbiased' could take for ever . . .

If energetic paths are traces then this data is used to further exploring nearby spaces of rays. The rays are coming from the ey to the light source(s) using bi-directional path tracing. Then a small modification is taking place the the former path. With the Metropolis algorithm the appropriate distribution of brightness and color are computed.

Paths are stored in a big list ('nodes' list), then the path's are modified and a new light path is created. During this proces the MLT algorithm decides how many new 'nodes' he have to add. And with the decision if the new noded do make a new path or not.



MLT is in theory UNBIASED method, where the rendering equation is converging quite fast to a physically good peforming picture. The speed of converging is higher then with other rendering equations like Unbiased path tracing or Bidirectional path tracing.

MLT not always the solution for everything

For relative simple scenes MLT might not be the best solution. Path tracing and BiDirectional path tracing could perform much better there.

MLT is not ment to finish all passes, it already reaches 95% of it's maximum quality after a few dozen passes.


In comparison to other Open Source renderers, Mitsuba places a strong emphasis on experimental rendering techniques, such as path-based formulations of Metropolis Light Transport and volumetric modeling approaches. That's why Mitsuba is frequently used by students to incorporate their own program inside.

About MLT and the NOX renderer (forum)

Dec. 2011

There are nearly any MLT based unbiased rendering engines (either commerical or non-commercial) out there in the wild. So two months my ass! Wow relax man, he said 'basic' unbiased engine.

This is only true if you stick to the simplest algorithm: Path tracer.

It becomes hell of a lot more complicated if you try to get some sophisticated sampling algorithms to cut down the rendering times which you will need pretty soon for example if you are thinking about using a Bidirectional Pathtracer. And it gets a lot more complex if you go even for Metropolis path strategies.

There are nearly any MLT based unbiased rendering engines (either commerical or non-commercial) out there in the wild.

I did write "path tracer", didn't I ;)

I don't think anyone would claim that writing a MLT renderer is a cakewalk, at least no one who has tried to do so. But this whole "unbiased" thing is way overblown, there's no inherent achievement in writing an unbiased renderer over a biased one.

I consider the whole point of biased vs unbiased moot anyway, since models built from flat triangles with Phong interpolated normals with their surface properties represented by finite resolution square pixels is already such a gross approximation of reality that it's almost absurd to be obsessed with the bias discussion.

Rendering anything with Bump maps and RGB colors is already so far detached from reality that it's not going to become "physically accurate" just by shoving it through the right render engine.

In production, all that counts is how good it looks and how long it takes me to get there.

The fine details of how QMC sampling or mip maps introduce bias is something for those of us who optimize with SSE prefetch instructions in their spare time, but the other 99.99% of the world couldn't (and shouldn't) care.

I haven't had a chance to play with Nox yet, but from the screenshots, it does look like many months of full time work (UI doesn't write itself either) and I wish the authors a lot of success and fun.

MLT Raytracer based on papers

James Cook

Program with source code link on the page.



MetropoLight is a simple freeware global illumination rendering program that uses the Metropolis Light Transport algorithm to render images.

MLT is a Monte Carlo method for solving the light transport problem. It is inspired by the Metropolis sampling method in computational physics.

In short, a sequence of light transport paths is generated (based on Monte Carlo Markov Chain sampling) by randomly mutating a single current path. The probability density of visiting each path is proportional to its contribution to the final image. This algorithm has the particularity to be unbiased and can be orders of magnitude more efficient than previous unbiased approaches. It is highly recommended for complex and delicate indirect lighting

I developed this small rendering project to study and to familiarize with this new approach in random walk global illumination algorithms. Metropolis Light Transport will be one of the numerous algorithms implemented into my "next generation" renderer (codename: A.E.R.E.)

Although some additional features will be progressively implemented to complete the project, MetropoLight doesn

Biased versus Unbiased

Physical correct or slightly (in)correct?

remarks in the metro.pdf

Metropolis Light Transport

Eric Veach Leonidas J. Guibas
Computer Science Department
Stanford University

On the other hand, many methods used in graphics are biased. To make any claims about the correctness of the results of these algorithms, we must bound the amount of bias.

In general this is very difficult to do; it cannot be estimated by simply drawing a few more samples. Biased algorithms may produce results that are not noisy, but are nevertheless incorrect. This error is often noticeable visually, in the form of discontinuities, excessive blurring, or objectionable surface shading.

In graphics, the first unbiased Monte Carlo light transport algorithm was proposed by Kajiya, building on earlier work by Cook et al. and Whitted. Since then many reifinements have been suggested. Often these improvements have been adapted from the neutron transport and radiative heat transfer literatures, which have a long history of solving similar problems.

However, it is surprisingly difcult to design light transport algorithms that are general, efficient, and artifact-free. From a Monte Carlo viewpoint, such an algorithm must efciently sample the transport paths from the light sources to the lens. The problem is that for some environments, most paths do not contribute signifcantly to the image, e.g. because they strike surfaces with low reflectivity, or go through solid objects. For example, imagine a brightly lit room next to a dark room containing the camera, with a door slightly ajar between them. Naive path tracing will be very ineffficient, because it will have difficulty generating paths that go through the doorway. Similar problems occur when there are glossy surfaces, caustics, strong indirect lighting, etc.

Some Renderers using MLT

Arion Render &endash; commercial unbiased renderer based on path tracing and providing an MLT sampler

Indigo Renderer &endash; commercial unbiased 3D renderer that uses MLT

Iray (external link) &endash; unbiased renderer that has an option for MLT

Kerkythea &endash; free unbiased 3D renderer with MLT

LuxRender &endash; open source unbiased renderer with MLT

Mitsuba Renderer A research-oriented renderer which implements several MLT variants

Mitsuba Renderer was used by YINING KARL LI to make use of the program parts to make a new and amasing render program called


Institutial Repository

Unbiased physically bsaed rendering on the GPU

A way to implement the MLT, BiDirectional Path Tracing and Physically based rendering Engines into the GPU


June 14, 2011

author: Dietger Van Antwerpen, born in Rotterdam.

see the thesis pdf ( 22.8 MB, 2010), for the Master of science n Computer science.


Since the introduction of General-Purpose GPU computing, significant increase has been made in performance for regular path tracing. However, more advanced versions of path tracing such as BiDirectional Path Tracing (BDPT) and Energy Redistribution Path Tracing (ERPT) have not been implemented successfully so far due to their stochastic sampling characteristics.

The goal of this thesis is to find efficient GPU implementations for these unbiased physically based rendering methods. In this thesis improved streaming versions of these algorithms have been developed that better exploit ray coherence, reduce memory-footprint, and improve convergence, in order to make the algorithms more feasible for the GPU. The performance of the GPU versions is compared with the CPU versions and it is shown that the convergence characteristics of the original methods are preserved in our GPU implementations, while the processing has been speeded up with an order of magnitude.

We therefore propose three streaming GPU-only rendering algorithms: a Path Tracer (PT), a BiDirectional Path Tracer (BDPT) and an Energy Redistribution Path Tracer (ERPT).

Speed advantage

The speed of physically based rendering can be improved by either using more advanced algorithms, or by optimizing the implementation of these algorithms. Since the advent of physically based rendering, several advanced physically based rendering algorithms, capable of rendering very complex scenes, have been developed and implemented on the CPU.

Photon map

source: Kerkythea Rendering System FAQ


Q. What is photon mapping?

Photon mapping is a render method that solves the global illumination problem in two passes. In the first pass, photons are shot from the light sources and stored in the computer memory. Afterwards, in the ray tracing step, the rays shot from the camera "collect" the photons and estimate the perceived brightness.

Q. What is global illumination?

Global illumination refers to the inclusion of complex light interactions between camera, objects and light sources, as opposed to local illumination where the interaction between the objects in the scene is not taken into account. Global illumination includes phenomena like reflections, refractions and diffuse interreflection.

Q. Are there other ways to solving the global illumination problem besides
photon mapping?

There are numerous techniques, each one having its pros and cons. Usually, these techniques are divided in two categories: biased and unbiased methods. Photon mapping is a biased method, meaning that the found solution differs from the real one. Unbiased methods, on the other hand, converge to the real solution.

Q. Can you say some examples of such techniques?
Examples of global illumination techniques are photon mapping and light cache
falling in biased category, and path tracing, bi-directional path tracing and
metropolis light transport falling in the unbiased category. In Kerkythea, all the
above techniques are available.
Q. What are the pros and cons of the biased versus unbiased techniques?
Biased techniques are usually much faster, because the estimation happens
sporadically and a large part of the image is usually interpolated between these
key points. This might lead though to disturbing artifacts known as blotches.
Unbiased techniques on the other hand take much longer but they are
guaranteed to solve accurately for all light interactions. The artifacts in their case
appear in the form of noise that is decreased over running time.
Q. I have strange shadows and/or light leaking in my image. What am I doing

If you have shadow problems or light leaking, it is probably due to a bad Photon map. Increase your photons shot to something like "Many &endash; 100000" or "Very Many &endash; 1000000". If you have a "bad quality" Photon map (not sufficient photons), it does not mater how much you increase your Final Gathering settings, it won't lead to a good render. It is always better to increase the Photon map quality (more Photon shooting) and have Final Gathering set to something like "Rays 900 &endash; Very Many" and Accuracy to "Good/Very Good 0.15/1.0". If you want caustics in your image, then you have to use much more Photons like "A Lot &endash;10000000 " or more, depending on your scene. Another important thing is to use some rules of thumb in the modeling. For example, in modeling a room or building, make sure that your walls, ceiling and floor have some thickness &endash; this effectively prevents light and shadow leaking.

Q. How do I know if my Photon map is good enough?
To see your Photon map you have to change your render method in the Global Illumination panel form "Photon Mapping + Final Gathering (SW)" to "Photon Mapping (Direct + Indirect)". Now, you will see that there are a lot of settings not available anymore because Final Gathering phase is omitted in this case &endash;
rendering will be also quicker. The result will not be of high quality, but it is good to find out the quality of your Photon map.
This is very much related to whether you can see "approximately good shadows" in your render (be aware that the image may appear quite irregular &endash; this is because Kerkythea uses a variant of photon mapping where photons are stored on your objects' faces). When you have a good Photon map, return back and use the method "Photon Mapping + Final Gathering (SW)" for your final render.
Q. I have bright random spots in my image. How can I eliminate them?
It is probable that is caused by reflected caustics (produced by shiny surfaces like mirrors, water metal, etc.). To avoid them, you have to increase the caustic density count to something around 1000 photons (this depends on your scene and may need a few trials until a sufficiently large number is set without over blurring the rendered image)