Rendering (computer graphics) - AbsoluteAstronomy.com

Rendering is the process of generating an image from a model (or models in what collectively could be called a scene file), by means of computer programs. A scene file contains objects in a strictly defined language or data structure; it would contain geometry, viewpoint, texture

Texture mapping

Texture mapping is a method for adding detail, surface texture , or color to a computer-generated graphic or 3D model. Its application to 3D graphics was pioneered by Dr Edwin Catmull in his Ph.D. thesis of 1974.-Texture mapping:...

, lighting

Lighting

Lighting or illumination is the deliberate application of light to achieve some practical or aesthetic effect. Lighting includes the use of both artificial light sources such as lamps and light fixtures, as well as natural illumination by capturing daylight...

, and shading

Shading

Shading refers to depicting depth perception in 3D models or illustrations by varying levels of darkness.-Drawing:Shading is a process used in drawing for depicting levels of darkness on paper by applying media more densely or with a darker shade for darker areas, and less densely or with a lighter...

information as a description of the virtual scene. The data contained in the scene file is then passed to a rendering program to be processed and output to a digital image

Digital image

A digital image is a numeric representation of a two-dimensional image. Depending on whether or not the image resolution is fixed, it may be of vector or raster type...

or raster graphics

Raster graphics

In computer graphics, a raster graphics image, or bitmap, is a data structure representing a generally rectangular grid of pixels, or points of color, viewable via a monitor, paper, or other display medium...

image file. The term "rendering" may be by analogy with an "artist's rendering" of a scene. Though the technical details of rendering methods vary, the general challenges to overcome in producing a 2D image from a 3D representation stored in a scene file are outlined as the graphics pipeline

Graphics pipeline

In 3D computer graphics, the terms graphics pipeline or rendering pipeline most commonly refers to the current state of the art method of rasterization-based rendering as supported by commodity graphics hardware. The graphics pipeline typically accepts some representation of a three-dimensional...

along a rendering device, such as a GPU

Graphics processing unit

A graphics processing unit or GPU is a specialized circuit designed to rapidly manipulate and alter memory in such a way so as to accelerate the building of images in a frame buffer intended for output to a display...

. A GPU is a purpose-built device able to assist a CPU

Central processing unit

The central processing unit is the portion of a computer system that carries out the instructions of a computer program, to perform the basic arithmetical, logical, and input/output operations of the system. The CPU plays a role somewhat analogous to the brain in the computer. The term has been in...

in performing complex rendering calculations. If a scene is to look relatively realistic and predictable under virtual lighting, the rendering software should solve the rendering equation

Rendering equation

In computer graphics, the rendering equation is an integral equation in which the equilibrium radiance leaving a point is given as the sum of emitted plus reflected radiance under a geometric optics approximation. It was simultaneously introduced into computer graphics by David Immel et al. and...

. The rendering equation doesn't account for all lighting phenomena, but is a general lighting model for computer-generated imagery. 'Rendering' is also used to describe the process of calculating effects in a video editing file to produce final video output.

Rendering is one of the major sub-topics of 3D computer graphics

3D computer graphics

3D computer graphics are graphics that use a three-dimensional representation of geometric data that is stored in the computer for the purposes of performing calculations and rendering 2D images...

, and in practice always connected to the others. In the graphics pipeline

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, it has become a more distinct subject.

Rendering has uses in architecture

Architectural rendering

Architectural rendering, or architectural illustration, is the art of creating two-dimensional images or animations showing the attributes of a proposed architectural design.-Computer-generated renderings:...

, video games, simulators

Simulation

Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....

, movie

Film

A film, also called a movie or motion picture, is a series of still or moving images. It is produced by recording photographic images with cameras, or by creating images using animation techniques or visual effects...

or TV visual effects

Visual effects

Visual effects are the various processes by which imagery is created and/or manipulated outside the context of a live action shoot. Visual effects involve the integration of live-action footage and generated imagery to create environments which look realistic, but would be dangerous, costly, or...

, 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

Optics

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

, visual perception

Visual system

The visual system is the part of the central nervous system which enables organisms to process visual detail, as well as enabling several non-image forming photoresponse functions. It interprets information from visible light to build a representation of the surrounding world...

, mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

and software development

Software engineering

Software Engineering is the application of a systematic, disciplined, quantifiable approach to the development, operation, and maintenance of software, and the study of these approaches; that is, the application of engineering to software...

.

In the case of 3D graphics, rendering may be done slowly, as in pre-rendering

Pre-rendered

Pre-rendering is the process in which video footage is not rendered in real-time by the hardware that is outputing or playing back the video. Instead, the video is a recording of a footage that was previously rendered on a different equipment...

, 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

Bitmap textures

Bitmap textures are digital images representing a surface, a material, a pattern or even a picture, generated by an artist or designer using a bitmap editor software such as Adobe Photoshop or Gimp or simply by scanning an image and, if necessary, retouching it on a personal computer.Textures can...

or procedural textures, lights, bump mapping

Bump mapping

Bump mapping is a technique in computer graphics for simulating bumps and wrinkles on the surface of an object. This is achieved by perturbing the surface normals of the object and using the perturbed normal during lighting calculations. The result is an apparently bumpy surface rather than a...

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
Shading
Shading refers to depicting depth perception in 3D models or illustrations by varying levels of darkness.-Drawing:Shading is a process used in drawing for depicting levels of darkness on paper by applying media more densely or with a darker shade for darker areas, and less densely or with a lighter...

— how the color and brightness of a surface varies with lighting
texture-mapping
Texture mapping
Texture mapping is a method for adding detail, surface texture , or color to a computer-generated graphic or 3D model. Its application to 3D graphics was pioneered by Dr Edwin Catmull in his Ph.D. thesis of 1974.-Texture mapping:...

— a method of applying detail to surfaces
bump-mapping
Bump mapping
Bump mapping is a technique in computer graphics for simulating bumps and wrinkles on the surface of an object. This is achieved by perturbing the surface normals of the object and using the perturbed normal during lighting calculations. The result is an apparently bumpy surface rather than a...

— a method of simulating small-scale bumpiness on surfaces
fogging/participating medium
Distance fog
Distance fog is a technique used in 3D computer graphics to enhance the perception of distance by simulating fog.Because many of the shapes in graphical environments are relatively simple, and complex shadows are difficult to render, many graphics engines employ a "fog" gradient so objects further...

— how light dims when passing through non-clear atmosphere or air
shadow
Shadow
A shadow is an area where direct light from a light source cannot reach due to obstruction by an object. It occupies all of the space behind an opaque object with light in front of it. The cross section of a shadow is a two-dimensional silhouette, or reverse projection of the object blocking the...

s — the effect of obstructing light
soft shadows — varying darkness caused by partially obscured light sources
reflection
Reflection (computer graphics)
Reflection in computer graphics is used to emulate reflective objects like mirrors and shiny surfaces.Reflection is accomplished in a ray trace renderer by following a ray from the eye to the mirror and then calculating where it bounces from, and continuing the process until no surface is found, or...

— mirror-like or highly glossy reflection
transparency (optics), transparency (graphic)
Transparency (graphic)
Transparency is possible in a number of graphics file formats. The term transparency is used in various ways by different people, but at its simplest there is "full transparency" i.e. something that is completely invisible. Of course, only part of a graphic should be fully transparent, or there...

or opacity
Opacity (optics)
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc...

— sharp transmission of light through solid objects
translucency — highly scattered transmission of light through solid objects
refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

— bending of light associated with transparency
diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

— bending, spreading and interference of light passing by an object or aperture that disrupts the ray
indirect illumination
Global illumination
Global illumination is a general name for a group of algorithms used in 3D computer graphics that are meant to add more realistic lighting to 3D scenes...

— surfaces illuminated by light reflected off other surfaces, rather than directly from a light source (also known as global illumination)
caustics
Caustic (optics)
In optics, a caustic or caustic network is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. The caustic is a curve or surface to which each of the light rays is tangent, defining a boundary of an...

(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
Depth of field
In optics, particularly as it relates to film and photography, depth of field is the distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image...

— objects appear blurry or out of focus when too far in front of or behind the object in focus
motion blur
Motion blur
Motion blur is the apparent streaking of rapidly moving objects in a still image or a sequence of images such as a movie or animation. It results when the image being recorded changes during the recording of a single frame, either due to rapid movement or long exposure.- Photography :When a camera...

— objects appear blurry due to high-speed motion, or the motion of the camera
non-photorealistic rendering
Non-photorealistic rendering
Non-Photorealistic rendering is an area of computer graphics that focuses on enabling a wide variety of expressive styles for digital art. In contrast to traditional computer graphics, which has focused on photorealism, NPR is inspired by artistic styles such as painting, drawing, technical...

— 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 particle of light

Photon

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

in a scene is nearly always completely impractical and would take a stupendous 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: rasterization, including scanline rendering

Scanline rendering

Scanline rendering is an algorithm for visible surface determination, in 3D computer graphics,that works on a row-by-row basis rather than a polygon-by-polygon or pixel-by-pixel basis...

, geometrically projects objects in the scene to an image plane, without advanced optical effects; ray casting

Ray casting

Ray casting is the use of ray-surface intersection tests to solve a variety of problems in computer graphics. It enables spatial selections of objects in ascene by providing users a virtual beam as a visual cue extending...

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

Monte Carlo method

Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...

techniques to reduce artifacts; 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. The fourth type of light transport techique, radiosity

Radiosity

Radiosity is a global illumination algorithm used in 3D computer graphics rendering. Radiosity is an application of the finite element method to solving the rendering equation for scenes with purely diffuse surfaces...

is not usually implemented as a rendering technique, but instead calculates the passage of light as it leaves the light source and illuminates surfaces. These surfaces are usually rendered to the display using one of the other three techniques.

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

Another distinction is between image order

Image and object order rendering

In computer graphics, image order algorithms iterate over the pixels in the image to be produced, rather than the elements in the scene to be rendered. Object order algorithms are those that iterate over the elements in the scene to be rendered, rather than the pixels in the image to be produced...

algorithms, which iterate over pixels of the image plane, and object order

Image and object order rendering

algorithms, which iterate over objects in the scene. Generally object order is more efficient, as there are usually fewer objects in a scene than pixels.

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 rendering of 3D models, triangles and polygons in space might be primitives.

If a pixel-by-pixel (image order) approach to rendering is impractical or too slow for some task, then a primitive-by-primitive (object order) 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

Cache coherency

In computing, cache coherence refers to the consistency of data stored in local caches of a shared resource.When clients in a system maintain caches of a common memory resource, problems may arise with inconsistent data. This is particularly true of CPUs in a multiprocessing system...

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

Interactivity

In the fields of information science, communication, and industrial design, there is debate over the meaning of interactivity. In the "contingency view" of interactivity, there are three levels:...

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 are not 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

In ray casting 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

Texture mapping

. 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.

Raycasting 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.

Ray tracing

Ray tracing aims to simulate the natural flow of light, interpreted as particles. Often, ray tracing methods are utilized to approximate the solution to the rendering equation

Rendering equation

by applying Monte Carlo methods to it. Some of the most used methods are Path Tracing

Path Tracing

Path tracing is a computer graphics rendering technique that attempts to simulate the physical behaviour of light as closely as possible. It is a generalisation of conventional ray tracing, tracing rays from the virtual camera through several bounces on or through objects...

, Bidirectional Path Tracing, or Metropolis light transport

Metropolis light transport

The Metropolis light transport is a SIGGRAPH 1997 paper by Eric Veach and Leonidas J. Guibas, describing an application of a variant of the Monte Carlo method called the Metropolis-Hastings algorithm to the rendering equation for generating images from detailed physical descriptions of three...

, but also semi realistic methods are in use, like Whitted Style Ray Tracing, or hybrids. While most implementations let light propagate on straight lines, applications exist to simulate relativistic spacetime effects.

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 distribution ray tracing, at each point of intersection, multiple rays may be spawned. In path tracing

Path Tracing

, however, only a single ray or none is fired at each intersection, utilizing the statistical nature of Monte Carlo

Monte Carlo

Monte Carlo is an administrative area of the Principality of Monaco....

experiments.

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

Photorealism

Photorealism is the genre of painting based on using the camera and photographs to gather information and then from this information creating a painting that appears photographic...

) 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.

Radiosity

Radiosity 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. Prior to the standardization of rapid radiosity calculation, some graphic artists used a technique referred to loosely as false radiosity

False radiosity

False Radiosity is a 3D computer graphics technique used to create texture mapping for objects that emulates patch interaction algorithms in radiosity rendering...

by darkening areas of texture maps corresponding to corners, joints and recesses, and applying them via self-illumination or diffuse mapping for scanline rendering. Even now, advanced radiosity calculations may be reserved for calculating the ambiance of the room, from the light reflecting off walls, floor and ceiling, 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.

Radiosity calculations are viewpoint independent which increases the computations involved, but makes them useful for all viewpoints. 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 is a prime component of leading real-time rendering methods, and has been used from beginning-to-end to create a large number of well-known recent feature-length animated 3D-cartoon films.

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

Continuous function

In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...

from image space to colors by using a finite number of pixels. As a consequence of the Nyquist–Shannon sampling theorem

Nyquist–Shannon sampling theorem

The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. Sampling is the process of converting a signal into a numeric sequence...

, any spatial waveform that can be displayed must consist of at least two pixels, which is proportional to image resolution

Image resolution

Image resolution is an umbrella term that describes the detail an image holds. The term applies to raster digital images, film images, and other types of images. Higher resolution means more image detail....

. In simpler terms, this expresses the idea that an image cannot display details, peaks or troughs in color or intensity, that are smaller than one pixel.

If a naive rendering algorithm is used without any filtering, high frequencies in the image function will cause ugly aliasing

Aliasing

In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...

to be present in the final image. Aliasing typically manifests itself as jaggies

Jaggies

"Jaggies" is the informal name for artifacts in raster images, most frequently from aliasing, which in turn is often caused by non-linear mixing effects producing high-frequency components and/or missing or poor anti-aliasing filtering prior to sampling....

, 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 use some kind of low-pass filter

Low-pass filter

A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...

on the image function to remove high frequencies, a process called antialiasing.

Optimizations 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 modeling, 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 optimizations 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'.

Academic core

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.

Meaning: at a particular position and direction, the outgoing light (L_o) is the sum of the emitted light (L_e) and the reflected light. The reflected light being the sum of the incoming light (L_i) 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
Bidirectional reflectance distribution function
The bidirectional reflectance distribution function is a four-dimensional function that defines how light is reflected at an opaque surface...

(BRDF) expresses a simple model of light interaction with a surface as follows:

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

Compact Disc

The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...

and DVD

DVD

A DVD is an optical disc storage media format, invented and developed by Philips, Sony, Toshiba, and Panasonic in 1995. DVDs offer higher storage capacity than Compact Discs while having the same dimensions....

s) and polarisation (as seen in LCDs

Liquid crystal display

A liquid crystal display is a flat panel display, electronic visual display, or video display that uses the light modulating properties of liquid crystals . LCs do not emit light directly....

). 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 does not 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

Tone mapping

Tone mapping is a technique used in image processing and computer graphics to map one set of colors to another in order to approximate the appearance of high dynamic range images in a medium that has a more limited dynamic range...

.

Mathematics used in rendering includes: linear algebra

Linear algebra

Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...

, calculus

Calculus

Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...

, numerical mathematics

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

, signal processing

Digital signal processing

Digital signal processing is concerned with the representation of discrete time signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing...

, and Monte Carlo methods.

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

Render farm

A render farm is a computer cluster built to render computer-generated imagery , typically for film and television visual effects, using off-line batch processing. This is different from a render wall, which is a networked, tiled display used for real-time rendering...

.

The current state of the art

State of the art

The state of the art is the highest level of development, as of a device, technique, or scientific field, achieved at a particular time. It also refers to the level of development reached at any particular time as a result of the latest methodologies employed.- Origin :The earliest use of the term...

in 3-D image description for movie creation is the mental ray

Mental Ray

mental ray is a production-quality rendering application developed by mental images . mental images was bought in December 2007 by NVIDIA.As the name implies, it supports ray tracing to generate images....

scene description language

Scene description language

A scene description language refers to any description language used to describe a scene to be rendered by a 3D renderer such as a ray tracer....

designed at mental images and the RenderMan shading language

Shading language

A shading language is a special programming language adapted to map on shader programming. Those kind of languages usually have special data types like color and normal...

designed at Pixar

Pixar

Pixar Animation Studios, pronounced , is an American computer animation film studio based in Emeryville, California. The studio has earned 26 Academy Awards, seven Golden Globes, and three Grammy Awards, among many other awards and acknowledgments. Its films have made over $6.3 billion worldwide...

. (compare with simpler 3D fileformats such as VRML

VRML

VRML is a standard file format for representing 3-dimensional interactive vector graphics, designed particularly with the World Wide Web in mind...

or APIs

Application programming interface

An application programming interface is a source code based specification intended to be used as an interface by software components to communicate with each other...

such as OpenGL

OpenGL

OpenGL is a standard specification defining a cross-language, cross-platform API for writing applications that produce 2D and 3D computer graphics. The interface consists of over 250 different function calls which can be used to draw complex three-dimensional scenes from simple primitives. OpenGL...

and DirectX

DirectX

Microsoft DirectX is a collection of application programming interfaces for handling tasks related to multimedia, especially game programming and video, on Microsoft platforms. Originally, the names of these APIs all began with Direct, such as Direct3D, DirectDraw, DirectMusic, DirectPlay,...

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
Ray casting
Ray casting is the use of ray-surface intersection tests to solve a variety of problems in computer graphics. It enables spatial selections of objects in ascene by providing users a virtual beam as a visual cue extending...

(Appel, A. (1968). Some techniques for shading machine renderings of solids. Proceedings of the Spring Joint Computer Conference 32, 37–49.)
1970 Scanline rendering
Scanline rendering
Scanline rendering is an algorithm for visible surface determination, in 3D computer graphics,that works on a row-by-row basis rather than a polygon-by-polygon or pixel-by-pixel basis...

(Bouknight, W. J. (1970). A procedure for generation of three-dimensional half-tone computer graphics presentations. Communications of the ACM 13 (9), 527–536
1971 Gouraud shading
Gouraud shading
Gouraud shading, named after Henri Gouraud, is an interpolation method used in computer graphics to produce continuous shading of surfaces represented by polygon meshes...

(Gouraud, H.
Henri Gouraud (computer scientist)
Henri Gouraud is a French computer scientist. He is the inventor of Gouraud shading used in computer graphics. He is the great nephew of general Henri Gouraud.During 1964–1967, he studied at École Centrale Paris. He received his Ph.D...

(1971). Continuous shading of curved surfaces. IEEE Transactions on Computers 20 (6), 623–629.)
1974 Texture mapping
Texture mapping
Texture mapping is a method for adding detail, surface texture , or color to a computer-generated graphic or 3D model. Its application to 3D graphics was pioneered by Dr Edwin Catmull in his Ph.D. thesis of 1974.-Texture mapping:...

(Catmull, E.
Edwin Catmull
Dr. Edwin Earl Catmull, Ph.D. is a computer scientist and current president of Walt Disney Animation Studios and Pixar Animation Studios. As a computer scientist, Catmull has contributed to many important developments in computer graphics....

(1974). A subdivision algorithm for computer display of curved surfaces. PhD thesis, University of Utah.)
1974 Z-buffering
Z-buffering
In computer graphics, z-buffering is the management of image depth coordinates in three-dimensional graphics, usually done in hardware, sometimes in software. It is one solution to the visibility problem, which is the problem of deciding which elements of a rendered scene are visible, and which...

(Catmull, E.
Edwin Catmull
Dr. Edwin Earl Catmull, Ph.D. is a computer scientist and current president of Walt Disney Animation Studios and Pixar Animation Studios. As a computer scientist, Catmull has contributed to many important developments in computer graphics....

(1974). A subdivision algorithm for computer display of curved surfaces. PhD thesis)
1975 Phong shading
Phong shading
Phong shading refers to an interpolation technique for surface shading in 3D computer graphics. It is also called Phong interpolation or normal-vector interpolation shading. Specifically, it interpolates surface normals across rasterized polygons and computes pixel colors based on the interpolated...

(Phong, B-T
Bui Tuong Phong
Bui Tuong Phong was a Vietnamese-born computer graphics researcher and pioneer. His publications are most often referred to using his family name, Bùi, which comes before his given name by Vietnamese name convention, but his inventions are remembered under his given name Phong, since it is...

. (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 volume
Shadow volume
Shadow volume is a technique used in 3D computer graphics to add shadows to a rendered scene. They were first proposed by Frank Crow in 1977 as the geometry describing the 3D shape of the region occluded from a light source...

s (Crow, F.C.
Franklin C. Crow
Franklin C. Crow or Frank Crow is a computer scientist who has made important contributions to computer graphics, including some of the first practical anti-aliasing techniques. Crow also proposed the shadow volume technique for generating geometrically accurate shadows...

(1977). Shadow algorithms for computer graphics. Computer Graphics (Proceedings of SIGGRAPH 1977) 11 (2), 242–248.)
1978 Shadow buffer (Williams, L.
Lance Williams
Lance J. Williams is a prominent graphics researcher who made major contributions to texture map prefiltering, shadow rendering algorithms, facial animation, and antialiasing techniques...

(1978). Casting curved shadows on curved surfaces. Computer Graphics (Proceedings of SIGGRAPH 1978) 12 (3), 270–274.)
1978 Bump mapping
Bump mapping
Bump mapping is a technique in computer graphics for simulating bumps and wrinkles on the surface of an object. This is achieved by perturbing the surface normals of the object and using the perturbed normal during lighting calculations. The result is an apparently bumpy surface rather than a...

(Blinn, J.F. (1978). Simulation of wrinkled surfaces. Computer Graphics (Proceedings of SIGGRAPH 1978) 12 (3), 286–292.)
1980 BSP trees (Fuchs, H.
Henry Fuchs
Prof. Henry Fuchs is a fellow of the American Academy of Arts and Sciences and the Association for Computing Machinery and the Federico Gil Professor of Computer Science at the University of North Carolina at Chapel Hill . He is also an adjunct professor in biomedical engineering...

, 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.
Robert L. Cook
Robert L. Cook is a computer graphics researcher and developer, and the co-creator of the RenderMan rendering software. Cook was born in Knoxville, Tennessee and educated at Duke University and Cornell University. While at Cornell, Cook worked with Donald P. Greenberg. He is now Vice President of...

, Torrance, K.E. (1981). A reflectance model for computer graphics. Computer Graphics (Proceedings of SIGGRAPH 1981) 15 (3), 307–316.)
1983 MIP maps
Mipmap
In 3D computer graphics texture filtering, MIP maps are pre-calculated, optimized collections of images that accompany a main texture, intended to increase rendering speed and reduce aliasing artifacts. They are widely used in 3D computer games, flight simulators and other 3D imaging systems. The...

(Williams, L.
Lance Williams
Lance J. Williams is a prominent graphics researcher who made major contributions to texture map prefiltering, shadow rendering algorithms, facial animation, and antialiasing techniques...

(1983). Pyramidal parametrics. Computer Graphics (Proceedings of SIGGRAPH 1983) 17 (3), 1–11.)
1984 Octree
Octree
An octree is a tree data structure in which each internal node has exactly eight children. Octrees are most often used to partition a three dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional analog of quadtrees. The name is formed from oct + tree,...

ray tracing (Glassner, A.S.
Andrew Glassner
Andrew S. Glassner is an American expert in computer graphics, well known in computer graphics community as the originator and editor of the Graphics Gems series and of An Introduction to Ray Tracing...

(1984). Space subdivision for fast ray tracing. IEEE Computer Graphics & Applications 4 (10), 15–22.)
1984 Alpha compositing
Alpha compositing
In computer graphics, alpha compositing is the process of combining an image with a background to create the appearance of partial or full transparency. It is often useful to render image elements in separate passes, and then combine the resulting multiple 2D images into a single, final image in a...

(Porter, T.
Thomas Porter
Thomas Porter is an American physician and cardiologist. He is the Theodore F. Hubbard Distinguished Chair of Cardiology and professor of Medicine at the University of Nebraska . The Section Chief is the highest ranking cardiologist but Dr...

, Duff, T.
Tom Duff
Thomas Douglas Selkirk Duff is a computer programmer. He was born in Toronto, Ontario, Canada and grew up in Toronto and Leaside. In 1974 he graduated from the University of Waterloo with a B.Math and, two years later, got an M.Sc...

(1984). Compositing digital images. Computer Graphics (Proceedings of SIGGRAPH 1984) 18 (3), 253–259.)
1984 Distributed ray tracing
Distributed ray tracing
Distributed ray tracing, also called distribution ray tracing and stochastic ray tracing, is a refinement of ray tracing that allows for the rendering of "soft" phenomena....

(Cook, R.L.
Robert L. Cook
Robert L. Cook is a computer graphics researcher and developer, and the co-creator of the RenderMan rendering software. Cook was born in Knoxville, Tennessee and educated at Duke University and Cornell University. While at Cornell, Cook worked with Donald P. Greenberg. He is now Vice President of...

, Porter, T.
Thomas Porter
Thomas Porter is an American physician and cardiologist. He is the Theodore F. Hubbard Distinguished Chair of Cardiology and professor of Medicine at the University of Nebraska . The Section Chief is the highest ranking cardiologist but Dr...

, Carpenter, L.
Loren Carpenter
Loren C. Carpenter is a computer graphics researcher and developer. He is co-founder and chief scientist of Pixar Animation Studios. He is the co-inventor of the Reyes rendering algorithm and is one of the authors of the PhotoRealistic RenderMan software which implements Reyes and which renders...

(1984). Distributed ray tracing. Computer Graphics (Proceedings of SIGGRAPH 1984) 18 (3), 137–145.)
1984 Radiosity
Radiosity
Radiosity is a global illumination algorithm used in 3D computer graphics rendering. Radiosity is an application of the finite element method to solving the rendering equation for scenes with purely diffuse surfaces...

(Goral, C., Torrance, K.E., Greenberg D.P.
Donald P. Greenberg
Donald Peter Greenberg is the Jacob Gould Schurman Professor of Computer Graphics at Cornell University.Greenberg earned his undergraduate and Ph.D. degrees from Cornell University, where he played on the tennis and soccer teams and was a member of Tau Delta Phi and the Quill and Dagger society...

, Battaile, B. (1984). Modeling 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.
Donald P. Greenberg
Donald Peter Greenberg is the Jacob Gould Schurman Professor of Computer Graphics at Cornell University.Greenberg earned his undergraduate and Ph.D. degrees from Cornell University, where he played on the tennis and soccer teams and was a member of Tau Delta Phi and the Quill and Dagger society...

(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
Rendering equation
In computer graphics, the rendering equation is an integral equation in which the equilibrium radiance leaving a point is given as the sum of emitted plus reflected radiance under a geometric optics approximation. It was simultaneously introduced into computer graphics by David Immel et al. and...

(Kajiya, J.
Jim Kajiya
Jim Kajiya is a pioneer in the field of computer graphics. He is perhaps best known for the development of the rendering equation.Kajiya received his PhD from the University of Utah in 1979, was a professor at Caltech from 1979 through 1994, and is currently a researcher at Microsoft Research.-...

(1986). The rendering equation. Computer Graphics (Proceedings of SIGGRAPH 1986) 20 (4), 143–150.)
1987 Reyes rendering
Reyes rendering
Reyes rendering is a computer software architecture used in 3D computer graphics to render photo-realistic images. It was developed in the mid-1980s by Loren Carpenter and Robert L. Cook at Lucasfilm's Computer Graphics Research Group, which is now Pixar. It was first used in 1982 to render images...

(Cook, R.L.
Robert L. Cook
Robert L. Cook is a computer graphics researcher and developer, and the co-creator of the RenderMan rendering software. Cook was born in Knoxville, Tennessee and educated at Duke University and Cornell University. While at Cornell, Cook worked with Donald P. Greenberg. He is now Vice President of...

, Carpenter, L.
Loren Carpenter
Loren C. Carpenter is a computer graphics researcher and developer. He is co-founder and chief scientist of Pixar Animation Studios. He is the co-inventor of the Reyes rendering algorithm and is one of the authors of the PhotoRealistic RenderMan software which implements Reyes and which renders...

, Catmull, E.
Edwin Catmull
Dr. Edwin Earl Catmull, Ph.D. is a computer scientist and current president of Walt Disney Animation Studios and Pixar Animation Studios. As a computer scientist, Catmull has contributed to many important developments in computer graphics....

(1987). The Reyes image rendering architecture. Computer Graphics (Proceedings of SIGGRAPH 1987) 21 (4), 95–102.)
1991 Hierarchical radiosity (Hanrahan, P.
Pat Hanrahan
Pat Hanrahan is a computer graphics researcher, the Canon USA Professor of Computer Science and Electrical Engineering in the Computer Graphics Laboratory at Stanford University....

, Salzman, D., Aupperle, L. (1991). A rapid hierarchical radiosity algorithm. Computer Graphics (Proceedings of SIGGRAPH 1991) 25 (4), 197–206.)
1993 Tone mapping
Tone mapping
Tone mapping is a technique used in image processing and computer graphics to map one set of colors to another in order to approximate the appearance of high dynamic range images in a medium that has a more limited dynamic range...

(Tumblin, J., Rushmeier, H.E. (1993). Tone reproduction for realistic computer generated images. IEEE Computer Graphics & Applications 13 (6), 42–48.)
1993 Subsurface scattering
Subsurface scattering
Subsurface scattering is a mechanism of light transport in which light penetrates the surface of a translucent object, is scattered by interacting with the material, and exits the surface at a different point...

(Hanrahan, P.
Pat Hanrahan
Pat Hanrahan is a computer graphics researcher, the Canon USA Professor of Computer Science and Electrical Engineering in the Computer Graphics Laboratory at Stanford University....

, Krueger, W. (1993). Reflection from layered surfaces due to subsurface scattering. Computer Graphics (Proceedings of SIGGRAPH 1993) 27 , 165–174.)
1995 Photon mapping
Photon mapping
In computer graphics, photon mapping is a two-pass global illumination algorithm developed by Henrik Wann Jensen that solves the rendering equation. Rays from the light source and rays from the camera are traced independently until some termination criterion is met, then they are connected in a...

(Jensen, H.W.
Henrik Wann Jensen
Henrik Wann Jensen is a Danish computer graphics researcher. He is best known for developing the photon mapping technique as the subject of his PhD thesis, but has also done important research in simulating subsurface scattering and the sky....

, 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
Metropolis light transport
The Metropolis light transport is a SIGGRAPH 1997 paper by Eric Veach and Leonidas J. Guibas, describing an application of a variant of the Monte Carlo method called the Metropolis-Hastings algorithm to the rendering equation for generating images from detailed physical descriptions of three...

(Veach, E., Guibas, L.
Leonidas J. Guibas
Leonidas John Guibas is a professor of computer science at Stanford University, where he heads the geometric computation group and is a member of the computer graphics and artificial intelligence laboratories. Guibas was a student of Donald Knuth at Stanford, where he received his Ph.D. in 1976...

(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
Precomputed Radiance Transfer
Precomputed Radiance Transfer is a computer graphics technique used to render a scene in real time with complex light interactions being precomputed to save time...

(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
Andrew Glassner
Andrew S. Glassner is an American expert in computer graphics, well known in computer graphics community as the originator and editor of the Graphics Gems series and of An Introduction to Ray Tracing...

(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
Computer Graphics: Principles and Practice
Computer Graphics: Principles and Practice is a textbook written by James D. Foley, Andries van Dam, Steven K. Feiner and John Hughes and published by Addison–Wesley....

. 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

External links

SIGGRAPH The ACMs special interest group in graphics — the largest academic and professional association and conference.
http://www.cs.brown.edu/~tor/ List of links to (recent) siggraph papers (and some others) on the web.

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

Usage

Features

Techniques

Scanline rendering and rasterisation

Ray casting

Ray tracing

Radiosity

Sampling and filtering

Optimizations used by an artist when a scene is being developed

Common optimizations for real time rendering

Academic core

The rendering equation

The bidirectional reflectance distribution function

Geometric optics

Visual perception

Chronology of important published ideas

See also

Books and summaries

External links