Definitions

# computer-graphics

Rendering is the process of generating an image from a model, by means of computer programs. The model is a description of three dimensional objects in a strictly defined language or data structure. It would contain geometry, viewpoint, texture, lighting, and shading information. The image is a digital image or raster graphics image. The term may be by analogy with an "artist's rendering" of a scene. 'Rendering' is also used to describe the process of calculating effects in a video editing file to produce final video output.

It is one of the major sub-topics of 3D computer graphics, and in practice always connected to the others. In the graphics pipeline, it is the last major step, giving the final appearance to the models and animation. With the increasing sophistication of computer graphics since the 1970s onward, it has become a more distinct subject.

Rendering has uses in architecture, video games, simulators, movie or TV special effects, and design visualization, each employing a different balance of features and techniques. As a product, a wide variety of renderers are available. Some are integrated into larger modeling and animation packages, some are stand-alone, some are free open-source projects. On the inside, a renderer is a carefully engineered program, based on a selective mixture of disciplines related to: light physics, visual perception, mathematics, and software development.

In the case of 3D graphics, rendering may be done slowly, as in pre-rendering, or in real time. Pre-rendering is a computationally intensive process that is typically used for movie creation, while real-time rendering is often done for 3D video games which rely on the use of graphics cards with 3D hardware accelerators.

## Usage

When the pre-image (a wireframe sketch usually) is complete, rendering is used, which adds in bitmap textures or procedural textures, lights, bump mapping, and relative position to other objects. The result is a completed image the consumer or intended viewer sees.

For movie animations, several images (frames) must be rendered, and stitched together in a program capable of making an animation of this sort. Most 3D image editing programs can do this.

## Features

A rendered image can be understood in terms of a number of visible features. Rendering research and development has been largely motivated by finding ways to simulate these efficiently. Some relate directly to particular algorithms and techniques, while others are produced together.

• shading — how the color and brightness of a surface varies with lighting
• texture-mapping — a method of applying detail to surfaces
• bump-mapping — a method of simulating small-scale bumpiness on surfaces
• fogging/participating medium — how light dims when passing through non-clear atmosphere or air
• shadows — the effect of obstructing light
• soft shadows — varying darkness caused by partially obscured light sources
• reflection — mirror-like or highly glossy reflection
• transparency, transparency or opacity — sharp transmission of light through solid objects
• translucency — highly scattered transmission of light through solid objects
• refraction — bending of light associated with transparency
• diffraction — bending, spreading and interference of light passing by an object or aperture that disrupts the ray
• indirect illumination — surfaces illuminated by light reflected off other surfaces, rather than directly from a light source (also known as global illumination)
• caustics (a form of indirect illumination) — reflection of light off a shiny object, or focusing of light through a transparent object, to produce bright highlights on another object
• depth of field — objects appear blurry or out of focus when too far in front of or behind the object in focus
• motion blur — objects appear blurry due to high-speed motion, or the motion of the camera
• non-photorealistic rendering — rendering of scenes in an artistic style, intended to look like a painting or drawing

## Techniques

Many rendering algorithms have been researched, and software used for rendering may employ a number of different techniques to obtain a final image.

Tracing every ray of light in a scene is impractical and would take an enormous amount of time. Even tracing a portion large enough to produce an image takes an inordinate amount of time if the sampling is not intelligently restricted.

Therefore, four loose families of more-efficient light transport modelling techniques have emerged: rasterisation, including scanline rendering, geometrically projects objects in the scene to an image plane, without advanced optical effects; ray casting considers the scene as observed from a specific point-of-view, calculating the observed image based only on geometry and very basic optical laws of reflection intensity, and perhaps using Monte Carlo techniques to reduce artifacts; radiosity uses finite element mathematics to simulate diffuse spreading of light from surfaces; and ray tracing is similar to ray casting, but employs more advanced optical simulation, and usually uses Monte Carlo techniques to obtain more realistic results at a speed that is often orders of magnitude slower.

Most advanced software combines two or more of the techniques to obtain good-enough results at reasonable cost.

### Scanline rendering and rasterisation

A high-level representation of an image necessarily contains elements in a different domain from pixels. These elements are referred to as primitives. In a schematic drawing, for instance, line segments and curves might be primitives. In a graphical user interface, windows and buttons might be the primitives. In 3D rendering, triangles and polygons in space might be primitives.

If a pixel-by-pixel approach to rendering is impractical or too slow for some task, then a primitive-by-primitive approach to rendering may prove useful. Here, one loops through each of the primitives, determines which pixels in the image it affects, and modifies those pixels accordingly. This is called rasterization, and is the rendering method used by all current graphics cards.

Rasterization is frequently faster than pixel-by-pixel rendering. First, large areas of the image may be empty of primitives; rasterization will ignore these areas, but pixel-by-pixel rendering must pass through them. Second, rasterization can improve cache coherency and reduce redundant work by taking advantage of the fact that the pixels occupied by a single primitive tend to be contiguous in the image. For these reasons, rasterization is usually the approach of choice when interactive rendering is required; however, the pixel-by-pixel approach can often produce higher-quality images and is more versatile because it does not depend on as many assumptions about the image as rasterization.

The older form of rasterization is characterized by rendering an entire face (primitive) as a single color. Alternatively, rasterization can be done in a more complicated manner by first rendering the vertices of a face and then rendering the pixels of that face as a blending of the vertex colors. This version of rasterization has overtaken the old method as it allows the graphics to flow without complicated textures (a rasterized image when used face by face tends to have a very block-like effect if not covered in complex textures; the faces aren't smooth because there is no gradual color change from one primitive to the next). This newer method of rasterization utilizes the graphics card's more taxing shading functions and still achieves better performance because the simpler textures stored in memory use less space. Sometimes designers will use one rasterization method on some faces and the other method on others based on the angle at which that face meets other joined faces, thus increasing speed and not hurting the overall effect.

### Ray casting

Ray casting is primarily used for realtime simulations, such as those used in 3D computer games and cartoon animations, where detail is not important, or where it is more efficient to manually fake the details in order to obtain better performance in the computational stage. This is usually the case when a large number of frames need to be animated. The resulting surfaces have a characteristic 'flat' appearance when no additional tricks are used, as if objects in the scene were all painted with matte finish.

The geometry which has been modeled is parsed pixel by pixel, line by line, from the point of view outward, as if casting rays out from the point of view. Where an object is intersected, the color value at the point may be evaluated using several methods. In the simplest, the color value of the object at the point of intersection becomes the value of that pixel. The color may be determined from a texture-map. A more sophisticated method is to modify the colour value by an illumination factor, but without calculating the relationship to a simulated light source. To reduce artifacts, a number of rays in slightly different directions may be averaged.

Rough simulations of optical properties may be additionally employed: a simple calculation of the ray from the object to the point of view is made. Another calculation is made of the angle of incidence of light rays from the light source(s), and from these as well as the specified intensities of the light sources, the value of the pixel is calculated. Another simulation uses illumination plotted from a radiosity algorithm, or a combination of these two.

Radiosity, also known as Global Illumination, is a method which attempts to simulate the way in which directly illuminated surfaces act as indirect light sources that illuminate other surfaces. This produces more realistic shading and seems to better capture the 'ambience' of an indoor scene. A classic example is the way that shadows 'hug' the corners of rooms.

The optical basis of the simulation is that some diffused light from a given point on a given surface is reflected in a large spectrum of directions and illuminates the area around it.

The simulation technique may vary in complexity. Many renderings have a very rough estimate of radiosity, simply illuminating an entire scene very slightly with a factor known as ambiance. However, when advanced radiosity estimation is coupled with a high quality ray tracing algorithim, images may exhibit convincing realism, particularly for indoor scenes.

In advanced radiosity simulation, recursive, finite-element algorithms 'bounce' light back and forth between surfaces in the model, until some recursion limit is reached. The colouring of one surface in this way influences the colouring of a neighbouring surface, and vice versa. The resulting values of illumination throughout the model (sometimes including for empty spaces) are stored and used as additional inputs when performing calculations in a ray-casting or ray-tracing model.

Due to the iterative/recursive nature of the technique, complex objects are particularly slow to emulate. Advanced radiosity calculations may be reserved for calculating the ambiance of the room, from the light reflecting off walls, floor and celiing, without examining the contribution that complex objects make to the radiosity -- or complex objects may be replaced in the radiosity calculation with simpler objects of similar size and texture.

If there is little rearrangement of radiosity objects in the scene, the same radiosity data may be reused for a number of frames, making radiosity an effective way to improve on the flatness of ray casting, without seriously impacting the overall rendering time-per-frame.

Because of this, radiosity has become the leading real-time rendering method, and has been used from beginning-to-end to create a large number of well-known recent feature-length animated 3D-cartoon films.

### Ray tracing

Ray tracing is an extension of the same technique developed in scanline rendering and ray casting. Like those, it handles complicated objects well, and the objects may be described mathematically. Unlike scanline and casting, ray tracing is almost always a Monte Carlo technique, that is one based on averaging a number of randomly generated samples from a model.

In this case, the samples are imaginary rays of light intersecting the viewpoint from the objects in the scene. It is primarily beneficial where complex and accurate rendering of shadows, refraction or reflection are issues.

In a final, production quality rendering of a ray traced work, multiple rays are generally shot for each pixel, and traced not just to the first object of intersection, but rather, through a number of sequential 'bounces', using the known laws of optics such as "angle of incidence equals angle of reflection" and more advanced laws that deal with refraction and surface roughness.

Once the ray either encounters a light source, or more probably once a set limiting number of bounces has been evaluated, then the surface illumination at that final point is evaluated using techniques described above, and the changes along the way through the various bounces evaluated to estimate a value observed at the point of view. This is all repeated for each sample, for each pixel.

In some cases, at each point of intersection, multiple rays may be spawned.

As a brute-force method, ray tracing has been too slow to consider for real-time, and until recently too slow even to consider for short films of any degree of quality, although it has been used for special effects sequences, and in advertising, where a short portion of high quality (perhaps even photorealistic) footage is required.

However, efforts at optimizing to reduce the number of calculations needed in portions of a work where detail is not high or does not depend on ray tracing features have led to a realistic possibility of wider use of ray tracing. There is now some hardware accelerated ray tracing equipment, at least in prototype phase, and some game demos which show use of real-time software or hardware ray tracing.

## Optimisation

### Optimisations used by an artist when a scene is being developed

Due to the large number of calculations, a work in progress is usually only rendered in detail appropriate to the portion of the work being developed at a given time, so in the initial stages of modelling, wireframe and ray casting may be used, even where the target output is ray tracing with radiosity. It is also common to render only parts of the scene at high detail, and to remove objects that are not important to what is currently being developed.

### Common optimisations for real time rendering

For real-time, it is appropriate to simplify one or more common approximations, and tune to the exact parameters of the scenery in question, which is also tuned to the agreed parameters to get the most 'bang for the buck'.

## Sampling and filtering

One problem that any rendering system must deal with, no matter which approach it takes, is the sampling problem. Essentially, the rendering process tries to depict a continuous function from image space to colors by using a finite number of pixels. As a consequence of the Nyquist theorem, the scanning frequency must be twice the dot rate, which is proportional to image resolution. In simpler terms, this expresses the idea that an image cannot display details smaller than one pixel.

If a naive rendering algorithm is used, high frequencies in the image function will cause ugly aliasing to be present in the final image. Aliasing typically manifests itself as jaggies, or jagged edges on objects where the pixel grid is visible. In order to remove aliasing, all rendering algorithms (if they are to produce good-looking images) must filter the image function to remove high frequencies, a process called antialiasing.

The implementation of a realistic renderer always has some basic element of physical simulation or emulation — some computation which resembles or abstracts a real physical process.

The term "physically-based" indicates the use of physical models and approximations that are more general and widely accepted outside rendering. A particular set of related techniques have gradually become established in the rendering community.

The basic concepts are moderately straightforward, but intractable to calculate; and a single elegant algorithm or approach has been elusive for more general purpose renderers. In order to meet demands of robustness, accuracy, and practicality, an implementation will be a complex combination of different techniques.

Rendering research is concerned with both the adaptation of scientific models and their efficient application.

### The rendering equation

This is the key academic/theoretical concept in rendering. It serves as the most abstract formal expression of the non-perceptual aspect of rendering. All more complete algorithms can be seen as solutions to particular formulations of this equation.

$L_o\left(x, vec w\right) = L_e\left(x, vec w\right) + int_Omega f_r\left(x, vec w\text{'}, vec w\right) L_i\left(x, vec w\text{'}\right) \left(vec w\text{'} cdot vec n\right) dvec w\text{'}$
Meaning: at a particular position and direction, the outgoing light (Lo) is the sum of the emitted light (Le) and the reflected light. The reflected light being the sum of the incoming light (Li) from all directions, multiplied by the surface reflection and incoming angle. By connecting outward light to inward light, via an interaction point, this equation stands for the whole 'light transport' — all the movement of light — in a scene.

### The Bidirectional Reflectance Distribution Function

The Bidirectional Reflectance Distribution Function (BRDF) expresses a simple model of light interaction with a surface as follows:

$f_r\left(x, vec w\text{'}, vec w\right) = frac\left\{dL_r\left(x, vec w\right)\right\}\left\{L_i\left(x, vec w\text{'}\right)\left(vec w\text{'} cdot vec n\right) dvec w\text{'}\right\}$

Light interaction is often approximated by the even simpler models: diffuse reflection and specular reflection, although both can be BRDFs.

### Geometric optics

Rendering is practically exclusively concerned with the particle aspect of light physics — known as geometric optics. Treating light, at its basic level, as particles bouncing around is a simplification, but appropriate: the wave aspects of light are negligible in most scenes, and are significantly more difficult to simulate. Notable wave aspect phenomena include diffraction — as seen in the colours of CDs and DVDs — and polarisation — as seen in LCDs. Both types of effect, if needed, are made by appearance-oriented adjustment of the reflection model.

### Visual perception

Though it receives less attention, an understanding of human visual perception is valuable to rendering. This is mainly because image displays and human perception have restricted ranges. A renderer can simulate an almost infinite range of light brightness and color, but current displays — movie screen, computer monitor, etc. — cannot handle so much, and something must be discarded or compressed. Human perception also has limits, and so doesn't need to be given large-range images to create realism. This can help solve the problem of fitting images into displays, and, furthermore, suggest what short-cuts could be used in the rendering simulation, since certain subtleties won't be noticeable. This related subject is tone mapping.

Mathematics used in rendering includes: linear algebra, calculus, numerical mathematics, signal processing, monte carlo.

Rendering for movies often takes place on a network of tightly connected computers known as a render farm.

The current state of the art in 3-D image description for movie creation is the Mental Ray scene description language designed at mental images and the RenderMan shading language designed at Pixar. (compare with simpler 3D fileformats such as VRML or APIs such as OpenGL and DirectX tailored for 3D hardware accelerators).

Other renderers (including proprietary ones) can and are sometimes used, but most other renderers tend to miss one or more of the often needed features like good texture filtering, texture caching, programmable shaders, highend geometry types like hair, subdivision or nurbs surfaces with tesselation on demand, geometry caching, raytracing with geometry caching, high quality shadow mapping, speed or patent-free implementations. Other highly sought features these days may include IPR and hardware rendering/shading.

## Chronology of important published ideas

• 1968 Ray casting (Appel, A. (1968). Some techniques for shading machine renderings of solids. Proceedings of the Spring Joint Computer Conference 32, 37–49.)
• 1970 Scanline rendering (Bouknight, W. J. (1970). A procedure for generation of three-dimensional half-tone computer graphics presentations. Communications of the ACM)
• 1971 Gouraud shading (Gouraud, H. (1971). Computer display of curved surfaces. IEEE Transactions on Computers 20 (6), 623–629.)
• 1974 Texture mapping (Catmull, E. (1974). A subdivision algorithm for computer display of curved surfaces. PhD thesis, University of Utah.)
• 1974 Z-buffering (Catmull, E. (1974). A subdivision algorithm for computer display of curved surfaces. PhD thesis)
• 1975 Phong shading (Phong, B-T. (1975). Illumination for computer generated pictures. Communications of the ACM 18 (6), 311–316.)
• 1976 Environment mapping (Blinn, J.F., Newell, M.E. (1976). Texture and reflection in computer generated images. Communications of the ACM 19, 542–546.)
• 1977 Shadow volumes (Crow, F.C. (1977). Shadow algorithms for computer graphics. Computer Graphics (Proceedings of SIGGRAPH 1977) 11 (2), 242–248.)
• 1978 Shadow buffer (Williams, L. (1978). Casting curved shadows on curved surfaces. Computer Graphics (Proceedings of SIGGRAPH 1978) 12 (3), 270–274.)
• 1978 Bump mapping (Blinn, J.F. (1978). Simulation of wrinkled surfaces. Computer Graphics (Proceedings of SIGGRAPH 1978) 12 (3), 286–292.)
• 1980 BSP trees (Fuchs, H., Kedem, Z.M., Naylor, B.F. (1980). On visible surface generation by a priori tree structures. Computer Graphics (Proceedings of SIGGRAPH 1980) 14 (3), 124–133.)
• 1980 Ray tracing (Whitted, T. (1980). An improved illumination model for shaded display. Communications of the ACM 23 (6), 343–349.)
• 1981 Cook shader (Cook, R.L., Torrance, K.E. (1981). A reflectance model for computer graphics. Computer Graphics (Proceedings of SIGGRAPH 1981) 15 (3), 307–316.)
• 1983 MIP maps (Williams, L. (1983). Pyramidal parametrics. Computer Graphics (Proceedings of SIGGRAPH 1983) 17 (3), 1–11.)
• 1984 Octree ray tracing (Glassner, A.S. (1984). Space subdivision for fast ray tracing. IEEE Computer Graphics & Applications 4 (10), 15–22.)
• 1984 Alpha compositing (Porter, T., Duff, T. (1984). Compositing digital images. Computer Graphics (Proceedings of SIGGRAPH 1984) 18 (3), 253–259.)
• 1984 Distributed ray tracing (Cook, R.L., Porter, T., Carpenter, L. (1984). Distributed ray tracing. Computer Graphics (Proceedings of SIGGRAPH 1984) 18 (3), 137–145.)
• 1984 Radiosity (Goral, C., Torrance, K.E., Greenberg D.P., Battaile, B. (1984). Modelling the interaction of light between diffuse surfaces. Computer Graphics (Proceedings of SIGGRAPH 1984) 18 (3), 213–222.)
• 1985 Hemicube radiosity (Cohen, M.F., Greenberg, D.P. (1985). The hemi-cube: a radiosity solution for complex environments. Computer Graphics (Proceedings of SIGGRAPH 1985) 19 (3), 31–40.)
• 1986 Light source tracing (Arvo, J. (1986). Backward ray tracing. SIGGRAPH 1986 Developments in Ray Tracing course notes)
• 1986 Rendering equation (Kajiya, J. (1986). The rendering equation. Computer Graphics (Proceedings of SIGGRAPH 1986) 20 (4), 143–150.)
• 1987 Reyes rendering (Cook, R.L., Carpenter, L., Catmull, E. (1987). The reyes image rendering architecture. Computer Graphics (Proceedings of SIGGRAPH 1987) 21 (4), 95–102.)
• 1991 Hierarchical radiosity (Hanrahan, P., Salzman, D., Aupperle, L. (1991). A rapid hierarchical radiosity algorithm. Computer Graphics (Proceedings of SIGGRAPH 1991) 25 (4), 197–206.)
• 1993 Tone mapping (Tumblin, J., Rushmeier, H.E. (1993). Tone reproduction for realistic computer generated images. IEEE Computer Graphics & Applications 13 (6), 42–48.)
• 1993 Subsurface scattering (Hanrahan, P., Krueger, W. (1993). Reflection from layered surfaces due to subsurface scattering. Computer Graphics (Proceedings of SIGGRAPH 1993) 27 165–174.)
• 1995 Photon mapping (Jensen, H.W., Christensen, N.J. (1995). Photon maps in bidirectional monte carlo ray tracing of complex objects. Computers & Graphics 19 (2), 215–224.)
• 1997 Metropolis light transport (Veach, E., Guibas, L. (1997). Metropolis light transport. Computer Graphics (Proceedings of SIGGRAPH 1997) 16 65–76.)
• 1997 Instant Radiosity (Keller, A. (1997). Instant Radiosity. Computer Graphics (Proceedings of SIGGRAPH 1997) 24, 49–56.)
• 2002 Precomputed Radiance Transfer (Sloan, P., Kautz, J., Snyder, J. (2002). Precomputed Radiance Transfer for Real-Time Rendering in Dynamic, Low Frequency Lighting Environments. Computer Graphics (Proceedings of SIGGRAPH 2002) 29, 527–536.)

## Books and summaries

• Pharr; Humphreys (2004). Physically Based Rendering. Morgan Kaufmann. ISBN 0-12-553180-X.
• Shirley; Morley (2003). Realistic Ray Tracing (2nd ed.). AK Peters. ISBN 1-56881-198-5.
• Dutre; Bala; Bekaert (2002). Advanced Global Illumination. AK Peters. ISBN 1-56881-177-2.
• Akenine-Moller; Haines (2002). Real-time Rendering (2nd ed.). AK Peters. ISBN 1-56881-182-9.
• Strothotte; Schlechtweg (2002). Non-Photorealistic Computer Graphics. Morgan Kaufmann. ISBN 1-55860-787-0.
• Gooch; Gooch (2001). Non-Photorealistic Rendering. AKPeters. ISBN 1-56881-133-0.
• Jensen (2001). Realistic Image Synthesis Using Photon Mapping. AK Peters. ISBN 1-56881-147-0.
• Blinn (1996). Jim Blinns Corner - A Trip Down The Graphics Pipeline. Morgan Kaufmann. ISBN 1-55860-387-5.
• Glassner (1995). Principles Of Digital Image Synthesis. Morgan Kaufmann. ISBN 1-55860-276-3.
• Cohen; Wallace (1993). Radiosity and Realistic Image Synthesis. AP Professional. ISBN 0-12-178270-0.
• Foley; Van Dam; Feiner; Hughes (1990). Computer Graphics: Principles And Practice. Addison Wesley. ISBN 0-201-12110-7.
• Glassner (ed.) (1989). An Introduction To Ray Tracing. Academic Press. ISBN 0-12-286160-4.
• Description of the 'Radiance' system