Rendering (computer graphics)

"Image synthesis" redirects here. Not to be confused with Text-to-image model. For other uses, see Computer graphics § Image types.

For 3-dimensional rendering, see 3D rendering. For rendering of HTML, see browser engine.

A variety of rendering techniques applied to a single 3D scene

An image created by using POV-Ray 3.6

Rendering or image synthesis is the process of generating a photorealistic or non-photorealistic image from a 2D or 3D model by means of a computer program. The resulting image is referred to as a rendering. Multiple models can be defined in a scene file containing objects in a strictly defined language or data structure. The scene file contains geometry, viewpoint, textures, lighting, and shading information describing 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 or raster graphics image file. The term "rendering" is analogous to the concept of an artist's impression of a scene. The term "rendering" is also used to describe the process of calculating effects in a video editing program to produce the final video output.

A software application or component that performs rendering is called a rendering engine, render engine, rendering system, graphics engine, or simply a renderer.

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

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

Though the technical details of rendering methods vary, the general challenges to overcome in producing a 2D image on a screen from a 3D representation stored in a scene file are handled by the graphics pipeline in a rendering device such as a GPU. A GPU is a purpose-built device that assists a CPU in performing complex rendering calculations. If a scene is to look relatively realistic and predictable under virtual lighting, the rendering software must solve the rendering equation. The rendering equation does not account for all lighting phenomena, but instead acts as a general lighting model for computer-generated imagery.

In the case of 3D graphics, scenes can be pre-rendered or generated in realtime. Pre-rendering is a slow, computationally intensive process that is typically used for movie creation, where scenes can be generated ahead of time, while real-time rendering is often done for 3D video games and other applications that must dynamically create scenes. 3D hardware accelerators can improve realtime rendering performance.

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 (optics), transparency (graphic) 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

Inputs

Before a 3D scene or 2D image can be rendered, it must be described in a way that the rendering software can understand. Historically, inputs for both 2D and 3D rendering were usually text files, which are easier than binary files for humans to edit and understand. For 3D graphics, text formats have largely been supplanted by more efficient binary formats, and by APIs which allow interactive applications to communicate directly with a rendering component without generating a file on disk (although a scene description is usually still created in memory prior to rendering).

Traditional rendering algorithms use geometric descriptions of 3D scenes or 2D images. Applications and algorithms that render visualizations of data scanned from the real world, or scientific simulations, may require different types of input data.

The PostScript format (which is often credited with the rise of desktop publishing) provides a standardized, interoperable way to describe 2D graphics and page layout. The Scalable Vector Graphics (SVG) format is also text-based, and the PDF format uses the PostScript language internally. In contrast, although there have been many attempts at standardization of 3D graphics file formats (including text-based formats such as VRML and X3D), different rendering applications typically use formats tailored to their needs, and this has led to a proliferation of formats, with binary files being more common.

2D vector graphics

A vector graphics image description may include:

• Coordinates and curvature information for line segments, arcs, and Bézier curves
• Center coordinates, width, and height, or bounding rectangle coordinates, of basic shapes such as rectangles, circles and ellipses
• Coordinates of points defining the outlines of complex shapes
• Color and width of lines
• Patterns used for rendering lines (such as dashed or dotted lines)
• Colors, patterns, and gradients used for filling shapes
• Bitmap image data (either embedded or in an external file) along with scale and position information
• Text to be rendered (along with size, position, orientation, and color)
• Clipping information, if only part of a shape or bitmap image should be rendered
• Transparency and compositing information for rendering overlapping shapes
• Information about the fonts used for rendering text
• Color space information, allowing the image to be rendered consistently on different displays and printers

3D geometry

A geometric scene description may include:

• Size, position, and orientation of geometric primitives such as spheres and cones (which may be combined in various ways to create more complex objects)
• Vertex coordinates and surface normal vectors for meshes of triangles or polygons (often rendered as smooth surfaces by subdividing the mesh)
• Transformations for positioning, rotating, and scaling objects within a scene (allowing parts of the scene to use different local coordinate systems).
• "Camera" information describing how the scene is being viewed (position, direction, focal length, and field of view)
• Light information (location, type, brightness, and color)
• Optical properties of surfaces, such as albedo, reflectance, and refractive index,
• Optical properties of media through which light passes (transparent solids, liquids, clouds, smoke), e.g. absorption and scattering cross sections
• References to external image files used as texture maps for surfaces
• Small scripts or programs for generating complex 3D shapes or scenes procedurally
• Description of how object and camera locations and other information change over time, for rendering an animation
• Settings controlling the quality and type of rendering

Many file formats exist for storing individual 3D objects or "models". These can be imported into a larger scene, or loaded on-demand by rendering software or games. A realistic scene may require hundreds of items like household objects, vehicles, and trees, and 3D artists often utilize large libraries of models. In game production, these models (along with other data such as textures, audio files, and animations) are referred to as "assets".

Volumetric data

Scientific and engineering visualization often requires rendering volumetric data generated by 3D scans or simulations. Perhaps the most common source of such data is medical CT and MRI scans, which need to be rendered for diagnosis. Volumetric data can be extremely large, and requires specialized data formats to store it efficiently, particularly if the volume is sparse (with empty regions that do not contain data).

Before rendering, level sets for volumetric data can be extracted and converted into a mesh of triangles, e.g. by using the marching cubes algorithm. Algorithms have also been developed that work directly with volumetric data, for example to render realistic depictions of the way light is scattered and absorbed by clouds and smoke, and this type of volumetric rendering is used extensively in visual effects for movies. When rendering lower-resolution volumetric data without interpolation, the individual cubes or "voxels" may be visible, an effect sometimes used deliberately for game graphics.

Photogrammetry and scanning

Photographs of real world objects can be incorporated into a rendered scene by using them as textures for 3D objects. Photos of a scene can also be stitched together to create panoramic images or environment maps, which allow the scene to be rendered very efficiently but only from a single viewpoint. Scanning of real objects and scenes using structured light or lidar produces point clouds consisting of the coordinates of millions of individual points in space, sometimes along with color information. These point clouds may either be rendered directly or converted into meshes before rendering. (Note: "point cloud" sometimes also refers to a minimalist rendering style that can be used for any 3D geometry, similar to wireframe rendering.)

Neural approximations and light fields

A more recent, experimental approach is description of scenes using radiance fields which define the color, intensity, and direction of incoming light at each point in space. (This is conceptually similar to, but not identical to, the light field recorded by a hologram.) For any useful resolution, the amount of data in a radiance field is so large that it is impractical to represent it directly as volumetric data, and an approximation function must be found. Neural networks are typically used to generate and evaluate these approximations, sometimes using video frames, or a collection of photographs of a scene taken at different angles, as "training data".

Algorithms related to neural networks have recently been used to find approximations of a scene as 3D Gaussians. The resulting representation is similar to a point cloud, except that it uses fuzzy, partially-transparent blobs of varying dimensions and orientations instead of points. As with neural radiance fields, these approximations are often generated from photographs or video frames.

Outputs

The output of rendering may be displayed immediately on the screen (many times a second, in the case of real-time rendering such as games) or saved in a raster graphics file format such as JPEG or PNG. High-end rendering applications commonly use the OpenEXR file format, which can represent finer gradations of colors and high dynamic range lighting, allowing tone mapping or other adjustments to be applied afterwards without loss of quality.

Quickly rendered animations can be saved directly as video files, but for high-quality rendering, individual frames (which may be rendered by different computers in a cluster or render farm and may take hours or even days to render) are output as separate files and combined later into a video clip.

The output of a renderer sometimes includes more than just RGB color values. For example, the spectrum can be sampled using multiple wavelengths of light, or additional information such as depth (distance from camera) or the material of each point in the image can be included (this data can be used during compositing or when generating texture maps for real-time rendering, or used to assist in removing noise from a path-traced image). Transparency information can be included, allowing rendered foreground objects to be composited with photographs or video. It is also sometimes useful to store the contributions of different lights, or of specular and diffuse lighting, as separate channels, so lighting can be adjusted after rendering. The OpenEXR format allows storing many channels of data in a single file.

Techniques

Choosing how to render a 3D scene usually involves trade-offs between speed, memory usage, and realism (although realism is not always desired). The algorithms developed over the years follow a loose progression, with more advanced methods becoming practical as computing power and memory capacity increased. Multiple techniques may be used for a single final image.

An important distinction is between image order algorithms, which iterate over pixels of the image plane, and object order algorithms, which iterate over objects in the scene. For simple scenes, object order is usually more efficient, as there are fewer objects than pixels.

2D vector graphics

The vector displays of the 1960s-1970s used deflection of an electron beam to draw line segments directly on the screen. Nowadays, vector graphics are rendered by rasterization algorithms that also support filled shapes. In principle, any 2D vector graphics renderer can be used to render 3D objects by first projecting them onto a 2D image plane.

3D rasterization

Adapts 2D rasterization algorithms so they can be used more efficiently for 3D rendering, handling hidden surface removal via scanline or z-buffer techniques. Different realistic or stylized effects can be obtained by coloring the pixels covered by the objects in different ways. Surfaces are typically divided into meshes of triangles before being rasterized. Rasterization is usually synonymous with "object order" rendering (as described above).

Ray casting

Uses geometric formulas to compute the first object that a ray intersects. It can be used to implement "image order" rendering by casting a ray for each pixel, and finding a corresponding point in the scene. Ray casting is a fundamental operation used for both graphical and non-graphical purposes, e.g. determining whether a point is in shadow, or checking what an enemy can see in a game.

Ray tracing

Simulates the bouncing paths of light caused by specular reflection and refraction, requiring a varying number of ray casting operations for each path. Advanced forms use Monte Carlo techniques to render effects such as area lights, depth of field, blurry reflections, and soft shadows, but computing global illumination is usually in the domain of path tracing.

Radiosity

A finite element analysis approach that breaks surfaces in the scene into pieces, and estimates the amount of light that each piece receives from light sources, or indirectly from other surfaces. Once the irradiance of each surface is known, the scene can be rendered using rasterization or ray tracing.

Path tracing

Uses Monte Carlo integration with a simplified form of ray tracing, computing the average brightness of a sample of the possible paths that a photon could take when traveling from a light source to the camera (for some images, thousands of paths need to be sampled per pixel). It was introduced as a statistically unbiased way to solve the rendering equation, giving ray tracing a rigorous mathematical foundation.

Each of the above approaches has many variations, and there is some overlap. Path tracing may be considered either a distinct technique or a particular type of ray tracing. Note that the usage of terminology related to ray tracing and path tracing has changed significantly over time.

Rendering of a fractal terrain by ray marching

Ray marching is a family of algorithms, used by ray casting, for finding intersections between a ray and a complex object, such as a volumetric dataset or a surface defined by a signed distance function. It is not, by itself, a rendering method, but it can be incorporated into ray tracing and path tracing, and is used by rasterization to implement screen-space reflection and other effects.

A technique called photon mapping or photon tracing uses forward ray tracing (also called particle tracing), tracing paths of photons from a light source to an object, rather than backward from the camera. The additional data collected by this process is used together with conventional backward ray tracing or path tracing. Rendering a scene using only forward ray tracing is impractical, even though it corresponds more closely to reality, because a huge number of photons would need to be simulated, only a tiny fraction of which actually hit the camera.

Real-time rendering, including video game graphics, typically uses rasterization, but increasingly combines it with ray tracing and path tracing. To enable realistic global illumination, real-time rendering often relies on pre-rendered ("baked") lighting for stationary objects. For moving objects, it may use a technique called light probes, in which lighting is recorded by rendering omnidirectional views of the scene at chosen points in space (often points on a grid to allow easier interpolation). These are similar to environment maps, but typically use a very low resolution or an approximation such as spherical harmonics. (Note: Blender uses the term 'light probes' for a more general class of pre-recorded lighting data, including reflection maps.)

Examples comparing different rendering techniques

• 
  A low quality rasterized image, rendered by Blender's EEVEE renderer with low shadow map resolution and a low-resolution mesh
• 
  A low quality path traced image, rendered by Blender's Cycles renderer with only 16 sampled paths per pixel and a low-resolution mesh
• 
  A ray traced image, using the POV-Ray program (using only its ray tracing features) with a low-resolution mesh
• 
  A higher quality rasterized image, using Blender's EEVEE renderer with light probes
• 
  A higher quality path traced image, using Blender's Cycles renderer with 2000 sampled paths per pixel
• 
  An image rendered using POV-Ray's ray tracing, radiosity and photon mapping features
• 
  A more realistic path traced image, using Blender's Cycles renderer with image-based lighting
• 
  A spectral rendered image, using POV-Ray's ray tracing, radiosity and photon mapping features

Scanline rendering and rasterization

Main article: Rasterization

Rendering of the Extremely Large Telescope

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 loop 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 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

Main article: 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. A more sophisticated method is to modify the color 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.

Ray casting involves calculating the "view direction" (from camera position), and incrementally following along that "ray cast" through "solid 3d objects" in the scene, while accumulating the resulting value from each point in 3D space. This is related and similar to "ray tracing" except that the raycast is usually not "bounced" off surfaces (where the "ray tracing" indicates that it is tracing out the lights path including bounces). "Ray casting" implies that the light ray is following a straight path (which may include traveling through semi-transparent objects). The ray cast is a vector that can originate from the camera or from the scene endpoint ("back to front", or "front to back"). Sometimes the final light value is derived from a "transfer function" and sometimes it's used directly.

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.

Ray tracing and path tracing

Spiral Sphere and Julia, Detail, a computer-generated image created by visual artist Robert W. McGregor using only POV-Ray 3.6 and its built-in scene description language

Main article: Ray tracing (graphics)

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 by applying Monte Carlo methods to it. Some of the most used methods are path tracing, bidirectional path tracing, or Metropolis light transport, 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, however, only a single ray or none is fired at each intersection, utilizing the statistical nature of Monte Carlo experiments.

As part of the approach known as physically based rendering, path tracing has become the dominant technique for rendering realistic scenes, including effects for movies. For example, the popular open source 3D software Blender uses path tracing in its Cycles renderer. Images produced using path tracing for global illumination are generally noisier than when using radiosity (the main competing algorithm), but radiosity can be difficult to apply to complex scenes and is prone to artifacts that arise from using a tessellated representation of irradiance.

Path tracing's relative simplicity and its nature as a Monte Carlo method (sampling hundreds or thousands of paths per pixel) make it attractive to implement on a GPU, especially on recent GPUs that support ray tracing acceleration technology such as Nvidia's RTX and OptiX. Many techniques have been developed to denoise the output of path tracing, reducing the number of paths required to achieve acceptable quality, at the risk of losing some detail or introducing small-scale artifacts that are more objectionable than noise; neural networks are now widely used for this purpose.

Advances in GPU technology have made real-time ray tracing possible in games, although it is currently almost always used in combination with rasterization. This enables visual effects that are difficult with only rasterization, including reflection from curved surfaces and interreflective objects, and shadows that are accurate over a wide range of distances and surface orientations. Ray tracing support is included in recent versions of the graphics APIs used by games, such as DirectX, Metal, and Vulkan.

Neural rendering

Neural rendering is a rendering method using artificial neural networks. Neural rendering includes image-based rendering methods that are used to reconstruct 3D models from 2-dimensional images.One of these methods are photogrammetry, which is a method in which a collection of images from multiple angles of an object are turned into a 3D model. There have also been recent developments in generating and rendering 3D models from text and coarse paintings by notably Nvidia, Google and various other companies.

Radiosity

Main article: Radiosity (computer graphics)

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 a 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 algorithm, 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 digital artists used a technique referred to loosely as false radiosity 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 from image space to colors by using a finite number of pixels. As a consequence of the Nyquist–Shannon sampling theorem (or Kotelnikov theorem), any spatial waveform that can be displayed must consist of at least two pixels, which is proportional to image resolution. 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 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 use some kind of low-pass filter on the image function to remove high frequencies, a process called antialiasing.

Optimization

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.

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

Main article: Unbiased rendering

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

Main article: 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.

$L_{o}(x,\omega )=L_{e}(x,\omega )+\int _{\Omega }L_{i}(x,\omega ')f_{r}(x,\omega ',\omega )(\omega '\cdot n)\,\mathrm {d} \omega '$

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

$f_{r}(x,\omega ',\omega )={\frac {\mathrm {d} L_{r}(x,\omega )}{L_{i}(x,\omega ')(\omega '\cdot {\vec {n}})\mathrm {d} \omega '}}$

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

Geometric optics

Rendering is practically exclusively concerned with the particle aspect of light physics – known as geometrical 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 a wide 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 will not be noticeable. This related subject is tone mapping.

Mathematics used in rendering includes: linear algebra, calculus, numerical mathematics, signal processing, and Monte Carlo methods.

Chronology of concepts

Rendering of an - ESTCube-1 satellite

• 1968 - Ray casting
• 1970 - Scanline rendering
• 1971 - Gouraud shading
• 1973 - Phong shading
• 1973 - Phong reflection
• 1973 - Diffuse reflection
• 1973 - Specular highlight
• 1973 - Specular reflection
• 1974 - Sprites
• 1974 - Scrolling
• 1974 - Texture mapping
• 1974 - Z-buffering
• 1976 - Environment mapping
• 1977 - Blinn shading
• 1977 - Side-scrolling
• 1977 - Shadow volumes
• 1978 - Shadow mapping
• 1978 - Bump mapping
• 1979 - Tile map
• 1980 - BSP trees
• 1980 - Ray tracing
• 1981 - Parallax scrolling
• 1981 - Sprite zooming
• 1981 Cook shader
• 1983 - MIP maps
• 1984 - Octree ray tracing
• 1984 - Alpha compositing
• 1984 - Distributed ray tracing
• 1984 - Radiosity
• 1985 - Row/column scrolling
• 1985 - Hemicube radiosity
• 1986 Light source tracing
• 1986 - Rendering equation
• 1987 - Reyes rendering
• 1988 - Depth cue
• 1988 - Distance fog
• 1988 - Tiled rendering
• 1991 - Xiaolin Wu line anti-aliasing
• 1991 Hierarchical radiosity
• 1993 - Texture filtering
• 1993 - Perspective correction
• 1993 - Transform, clipping, and lighting
• 1993 - Directional lighting
• 1993 - Trilinear interpolation
• 1993 - Z-culling
• 1993 - Oren–Nayar reflectance
• 1993 - Tone mapping
• 1993 - Subsurface scattering
• 1994 - Ambient occlusion
• 1995 - Hidden-surface determination
• 1995 - Photon mapping
• 1996 - Multisample anti-aliasing
• 1997 - Metropolis light transport
• 1997 Instant Radiosity
• 1998 - Hidden-surface removal
• 2000 - Pose space deformation
• 2002 - Precomputed Radiance Transfer

See also

• 2D computer graphics – Computer-based generation of digital images
• 3D computer graphics – Graphics that use a three-dimensional representation of geometric data
• 3D rendering – Process of converting 3D scenes into 2D images
• Artistic rendering – Style of renderingPages displaying short descriptions of redirect targets
• Architectural rendering – creating two-dimensional images or animations showing the attributes of a proposed architectural designPages displaying wikidata descriptions as a fallback
• Chromatic aberration – Failure of a lens to focus all colors on the same point
• Displacement mapping – Computer graphics technique
• Font rasterization – Process of converting text from vector to raster
• Global illumination – Group of rendering algorithms used in 3D computer graphics
• Graphics pipeline – Procedure to convert 3D scenes to 2D images
• Heightmap – Type of raster image in computer graphics
• High-dynamic-range rendering – Rendering of computer graphics scenes by using lighting calculations done in high-dynamic-range
• Image-based modeling and rendering
• List of 3D rendering software
• Motion blur – Photography artifact from moving objects
• Non-photorealistic rendering – Style of rendering
• Normal mapping – Texture mapping technique
• Painter's algorithm – Algorithm for visible surface determination in 3D graphics
• Per-pixel lighting
• Physically based rendering – Computer graphics technique
• Pre-rendering – Process in which video footage is not rendered in real-time
• Raster image processor – component used in a printing system which produces a raster image also known as a bitmapPages displaying wikidata descriptions as a fallback
• Radiosity – Computer graphics rendering method using diffuse reflection
• Ray tracing – Rendering method
• Real-time computer graphics – Sub-field of computer graphics
• Reyes – Computer software architecture in 3D computer graphics
• Scanline rendering/Scanline algorithm – 3D computer graphics image rendering method
• Software rendering – Generating images by computer software
• Sprite (computer graphics) – 2D bitmap displayed on top of a larger scene
• Unbiased rendering – Type of rendering in computer graphics
• Vector graphics – Computer graphics images defined by points, lines and curves
• VirtualGL
• Virtual model – Form of computer-aided engineeringPages displaying short descriptions of redirect targets
• Virtual studio – Technology for television and film productionPages displaying short descriptions of redirect targets
• Volume rendering – Representing a 3D-modeled object or dataset as a 2D projection
• Z-buffer algorithms – Type of data buffer in computer graphics

Further reading

• Akenine-Möller, Tomas; Haines, Eric; Hoffman, Naty; Pesce, Angelo; Iwanicki, Micał; Hillaire, Sébastien (2018). Real-time rendering (4 ed.). Boca Raton, FL, USA.: AK Peters. ISBN 978-1-13862-700-0.
• Blinn, Jim (1996). Jim Blinn's corner : a trip down the graphics pipeline. San Francisco, Calif.: Morgan Kaufmann Publishers. ISBN 978-1-55860-387-5.
• Cohen, Michael F.; Wallace, John R. (1998). Radiosity and realistic image synthesis (3 ed.). Boston, Mass. [u.a.]: Academic Press Professional. ISBN 978-0-12-178270-2.
• Philip Dutré; Bekaert, Philippe; Bala, Kavita (2003). Advanced global illumination ([Online-Ausg.] ed.). Natick, Mass.: A K Peters. ISBN 978-1-56881-177-2.
• Foley, James D.; Van Dam; Feiner; Hughes (1990). Computer graphics : principles and practice (2 ed.). Reading, Mass.: Addison-Wesley. ISBN 978-0-201-12110-0.
• Andrew S. Glassner, ed. (1989). An introduction to ray tracing (3 ed.). London [u.a.]: Acad. Press. ISBN 978-0-12-286160-4.
• Glassner, Andrew S. (2004). Principles of digital image synthesis (2 ed.). San Francisco, Calif.: Kaufmann. ISBN 978-1-55860-276-2.
• Gooch, Bruce; Gooch, Amy (2001). Non-photorealistic rendering. Natick, Mass.: A K Peters. ISBN 978-1-56881-133-8.
• Jensen, Henrik Wann (2001). Realistic image synthesis using photon mapping ([Nachdr.] ed.). Natick, Mass.: AK Peters. ISBN 978-1-56881-147-5.
• Pharr, Matt; Humphreys, Greg (2004). Physically based rendering from theory to implementation. Amsterdam: Elsevier/Morgan Kaufmann. ISBN 978-0-12-553180-1.
• Shirley, Peter; Morley, R. Keith (2003). Realistic ray tracing (2 ed.). Natick, Mass.: AK Peters. ISBN 978-1-56881-198-7.
• Strothotte, Thomas; Schlechtweg, Stefan (2002). Non-photorealistic computer graphics modeling, rendering, and animation (2 ed.). San Francisco, CA: Morgan Kaufmann. ISBN 978-1-55860-787-3.
• Ward, Gregory J. (July 1994). "The RADIANCE lighting simulation and rendering system". Proceedings of the 21st annual conference on Computer graphics and interactive techniques - SIGGRAPH '94. pp. 459–72. doi:10.1145/192161.192286. ISBN 0897916670. S2CID 2487835.

External links

• SIGGRAPH – the ACMs special interest group in graphics – the largest academic and professional association and conference